Physics II - Test 2

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**What actions would EXACTLY DOUBLE the flow of charge per second through a metal cylinder connected to a 3 V battery?

(FALSE) I. Replace the metal cylinder with one TWICE as long (FALSE) II. Replace the metal cylinder with one TWICE as wide (in diameter) (TRUE) III. Replace the 3 V battery with a 6 V battery If you want to double the flow of charge per second, then you want to double the current. There are two ways to do that through this metal object attached to a battery: 1.) you can lower its resistance by a factor of two, or 2.) you can increase the voltage across it by a factor of two. If we do (I) from the list above, that will double the resistance, so that won't help. If we do (II), that will increase the diameter of the metal cylinder by a factor of two, but that increases the cross-sectional area by a factor of FOUR, which cuts the resistance down to one-fourth of its original, and that QUADRUPLES the current. That's too much, so that doesn't work either. Finally, if we do (III), that actually will work, because it doubles the voltage across the metal cylinder, which, according to Ohm's Law, should increase the current by a factor of exactly two.

**An circuit is shown with a battery attached. What will be zero IMMEDIATELY AFTER the switch is closed if the capacitor is initially NOT charged?

(FALSE) I. The current will be zero (TRUE) II. The voltage across the capacitor will be zero (FALSE) III. The voltage across the resistor will be zero When the capacitor is empty, the current in the RC circuit can be maximized, because why not? However, as the capacitor fills up with charge, it starts to impede current flow more and more until it eventually shuts down the current altogether. The voltage across the resistor (according to Georg Ohm) must be ∆v(R)=I⋅R, so if I is not 0A at the beginning, then neither can the voltage across the resistor be zero at the beginning either (of course, ∆v(R) will become 0V eventually, but NOT at first as the question asks - not until the current dies because the capacitor fills up with charge).

**Two circuits are shown below. Each circuit contains three identical light bulbs(A-G), and an identical battery. Suppose the battery has a voltage of 10 V. What is true? Circuit 1: A,B,C are in series Circuit 2: D,F,G are in Parallel

(FALSE) I. The voltage across Bulb B is 10 V (TRUE) II. The voltage across Bulb E is 10 V (TRUE) III. The voltage across Bulb C is more than 0 V, but less than 10 V The voltage across any of the bulbs on the left cannot be as much as 10 V, because that's the entire difference in potential across all of them (and it has to be, because the high side of Bulb A touches the high side of the battery, which must be at 10 V, and the low side of Bulb C touches the low side of the battery, which must be at 0 V). The voltage across any one of the bulbs on the left will be some amount along the stairs of resistors that take us down from 10 V to 0 V, but not all in one step. Therefore, (III) is correct and (I) is wrong. By contrast, the high side of the battery is touching the high side of every bulb in the right circuit, and the low side of the battery is touching the low side of every bulb in the right circuit. Therefore, the step down in potential from one side of each bulb to the other is actually the full 10 V drop.

**Two circuits are shown below. Each circuit contains three identical light bulbs (A-G), and an identical battery. Now suppose that a NEW identical light bulb is added to the left circuit AFTER Bulb C. Additionally, a new identical light bulb is added in PARALLEL with bulbs D, E, and F. What is true? Circuit 1: A,B,C are in series Circuit 2: D,F,G are in Parallel

(TRUE) I. Bulbs A, B, and C grow dimmer (FALSE) II. Bulbs D, E, and F grow dimmer (FALSE) III. The current flowing through the battery in the RIGHT circuit is NOT changed Adding a new bulb in series on the left will increase the equivalent resistance, so the current in the entire circuit slows down a bit, and the bulbs will not be as bright as before. So (I) is correct. But, on the right, adding a new bulb in parallel actually reduces the equivalent resistance, so the current running through the battery can actually speed up (because it has more room to run spread out now). So (III) cannot be correct. But (II) is also incorrect, because although there's another bulb with whom D, E, F have to share current, there's also just more current overall to share now, because of the previous sentence in this paragraph. So the two effects (more bulbs that have to share current between them vs. more current available to share due to lower equivalent resistance) actually balance out and the bulbs stay the same brightness, but now the new fourth bulb also has that brightness too.

What is the Lorentz force law? Equation?

(the one thing that RHR doesn't do is tell us how strong that force will be in newtons or pounds or whatever units of force) F(B)=qvBsin(θ)

In what way do magnetic field to apply forces to these electric charges?

- they have to be MOVING -only pushing on electric charges at right angles to where the charge is already going (magnetic fields only apply forces at a 90 degree angle to where the charge is already going)

Large Hadron Collider

-it's a device that collides protons head-on at almost the speed of light and when they collide they do so at specific locations called detectors -you can learn a lot about the early conditions of the universe

How are bar magnet and electric dipole similar and different?

-just like the electric dipole, bar magnets too has two poles, north and south and the magnetic field lines look very similar to the electric field lines they seem to point out of the N and into the S -unlike electricity there is no such thing as a singular magnetic charge as far as we know (NO magnetic monopoles) -bar magnets are always found with both a north and a south (dipoles) (you never get separate north and south monopoles) -it is true that just like electric charges opposite poles do attract in magnetism the north pole of one magnet will always be attracted to the south pole of another and the north pole of one magnet will always be repelled by the north pole of another

How are bar magnet and electric field similar and different?

-stationary charges make electric fields -moving charges make electric and magnetic fields -electric fields surround the space of stationary electric charges or really any electric charges they make their own electric fields and the electric fields exist in the space around individual charges and we explained them because we needed a way to understand how electric charges could push and pull on each other across great distances and we said it's the fields that they create that stretch out into space to apply forces to other electric charges but something special happens if a charge is seen to be moving relative to us because if we're making measurements about an electric charge and it happens to be moving relative to us, we detect also a magnetic field in the space surrounding that charge, *it doesn't point in the same direction as the electric field* you notice that it doesn't seem to be emanating out of the charge or terminating into it, it actually seems to be encircling the charge and it seems to depend on which way the charge is moving

What angles θ cause(s) the sine function to equal 0?

0 and 180 Sine, which is represented on the vertical axis in a unit circle, is zero whenever the the position around the circle is on the sides, neither up nor down. The sides of the unit circle occur at 0º and 180º.

What does the first right-hand-rule show you versus the second right-hand-rule?

1 RHR: v, B, FB (force) 2 RHR I, B (Currents and the magnetic fields they create only)

Magnetic Fields and Electric Charges - B fields interact with electric charges in two ways:

1.Moving charges create their own magnetic fields 2.External magnetic fields push and pull on moving charges

What other equation is equivalent to 1 Q (Ohm)?

1V/1(C/s) =1(V⋅s)/C

**A student connects a battery to the ends of a tiny light bulb and measures the current flowing through the bulb to be I(0). If the student had instead used a battery with TWICE as much voltage, the current in the bulb would have been:

2⋅I(0) This is as simple as Ohm's Law. If the circuit consists of a single battery and a single light bulb (a resistor), then the voltage across the battery, ∆v(B), will have to be the same difference in potential across the bulb, but the voltage across the bulb is known to be ∆v(R) = I(0) ⋅ R due to Ohm's Law. Since ∆v(B) = ∆v(R), then if we had used 2⋅∆v(B), we would've had 2⋅∆v(B)=2⋅I(0)⋅R. Since doesn't change, it must mean that I(0) goes to 2⋅I(0), or in words, the current doubled.

What are the symbols for the 3d vectors? explain

3d vectors that point: out of your screen (o) (dot) (toward your face) which we show as a dot the dot perhaps a little bit morbidly can be imagined as a vector that's pointing straight at you straight out of the screen, the last thing that you see before you get hit in the face with this arrow into the screen (X) (in the same direction that your eyes are facing right now) if the X is big, it means the vector is strong -think about archery if you fire a spent arrow the last thing that you see as it leaves your bow is the tail feathers which make an x as it moves away from you (tail)

An __________, it has two electric poles it has a positive charge and a negative charge, and we recognize that it has ____________ they seem to emanate out of the positive charge and terminate into the minus charge. (ex: proton and electron). It has two ______________.

An electric dipole, it has two electric poles it has a positive charge and a negative charge, and we recognize that it has electric field lines they seem to emanate out of the positive charge and terminate into the minus charge. (ex: proton and electron). It has two electric poles. (Dipoles) this could be a proton and electron, it could be a piece of dust

Lorentz: F(B)=qvBsin(θ) Explain theta

Angle between the velocity and magnetic field vectors, those two vectors whichever way they point can be placed tail to tail so that you can see the angle between them in my case, it happens to look something like 90 degrees although that's a coincidence in reality it can be any number from 0 degrees up to 180 degrees it just depends on how the charge is moving through the magnetic field and which way those two vectors point relative to each other -but that force is never responsible for speeding up or slowing down an electric charge all it does is bend the trajectory

Two wires carry current in opposite directions (I1 points out of the screen and I2 points into the screen). I1 directly above I2. What is the direction of the magnetic field vector B(1) (created by I1) at the location of I2?

B points to the right at the location of I2

The number e is the base of the natural logarithm. Using at least three digits after the decimal place, type the numerical value of the quantity e^1

Between 2.718 and 2.719

For which of the following materials does Ohm's Law best describe the resultant current from an applied voltage?

Conductors, like metals This is why it works well with wires and other common circuit components, as they're usually made of metal Ohm's Law is an experimental observation, which means it was discovered to be generally true under certain laboratory conditions. This is not like, say, Newton's 2nd Law of Motion, which was rigorously mathematically theorized from fundamental principles, and is thereby universally true. By contrast, there are plenty materials that are said to be "non-Ohmic," because they don't fit well with Ohm's Law.

Which sketch shows the current flowing through the charging RC circuit over time?

Current vs. Time in an RC Circuit üInitially, the capacitor is empty and allows lots of charge to flow in (high I early on) üAs the capacitor fills up with charge, it accepts less and less üThis causes the current in the circuit to gradually die down to 0 A over time üWhen it comes to the current they allow: üEmpty capacitors are like closed switches üFull capacitors are like open switches üIf a capacitor fills up, it eventually prevents all current from flowing through it. •The shape of this graph is related to the exponential decay function, e^(-x) e^0=1, e^(-x)=1/e^x •As an example, e^(-2)=1/e^2 =1/〖2.718...〗^2 ≈0.14 •And, e^(-10)=1/e^10 =1/〖2.718...〗^10 ≈1/22026=0.00005 •And, e^(-100)=1/e^100 =1/〖2.718...〗^100 ≈3.72×〖10〗^(-44) •Raising e^(-x) to larger powers of x yields smaller and smaller numbers overall because the denominator gets bigger and bigger in e^(-x)=1/e^x •Eventually, as x approaches ∞, e^(-x) approaches 0.

Lorentz force of single charge vs current equations?

Current: F(B)=ILBsinθ (angle of IB) Single charge: F(B)=qvBsin(θ)

Remember that the earth's magnetic field points from the south pole towards the north pole, and where we're located, it generally points due north. In that case, which way would an electron be pushed by earth's magnetic field if the electron were initially traveling in each of the directions listed below? Earth's magnetic field vectors point north near the surface of the earth (as long as you're not close to the poles). southeast (as seen standing on the ground)

DOWN magnetic field pointing up velocity vector pointing south east Electron so flipped

Two wires carry current in opposite directions (I1 points out of the screen and I2 points into the screen). I1 directly above I2. what is the direction of the Lorentz Force (F(21))(the force on I2 due to B(1))?

Down

How can external magnetic fields push and pull on charges versus electric fields?

Electric fields are created by individual electric charges and individual electric charges can be pushed and pulled by electric fields however there is one notable difference in this case it would have been perfect symmetry but in the case of magnetic fields notice the word MOVING the charges have to be moving if you're going to measure a magnetic field created by one of these charges it has to be moving

**Voltmeters have extremely high internal resistance. Ammeters have extremely low internal resistance. What is true?

Everything about this is wrong. Most of the current should NOT flow through a voltmeter when measuring a voltage. First of all, how could it? The resistance of the voltmeter is in the millions of Ohms - almost no current will go through it. Second of all, why would you want that anyway? Imagine trying to measure the voltage across, say, a resistor, where is the thing you want to measure. If most of the current goes through the meter and not the resistor, then through the resistor is way too small, and is way too small, and your measurement is ruined. Also, never place voltmeters in series with circuit elements, because they have mega-Ohm resistance. That will wreck your circuit and kill all the current down the line. Conversely, ammeters have to be placed in series so that the current is forced to go through the circuit element (like a resistor) and ammeter (both), because if you put the ammeter in parallel with a resistor, it has such a small resistance that almost none of the current will go through the resistor at all, and once again: circuit = ruined. a) Most of the current should flow through a voltmeter when measuring . b) Very little of the current should flow through an ammeter when measuring . c) Voltmeters should be placed in series with circuit elements when measuring . d) Ammeters should be placed in parallel with circuit elements when measuring . e)None of these answers is correct.

**A circuit, labeled "Circuit 2" is shown with a 10 V battery and three resistors connected in series, each having an identical resistance . If the two leads of a voltmeter are clipped onto the points "C" and "D" (between R's and battery), what will the voltmeter read? --R---R---R-- --(-) 10 V (+) ---

Exactly 0 V Connecting the two leads of the voltmeter between points C and D will result in us comparing the potential at point C to the potential at point D. If the voltmeter is looking for a difference in potential between those two points, it's not going to find one: they're the same wire with nothing in between. The voltage will be shown as 0 V.

The Lorentz Force on a current-carrying wire in the vicinity of an external magnetic field looks like? For each of the following symbols, select the best physical description for each: F(B) = I l B sin ⁡ θ.

F(B) = Lorentz Force ( The magnetic force on moving charges due to a magnetic field) I =Current flowing through the wire L =Length of the current-carrying wire B =Magnetic field strength θ = Angle between the current flow and magnetic field vectors

F(B)=qvBsin(θ) What is: F(B), q,v,B, θ What are the units for each?

F(B): Lorentz force the magnetic force on a moving charge due to a magnetic field Unit: Newtons q: An individual electric charge Unit: coulombs v: The speed that an electric charge moves related to an external magnetic field Units: meters/second B: The strength of an external magnetic field Unit: Tesla Theta: The angle between the velocity and magnetic FIELD vectors

force due to a magnetic field on an electric charge depends on?

F(B)=qvBsin(θ) the charge is q how fast it's moving v how strong the field is B and the sine of some angle θ of (VB)

True or false regarding the magnetic force on a current-carrying wire? The shorter the current-carrying wire, the greater the magnetic force on that wire

FALSE

True or false of magnetic fields and the Lorentz Forces they apply to electric charges. Magnetic fields can speed up or slow down electric charges

FALSE This is the one thing they can't do. The Lorentz Force can only change the charge's direction, not its speed. If you want to change the charge's speed, you'll need an electric field. That's what a Coulomb Force can do.

•What is the strength of the Lorentz Force on this wire?

F_B=ILB sin⁡(θ_IB ) =(2×〖10〗^3 A)(64 m)(5×〖10〗^(-5) T) sin⁡(65°) =▭(5.8 N)

Is this true or false regarding magnetic materials and properties of magnets? Cutting a bar magnet in half will produce a single North pole magnet and a single South pole magnet, which will attract one another

False

**A circuit is shown with multiple batteries and multiple resistors and a single capacitor on the far left side between points and . The potential differences of the three batteries are V, V, and V. Assume that the circuit has been connected and running for a VERY LONG TIME already. a. How much current flows through the 3 V battery? Explain how you know.

Fun fact: it actually already says "" A right on the diagram between points and . Did you notice? Go back and look - I promise it was always labeled that way. And it's true: there will be no current between points and as long as we wait long enough for the capacitor to totally fill up with charge. That effectively eliminates that entire branch from the circuit, because no current will flow there anyway (at least not after enough time passes, which the question says it has). Capacitors start out (empty) like a closed switch/normal wire - they have almost no resistance initially and they don't impede current at all. But they end their life (full of charge) like an open switch/broken wire - they have impenetrable impedance and don't permit any current to flow at all.

Two wires, top wire I1 pointing right, bottom wire I2 pointing left. In which direction does the magnetic field B(2) (the field created by the bottom wire) point at the location of wire 1?

I2 (thumb): Left B(2) "(fingers): Into the screen"

What is the equation for electric current? Unit?

I= (ΔQ/Δt) Current is the rate at which charge flows per second measured in coulombs per second Unit: Ampere (Amp) (A)

If a table shows the room temperature (20 ºC) resistivities and their temperature coefficients for a variety of common metals. If we want to manufacture a simple wire to use in a room temperature circuit, which of the listed materials would allow the most current to flow through it with the least impedance (all else equal)?

If the size and shape of the wire are equal across all options, then the least resistive material will provide the lowest resistance, and therefore the most current when connected to the same battery. The lowest resistivity among those listed belongs to silver

**A LITHIUM NUCLEUS travels travels along the path going Northeast and passes through a region of magnetic field then turns Northwest. There are no other charges present, and the magnetic field is ZERO everywhere EXCEPT in the gray region. What is a possible direction for the B field?

Into Page I don't care what this object is - as soon as I hear that it's the nucleus of an atom, I know for a fact that it has a POSITIVE charge. That means that if I use the RHR to determine the direction of the force it feels, nothing will need to be reversed at the end, because it's not a negative charge. The object had velocity up-right, so the first Right Hand Rule (RHR1, for finding magnetic forces) dictates that our arm point up right. Our thumb, representing the force that the object feels, should point roughly to the left. This only leaves our fingers to bend towards the screen/page to indicate the magnetic field direction. We can be guaranteed that, among the choices shown, the only one that would actually result in this force is the field that points into the page. In real life, it might not point directly into the page, but it would definitely have to have at least some vector component that points into the page, or this force would never happen as it did.

You have two parallel wires carrying currents in the same direction. What is the direction of the magnetic field at the position where I2 is located that is created by I1? I1 going right, I2 going right

Into the screen

•In the past, I asked on a pre-lecture quiz if students believed that this Lorentz Force on a wire would visibly/physically affect the wire in a circuit •Many students said "Nah, not really." •Some said, "Yes, it's real, and you can see it." •So I'll ask you the same question.

Jumping wire

An electric charge moves down through a uniform magnetic field pointing out of the screen. What is the direction of the Lorentz Force on this charge?

Lorentz Force charge is left arm: down fingers: out of screen

An electric charge moves right through a uniform magnetic field pointing out of the screen. What is the direction of the Lorentz Force on this charge?

Lorentz Force on this charge is down arm:right fingers:out of screen

magnetic fields can only apply forces to charges that are what? Explain the equation that shows this.

Lorentz: F(B)=qvBsin(θ) Single charge: Only moving forces -if v for velocity is zero, the entire force is zero charges that aren't moving relative to the magnetic field, don't get magnetic forces -if a charge is stationary a magnetic force cannot be used to cause it to start moving

**Two concentric wire loops carry currents and in opposite directions going down. The wire loops have radii r(1) and r(2), respectively, where r(1) > r(2). What is the direction of the total magnetic field at the center of the two loops?

More information is needed It's impossible to know. They both create magnetic fields that point either into the page (as RHR2 predicts for Wire 1) or out of the page (as RHR2 predicts for Wire 2), and the total magnetic field will be one of those directions, but without knowing the magnitude of each field contribution, we can't know which direction will win. Now, you might recognize that the center of the loops is closer to Wire 2, so maybe the field created by Wire 2 is a little bit stronger at the center of the loop. But what if (i.e., what if the current in Wire 1 is just so much stronger than the current in Wire 2 that the field it creates vastly overpowers the field created by Wire 2)? We can't know, because we don't know how the currents compare to each other.

magnetic field lines terminate?

No in reality there's also no such thing as terminating magnetic field lines although we don't always draw it this way the truth is they're always continuous unbroken loops even if we draw magnetic field lines as terminating they really don't they even continue inside the bar magnet

**A proton is INITIALLY MOVING DOWNWARD in a uniform magnetic field pointing to the RIGHT as seen in the figure below. What is the direction of the magnetic force on the proton now?

Out of Page PROTON! Point your arm downward to show the velocity of the proton ("Where arm you going?" Get it? It's funny. Laugh. Fine, it wasn't that funny. But if it helps you remember it, then I'm happy.) Now, your fingers should bend to point towards the magnetic field (right). Your thumb can only point out of the screen/page.

**Two concentric wire loops carry currents and in opposite directions going down. The wire loops have radii r(1) and r(2), respectively, where r(1) > r(2). Suppose the currents are adjusted so that I(1)=I(2). What is the direction of the total magnetic field at the center of the two loops now?

Out of the page If the currents are equal, then just defer to Wire 2, because it's closer to the center than Wire 1, and the field that it creates will overpower the field created by Wire 1 with superior strength due to proximity.

An electric charge moves down through a uniform magnetic field pointing out of the screen. Lorentz Force on this charge is left. What is the sign of this charge?

POSITIVE •At every point along the circular trajectory of this charge, it feels a Lorentz Force that points toward the center of the circle. •Because the predictions of the RHR accurately describe this charge's motion, it must be a positive charge. •Had the RHR made backward predictions for the direction of the Lorentz Force, it would be an indication that this is a negative charge.

•Imagine that all the "stuff" in your house functions as a single (big) resistor. •How should you connect the houses in your neighborhood to the power grid? Series or Parallel Resistance

Parallel

What is the equation for Resistance? Explain

R=ρ⋅(L/A) -if you make rho (ρ) (resistivity) bigger obviously R (Resistance) should get bigger -resistance but it also increases with length (L) (numerator) -If Length (L) increases, R increases -cross-sectional area (A) decreases resistance

How would you calculate resistance of the aluminum wire

R_A=ρ_Al⋅L/A =(2.82×〖10〗^(-8) Ω⋅m)⋅((0.2 m))/((π⋅(0.001 m)^2 ) )

**Three long, parallel wires carry currents of A. The figure below is an end view of the conductors, with each current coming out of the screen. Given that m, determine the magnitude and direction of the magnetic field at points A, B, and C. Suppose a new wire with identical current (magnitude and direction) were placed at Point B. a. In which direction were would this new wire feel a magnetic force due to the other wires?

Right If a new wire is placed at Point B with identical current, it'll have a current that points out of the screen with magnitude A. According to the (first) RHR, with a current that comes out of the screen (arm), a magnetic field that points downward at Point B (fingers; caused by the other three wires, discovered in the previous question), the force on that new wire must point to the right (thumb).

**The circuit shown contains a battery and a switch. Suppose the switch is closed. The circuit now creates a magnetic field inside its cardboard tube. In which direction does this magnetic field point? Solenoid (S)--(-) (+)-- ((S)=switch)

Right The second right hand rule is very versatile. You can use your fingers to represent the current around a loop/coil of wire, and your thumb will show you the magnetic field inside it. But you can also use your thumb to represent current through a straight wire, your fingers will curl around to show you the magnetic field surrounding it. You really can't go wrong - curl your fingers towards something that can curl in the context of whatever problem you're doing, and your thumb (by being straight) will point towards the other thing. If the current can curl (because it's moving through a circular wire), then curl your fingers to make the current. If the magnetic field can curl (because it encircles a long straight wire - not a wire loop), then curl your fingers to make the magnetic field. Whichever quantity can curl in a given question (B or I), curl your fingers towards that, and your thumb will automatically show you the other one that doesn't curl. It's really a win-win no matter the situation. In our case, we have to curl our fingers around the coil of wire to represent its current, and point our thumb to see the magnetic field inside it. Conventional current flows from the positive terminal of the battery (on the right side underneath the circuit) to the negative terminal of the battery. That makes it look like our fingers will be following the current in the coil if we curl them up and behind, and out of the screen/over the top of it. The thumb can only point right in this scenario.

What is resistivity? Symbol?

Some materials resist the flow of current better than others (like rubber). We named this property (unique to each material) resistivity. Every material has a different (electrical) resistivity Symbol rho "ρ"

True or false of magnetic fields and the Lorentz Forces they apply to electric charges. Magnetic fields bend the motion of electric charges into circular arcs

TRUE

True or false regarding the magnetic force on a current-carrying wire? Current is made of moving charged particles, and magnetic fields exert forces on moving electric charges. Therefore, wires carrying current will experience Lorentz Forces due to external magnetic fields.

TRUE

True or false regarding the magnetic force on a current-carrying wire? If I point my right arm in the direction of the current flow in a wire, and I point my fingers in the direction of the magnetic field, then my extended right thumb will show the direction of the Lorentz Force on the current-carrying wire.

TRUE

True or false regarding the magnetic force on a current-carrying wire? The stronger the magnetic field in the vicinity of the current-carrying wire, the stronger the force on that wire.

TRUE

True or false of magnetic fields and the Lorentz Forces they apply to electric charges. Magnetic fields can accelerate electric charges

TRUE Acceleration means an object's velocity vector changes. Magnetic fields can change the velocity vector of an electric charge by bending its direction.

**Two circuits are shown below. Each circuit contains three identical light bulbs, and an identical battery. Which light bulb is brightest? Circuit 1: A,B,C are in series Circuit 2: D,F,G are in Parallel

The equivalent resistance of the circuit on the left is R=R+R+R=3R. The equivalent resistance of the circuit on the right is R=(1/((1/R)+(1/R)+(1/R)) = (1/(3/R)) = R/3. If both equivalent resistors (in the left circuit and right circuit) are connected to the same battery potential ∆v(battery), then the current running through each battery will be I(series)=((∆v(battery))/3R)=(1/3 ⋅ (∆v(battery))/R) and ((∆v(battery))/(R/3))=(3 ⋅ (∆v(battery))/R) . The current on the right has to split (equally, because all three resistors are identical), but it's still 9x as large as the current on the left, so even though each bulb only takes one third of the available current in the right circuit, the bulbs will be plenty brighter than the bulbs on the left, which all receive the same weak trickle of a current.

**Two long, straight wires cross each other at right angles(looks like +), and each carries the same current as in the figure below. Which of the following statements is TRUE regarding the TOTAL magnetic field at each labeled point? (I up) B A (I right) C D

The field is out of the page at point B and into the page at point D. It's true that the field is out of the page at Point B and into the page at Point D. Those are the two labeled locations in which both wires create magnetic fields that actually help each other, instead of trying to cancel each other out in opposite directions. The RHR2 will show you this if you point your thumb towards the current (for either wire) and watch your fingers curl around it to illustrate the magnetic field

**Three long, parallel wires carry currents of A. The figure below is an end view of the conductors, with each current coming out of the screen. Given that m, determine the magnitude and direction of the magnetic field at points A, B, and C. Suppose a new wire with identical current (magnitude and direction) were placed at Point B. If the new wire were 5 meters long, calculate the strength of the magnetic force on it due to the other wires.

The magnetic force on this new wire will be: It's a tiny force. Sorry, new wire. No exciting pushes/pulls for you. By the way: notice that that 1.3 A current is that of the new (fourth) wire placed at Point B, because, after all, it's the one being pushed by the external magnetic field created by the other three wires, so it should be the new wire's current and length that are pushed when writing the expression for the force on it.

The next few are going to go much more quickly, because I don't have to explain every minute detail like I did in Part (a). The total magnetic field at Point B looks like: Note that it's a complete coincidence that those orange and green magnetic field vector arrows touch the vertices of that square. There is zero significance to that; I just accidentally drew it that way. However, they are drawn to scale compared to the blue magnetic field vector, as it should be one half as large given that its source wire is twice as far away from Point B as the other two wires. Clearly, the horizontal directions are once again going to cancel. The only surviving term will be the blue magnetic field, which points straight down (unopposed). The magnitude of each magnetic field vector is as follows: So the components of the total magnetic field will be: Then the magnitude of the total magnetic field is just the surviving vertical component:

Which of these statements best explains Kirchhoff's First Rule? Example?

The sum of the currents flowing into a junction must be equal to the sum of the currents flowing out of a junction I_2=I_1+I_3

The total magnetic field at Point A will be the vector sum of all magnetic field contributions from all sources of wire. These -field contributions will be superposed at Point A. For a diagram illustrating each magnetic field contribution from each wire at Point A, see the figure below. Notice that when you illustrate the components of each magnetic field vector, all horizontal components (orange and green) cancel, leaving only the vertical components of each vector (orange, green, blue). How would I know that these components will cancel exactly? Because both the orange and green wires are equidistance from Point A, and they have the same current, so they'll have the same strength of magnetic field at Point A, since that's all it depends on (i.e., distance from the wire and the current therein). So that means that the green magnetic field vector and the orange magnetic field vector will be exactly the same size, albeit in different directions based on the RHR2. Notably, the blue magnetic field vector is much smaller, because it's much farther away than the others from Point A. Incidentally, we'll have a total magnetic field that looks like this (again, everything else cancels, but these downward components help each other become bigger): Let's calculate the two components of the total magnetic field (taking right and up to be the positive directions). By the way, pretty much every acute angle in this entire picture is 45º, because every one of them bisects a 90º angle. The horizontal component of the total magnetic field looks like: The vertical component of the total magnetic field looks like: Now we just have to figure out how strong each -field vector is at Point A. Remember that this is exclusively determined by how much current each wire carries, and the distance from that current to Point A: Therefore, the total magnetic field looks like: If you want to factor out all of the commonalities in each term, you'll wind up with this: If you don't want to factor (knowing my audience) and you just want to plug in numbers as fast as possible to the detriment of your poor fingers when trying to type this into a calculator, you'll find: As expected, the magnetic field at Point A was entirely determined by the vertical direction, with a magnitude of , and all the terms added together (downward, as minus signs) in the same direction. The horizontal direction canceled to zero.

Now suppose you replace a wire with an identical wire, but having twice the cross-sectional area. This new wire's resistance will be exactly _________ as large as the old wire.

This new wire's resistance will be exactly 1/2 as large as the old wire. R=ρ⋅(L/A)

Suppose you replace a wire with an identical wire, but having twice the original length. This new wire's resistance will be exactly ________ as large as the old wire.

This new wire's resistance will be exactly 2x as large as the old wire. R=ρ⋅(L/A)

Is this true or false regarding magnetic materials and properties of magnets? All magnetic field lines form continuous loops

True

Is this true or false regarding magnetic materials and properties of magnets? All magnets have at least two poles, called "North" and "South"

True

Is this true or false regarding magnetic materials and properties of magnets? Magnetic field lines (similarly in concept to electric field lines) point out of the North pole and into the South pole

True

Is this true or false regarding magnetic materials and properties of magnets? Stationary electric charges produce static electric fields. Moving electric charges produce electric fields too, but they also produce magnetic fields

True

True/false: If you reduce the voltage across an object by a factor of two, you will reduce the current flowing through that object by a factor of two.

True

UP magnetic field up west velocity vector (out of screen) (flip direction of force- electron)

The direction of the Lorentz Force on an electric charge moving through an external magnetic field can be determined using the Right Hand Rule (RHR). Match each vector symbol to the body part associated with it. v, B, F(B)

V: arm B: Fingers F(B): Thumb

What are the components of the first right hand rule? Explain each.

Velocity (v) (ARM): Point arm where the moving charge is currently going Magnetic field (B) (FINGERS) (NOT wrist) Bend fingers in the direction of the magnetic field vectors Force (F(B)) (THUMB): Extend thumb outwards to see the direction a POSITIVE charge will feel a force. (OPPOSITE if NEGATIVE CHARGE)

Voltmeters measure? Symbol?

Voltmeters measure voltage/ potential difference Symbol: ⓥ (V) (has some internal resistance that cannot be helped)

WEST hovering over ground X velocity vector earth's Magnetic always field up (east but since electron -flip)

Two wires, top wire I1 pointing right, bottom wire I2 pointing left. In which direction does the magnetic force F(1,2) (the force on wire 1 due to wire 2) point?

What is the direction of the Lorentz Force F ⃗_12 (on I_1 due to B ⃗_2)? üI_1 (arm): Right üB ⃗_2 "(fingers): Into the screen" üF ⃗_12 (thumb): Up

ZERO deflection lorentz force is zero If v goes in same direction as magnetic field Zero if 0 or 180 (Electron)

**A proton is INITIALLY MOVING RIGHT in a uniform magnetic field pointing to the RIGHT as seen in the figure below. There are no other charges present. What is the direction of the magnetic force (F(B)) on the proton?

Zero The best place to hide a charged particle from a magnetic field is to aim the charge right at the field (or directly against it). In other words, if the angle between v and B for a charged particle is θ(vB) = 0° or 180°, then F(B)=q⋅v⋅B⋅sinθ(vB) =0 necessarily.

**A circuit is shown with multiple batteries and multiple resistors and a single capacitor on the far left side between points and . The potential differences of the three batteries are V, V, and V. Assume that the circuit has been connected and running for a VERY LONG TIME already. Show that the current flowing through the 9.3 V battery is 1.68 A

a. The goal will be to calculate , because that's the current that flows through the battery . Remember: the current doesn't actually split at the junction , because the capacitor won't let anyone through at the moment - it's too full. The strategy is to NOT solve for first, because that will eliminate the symbol we want. Solve for the things that you DON'T want first (such as and ) and find expressions for them in terms of the thing that you DO want (). Start with the equation from part (d) (which I'll call Eqn. d), because it has already solved for one of the things we don't want (namely, ). Tell Eqn. (c) about Eqn. (d) by substituting that expression for into Eqn. (c): Goes into this: Resulting in: Let's combine terms and simplify everything in this equation: Now, we need to tell our new version of Eqn (c) (directly above this line) about Eqn (b) (the equation from part (b)), which it doesn't know about yet. To do that, let's again maintain our strategy of solving for the thing that we DON'T want first by solving for in Eqn (b): This information will now be inserted into our improved version of Eqn (c) so that we'll only have the symbol left, whereupon we can solve for it: Now, let's simplify and solve for :

two wires and they each have a current that's moving upwards so their currents are in the same direction and i want to know about the magnetic field around the wire on the left the red wire

according to the second right hand rule it has a magnetic field that encircles it where my thumb points upward to show me the current and my fingers bend at a right angle around it to show me the magnetic field that it creates

how do bar magnets create their own magnetic fields they're not moving? Explain.

bar magnets are made of atoms and if there's one thing we know about atoms it's that they feature moving electric charges so moving electrons within individual atoms create their own little magnetic fields as they orbit. Now on average all these little magnetic contributions created by individual electrons in the atoms of a material probably point in random directions, there's no overall accumulated contribution to a large scale magnetic field because they just point all over the place there's no coherence but if on average there is some coherence to the little individual magnetic fields that atoms make then you can create large-scale magnetic fields even in solid matter like a chunk of iron you just have to make sure that all of these little orbits at least on average contribute magnetic field more in one direction than any other -some materials naturally do that anyway, some materials are willing to do that under the right conditions and other materials are not very willing to do it ever (that's why some metals are not especially susceptible to magnetization at all)

________ have poles which are usually labeled you can see n and s they're found at the two ends of any ___________object that you're holding and __________ are called __________

bar magnets have poles which are usually labeled you can see n and s they're found at the two ends of any magnetic object that you're holding and bar magnets are called magnetic dipoles

Charges are at a higher or lower potential, but the _______ is unchanged throughout the whole wire

current

Ammeters measure? Symbol?

current through an object Symbol: Ⓐ (A) (has some internal resistance that cannot be helped)

what does the first right hand rule show you?

direction the magnetic forces are applied to electric charges due to magnetic fields

Current naturally moves? Why?

drawing these currents as if they're made of positive charges why would they lose potential energy by falling from high potential to low (we say conventional current we do in fact mean that it is made of positive charges moving from high potential to low potential)

Where does E usually point? Where does B usually point?

e typically points in really casual language from positive to negative b typically points from north to south

Suppose the quantity τ is a constant (i.e., it doesn't change) and the quantity t is a variable (i.e., it can take on many values, and it does change). What happens to the quantity e^(− t / τ) as t → ∞?

e^(− t / τ) → 0 Try it on a calculator if you're not sure. In particular, try typing e^− x where x is a very large number. Now make x an even larger number. Can you spot the pattern? Where is this ultimately heading?

electric charges can create?

electric charges can create magnetic fields

How to get electric charges to move in a circle

electric charges would move in a circle if you made electric fields that pointed centrally everywhere and you would get a central net force so it can be done but it's extremely hard to do

What is coherent behavior of orbiting electrons

even stationary objects are made of moving electric charges, under the right conditions you can still see large magnetic fields in stationary objects like a bar magnet thanks to the coherent behavior of orbiting electrons

external magnetic field, you could apply a ___________ to a current in a wire and if you do this you can apply a force to all of the charges that move through this wire as part of the current

external magnetic field, you could apply a magnetic force a lorentz force to a current in a wire and if you do this you can apply a force to all of the charges that move through this wire as part of the current

how can we predict the movement of a charge caused by magnetic fields?

first right hand rule

lorentz force of current depends on? Equation?

for current in a wire it depends on how quickly the current moves, it depends on how long the wire is, it depends on the strength of the magnetic field that you're subjecting this wire to and of course once again it depends on the angle between the moving charges and the magnetic field F(B)=ILBsinθ (angle of IB)

hard magnets vs. soft magnets. Explain

hard magnets are those that are permanently magnetized at least until you subject them to extremely high temperatures neodymium is a great example if you have any permanent magnets like maybe in a watch band or in a computer charging cable permanent magnets have to be mined out of the ground but then there's also soft magnets these are things like iron things that can become magnetized in the presence of other magnetic objects but as soon as you take that magnetic field away these soft magnets are no longer magnetized they just go back to being pieces of metal

What is electric current? Symbol? Unit?

how much charge flows per second but you may ask flows where well it doesn't really matter anywhere if charge moves past a certain location you count how much charge has moved in that amount of time and we call that a current we use the symbol "i" to denote current measured in coulombs per second Unit: Ampere (Amp) (A)

How can a moving charge in a magnetic field experience zero Lorentz Force?

if the sine of that angle just so happens to be zero, in other words there are certain angles between v and b that can cause even moving charges not to feel any lorentz force. All you got to do is know when is sine equal to zero, there are other angles that might cause the lorentz force to be the strongest it can possibly be those are times when sine is equal to one or minus one

in the same way that an equivalent capacitance could help us understand ________________, equivalent resistances can help us understand ______________

in the same way that an equivalent capacitance could help us understand **how much charge was stored**** equivalent resistances can help us understand *****how much current flows through a circuit****

What is the direction of the magnetic field at point P, which is exactly in the middle of two parallel wires carrying equal currents I in opposite directions? Wire 1's current is up, wire 2's current is down

into the screen

How to control current from being harmful to people? (General guidelines)

it actually depends much more on duration and location you apply this amount of current general rule: -one to five milliamps feel a tingle - a slight shock if you take 5 to 10 Milliamps, it's not going to feel good it might hurt - if it becomes 10 to 20 milliamps you might start involuntarily contracting your muscles - once it starts to get above 20 milliamps and into the 100 milliamp range, it could kill you -if more than one amp, could turn into a smoldering ash heap

it's magnetic fields that we use when we want to _____________ because ______________

it's magnetic fields that we use when we want to bend charges in a circular orbit because that's exactly what they're good for magnetic fields do that naturally, the Lorentz force any one of these protons rotating and counter rotating in this beam pipe always bends their trajectory into a circle and we can thank magnetic fields for that

key feature of the Lorentz force is that magnetic fields push charges ____________ to where they're already going, they can't speed you up or slow you down, they can't push you forwards or backwards, all they can do is provide a force that ____________ to where you're already going

key feature of the Lorentz force is that magnetic fields push charges at a right angle to where they're already going, they can't speed you up or slow you down, they can't push you forwards or backwards, all they can do is provide a force that bends your trajectory at a right angle to where you're already going

lorentz force says that the magnetic force that an electric charge feels depends on?

lorentz force says that the magnetic force that an electric charge feels depends on how big the charge is and its sign, how fast it's moving, how strong the magnetic field is and the angle between v and b

Magnetic Field strength symbol? Units?

magnetic field strength we're going to call "B" units of a magnetic field strength are called tesla one tesla is the si metric unit for magnetic field strength and it's equivalent to a kilogram per coulomb second

Can magnetic fields slow the charge down or speed it up by pushing or pulling?

magnetic fields CANNOT slow the charge down or speed you up by pushing or pulling -all they can really do is curve the trajectory

magnetic fields tend to bend trajectories of electric charges into __________ paths

magnetic fields tend to bend trajectories of electric charges into circular paths

if you're detecting a magnetic field you're probably detecting it because of what?

moving charges

magnetic fields are created by?

moving charges there are some situations where you can have magnetic fields without the presence of electric charges

How to move current in a certain direction? Why?

no telling where the electrons in current are going to go from one moment to the next it is more or less a random walk but if you connect a battery, the battery creates a difference in potential it creates a voltage in the wire the voltage by there being a difference in potential because the potential changes there is therefore an electric field because there's an electric field in the wire there will be a coulomb force on the electrons in that wire and so eventually they will make their way down the wire. It goes in a direction that is exactly opposite the electric field, it goes towards higher potential, it doesn't take a straight path to get there

Current is flowing to the right in a straight wire. The magnetic field at the position P above the wire points

out of the screen

Positive Charge is moving to the left, magnetic field is pointing into the screen. what kind of lorentz force does it feel?

point your arm to the left you bend your fingers into the screen your thumb will point down so the lorentz force on this charge now must be down

What is the direction of the magnetic field inside the solenoid? (top leaning to right) (current upward on side nearest you) (current going up into solenoid on left and leaving solenoid down on right)

right

we have a positive charge that moves to the right and so I'm going to draw its velocity it's moving to the right and we introduce a uniform external magnetic field, going to make this magnetic field point into the screen. what kind of Lorentz force do you get?

right hand rule your arm would go to the right your fingers would bend into the screen and the Lorentz force on that charge would point (thumb) up -that would mean this charge feels a force up POSITIVE

what's interesting about one tesla is equivalent to a kilogram per coulomb second

simply inside the unit itself you get a hint that electricity and magnetism are connected because if a tesla measures magnetic field strength then why is there coulombs in its unit? coulombs measures electric charge so you can already get a sense that somehow there is a connection between electric charge and how strong magnetic fields are both E and B are vectors

the idea of magnetism as ___________ counterpart they're like two halves of the same overall phenomenon we call it ________________.but it's true that magnetism is actually an unavoidable consequence of electricity and electric charges

the idea of magnetism a electricity's counterpart they're like two halves of the same overall phenomenon we call it electromagnetism but it's true that magnetism is actually an unavoidable consequence of electricity and electric charges

Explain current in a series combination resistor? Equation?

the longer the distance a current has to travel to get through an object the more resistance it encounters so more resistors in series should increase the effective length of the resistor and that should increase the resistance of the circuit R=ρ⋅(L/A) so when it comes to adding resistors in series it makes sense that they should add directly because they basically make longer resistors there's simply more stuff R(series)=R1+R2+...

In bar magnets, the origin of the n and the s, it comes from _______

the origin of the n and the s, it comes from navigation the direction the names north and south don't really mean anything other than they are conventions that we discovered and made up based on the direction that we saw magnetized needles point when we held them suspended on a string we saw them point toward the north or south

the right hand rule will tell you ____________ electric charge points when pushed by magnetic field. the lorenz force will tell you _____________

the right hand rule will tell you which direction it points the Lorentz force will tell you how strong it is

What is the the simplest magnet? Explain.

the simplest magnet that you can find is a bar magnet it's usually made of some type of metal often something relating to iron maybe aluminum other metals and hard magnets are those that are permanently magnetized at least until you subject them to extremely high temperatures

How do magnetic fields interact with electric charges? Explain

two ways: 1. moving charges create their own magnetic fields 2. use a magnetic field to apply forces to these electric charges but they have to be MOVING

two wires, both pointing up. What direction of force does the wire on the right feel from the magnetic field from the left wire?

two wires and they each have a current that's moving upwards. the magnetic field around the wire on the left according to the SECOND right hand rule it has a magnetic field that encircles it where my thumb points upward to show me the current and my fingers bend at a right angle around it to show me MAGNETIC FIELD LEFT WIRE CREATES. location of the right wire there is a magnetic field that points INTO SCREEN. in the presence of an external magnetic field such as the red in inward pointing magnetic field will feel a LORENTZ force and so if you use the FIRST right hand rule due to those moving charges. Finger should point LEFT. means this wire feels a LEFTWARD force because of the magnetic field from the left wire

You have two parallel currents with the same direction. What is the direction of the magnetic force due to I1 that acts on I2? I1 going right, I2 going right

electric field strength symbol? Units?

we called electric field strength "E" units of newtons per coulomb or volts per meter

All the charges were moving to the right in the wire as part of the current if you subject them to a magnetic field that points into the screen the right hand rule predicts?

your arm is moving to the right because that's where the charges are your fingers bend into the screen to show the magnetic field then there will be a Lorentz force on these charges that points up and you'll notice they appear to slam into the top of the wire they can't help it

we have a positive charge that is moving up, magnetic field pointing into the screen. what kind of Lorentz force does it feel?

your arm would now point up your fingers would bend into the screen and your thumb would point to the left so that means that this charge now feels a force to the left POSITIVE CHARGE

A positive charge travels upward in an external magnetic field that points into the screen. What is the direction of the Lorentz force on this charge?

¡Velocity of the electric charge, v ⃗ ("Where arm you going?"): Point your arm where the moving charge is presently going üArm points upward ¡Magnetic field, B ⃗ ("Bend"): Bend your fingers (not your wrist) in the direction of the magnetic field üFingers point into the screen ("×" vector means "into") ¡Lorentz Force, F ⃗_B: Extend your thumb to see the direction the charge will feel a force üThumb extends toward left

A positive charge travels upward in an external magnetic field that points to the right. What is the direction of the Lorentz force on this particle?

¡Velocity of the electric charge, v ⃗ ("Where arm you going?"): Point your arm where the moving charge is presently going üArm points upward ¡Magnetic field, B ⃗ ("Bend"): Bend your fingers (not your wrist) in the direction of the magnetic field üFingers point right ¡Lorentz Force, F ⃗_B: Extend your thumb to see the direction the charge will feel a force üThumb extends towards screen

Complex Circuit: •Suppose we want to know about the current flowing throughout this circuit. •How could we determine the current flowing through the battery (call it I_1)? •I need strategies. •Devise a solution to determine the value of I_1

üIf we replace all the resistors with an equivalent resistor... ü...Then we can know how much current flows through it. Because ΔV_(R_equiv)=I_1∙R_equiv

Charge accumulating on the capacitor over time. Which of the following equations accurately describes the charge on the capacitor Q over time? [The symbol tau (τ) is a constant with units of time]

üIn our charging RC circuit, the charge on the cap must look like Q=Q_max⋅(1-e^(-t/τ) ) üAt t=0 s (when the switch is first closed), we have: Q(0 s)=Q_max⋅(1-e^(-0/τ) )=Q_max⋅(1-1)=▭(0 C) üAfter a long time, as t gets large, e^(-t/τ)→0 üSo Q=Q_max⋅(1-e^(-t/τ) )→Q_max⋅(1-0)=▭(Q_max )

Which of the following equations accurately describes the current in this circuit 'I' over time? The symbol τ( tau) is a constant with units of time and the symbol I_0 refers to the current immediately when the switch is closed.

üIn our charging RC circuit, the current looks like I=I_0⋅e^(-t/τ) üAt t=0 s (when the switch is first closed and we start the clock), we have: I(0 s)=I_0∙e^(-0/τ)=I_0∙e^0=I_0∙1=▭(I_0 ) üIt should be I_0 when the switch is first closed at t=0 s. üAfter a long time, as t gets very large, the current I=I_0⋅e^(-t/τ) becomes very small and approaches ▭(0 A) üThis is also as predicted, and it matches our graph

Will Delta V_{R_{equiv}} (the voltage across the equivalent resistor) be equal to Delta V_{battery}=60 V in this circuit?

üThe equivalent resistor is the only object in the circuit besides the battery. üThe high potential side of the resistor must be at 60 V, and the low potential side of the resistor must be at 0 V. üSince both voltages feature a gap of 60 V (red to blue or blue to red), ΔV_(R_eq )=ΔV_Battery

Using the system of equations we found from the Junction and Loop Rules, calculate the currents I_2 and I_3 in Amps.

üWe found these equations to help us find I_2 and I_3 1) I_1=I_2+I_3 2) 60 V-(10Ω)∙I_1-(20Ω)∙I_2=0 3) 60 V-(10Ω)∙I_1-(30Ω)∙I_3=0 üBut we actually already knew I_1=2.73 A from Q1, so only Eqn. 2 and 3 are necessary to find I_2 and I_3 üSo 60 V-(10Ω)∙(2.73 A)-(20Ω)∙I_2=0 ü I_2=(60 V-(10Ω)∙(2.73 A))/((20Ω) )=▭(1.64 A) üAnd 60 V-(10Ω)∙I_1-(30Ω)∙I_3=0 I_3=(60 V-(10Ω)∙(2.73 A))/((30Ω) )=▭(1.09 A) ü üNotice that this already agrees with Eqn. 1: üI_1=I_2+I_3→2.73 A=1.64 A+1.09 A

Using the table in the previous question, if you heat a copper wire from 20 ºC to 100 ºC, what is the ratio of its new resistivity compared to its original resistivity?

ρ = (ρ_(0)) ( 1 + α ( Δ T )) =(1.7e-8) (1+ (3.9e-3 (-80))) =1.16e-8 1.7e-8/ 1.16e-8 =1.45

Add resistors in series [always, sometimes, never] increases resistance?

•Add resistors in series: •Only makes the resistors effectively "longer" which increases resistance R_series=R_1+R_2+...

How does the capacitance C change in this circuit when the switch is closed?

•Does C change? •No. Why would it change? •It's printed on the label of the capacitor. •Putting the capacitor in the circuit and closing the switch can't have any effect on how efficient the capacitor is.

Two current-carrying wires of the same length are parallel and seen to attract. If wire 1 carries twice as much current as wire 2, then wire 1 creates a magnetic field twice as strong at the location of wire 2 than the magnetic field created by wire 2 at the location of wire 1. True/False?

•If I_1=2⋅I_2, then B_1=2⋅B_2 when measured at the same distance away from each wire. üTrue. ✅ üWe know that the magnetic field strength due to a wire is proportional to how much current is flowing through that wire. üB_wire=(μ_0 I)/2πd

Two current-carrying wires of the same length are parallel and seen to attract. If wire 1 carries twice as much current as wire 2, then wire 1 pushes on wire 2 with a force twice as strong as the force that wire 2 pushes on wire 1.

•If I_1=2⋅I_2, then wire 1 pushes on wire 2 with a force twice as strong as the force that wire 2 pushes back on wire 1. üFalse. ❌ üThis is wrong for two reasons: 1.Newton's 3rd Law. 2.Weak I_2, so weak B_2. But strong I_1, so medium F_B. üSimilarly, strong I_1, so strong B_1. But weak I_2, so medium F_B.

How to find Lorentz Force on a Moving Charge

•Pause the moving charges at some moment; examine the velocity vector. •The Lorentz Force on these charges must point toward the center. •The RHR would predict that a magnetic field pointing out of the screen would achieve this - for positive charges. •But these are electrons. This field must point into the screen to bend their trajectory in this direction.

How does the charge Q on the capacitor change in this circuit when the switch is closed?

•The charge on the cap increases quickly at first (with basically no impedance from the cap at all initially) •Later, Q gradually approaches a maximum value and plateaus • Why? The cap accepts less and less charge until eventually stopping altogether

Two current-carrying wires of the same length are parallel and seen to attract. The currents flowing through each wire point in opposite directions. True/false?

•The currents flowing through each wire point in opposite directions. üFalse. ❌ üWe just saw currents in opposite directions repel each other. üAnd in the Pre-Lecture, we saw currents in the same direction attract each other. üIf we already know the result of this arrangement is attraction, then we can deduce that the currents probably point in the same direction based on our prior analyses.

Does ∆V_c change? If so, how?

•The difference in potential from one plate to the other plate grows as more opposite-sign charge collects on the opposing plates •It'll eventually reach the same voltage as the battery It'll grow proportionally to the stored charge Q because: ΔV_C=Q/C

Two wires, top wire I1 pointing right, bottom wire I2 pointing left. In which direction does the magnetic force F(2,1) (the force on wire 2 due to wire 1) point?

•What is the direction of the magnetic field B ⃗_1 (created by the top wire) at the location of I_2? üI_1 (thumb): Left üB ⃗_1 "(fingers): Into the screen" What is the direction of the Lorentz Force F ⃗_21 (on I_2 due to B ⃗_1)? üI_2 (arm): Left üB ⃗_1 "(fingers): Into the screen" üF ⃗_21 (thumb): Down

Two current-carrying wires of the same length are parallel and seen to attract. The magnetic fields created by each wire point in opposite directions at the location of the other wire. True/ False?

•Whichever direction B ⃗_1 points at the location of I_2, B ⃗_2 must point in the opposite direction at the location of I_1. üTrue. ✅ üI actually revealed that on the previous slide, but I suspected that many people wouldn't notice or remember. üWe also saw this in the Pre-Lecture too.

Magnetic Forces Between Current-Carrying Wires. •Wires that carry current ________their own magnetic fields. •Wires that carry current ______ Lorentz Forces due to external magnetic fields. •It should come as no surprise, then, that two current-carrying wires placed close together may apply ________ forces to each other.

•Wires that carry current CREATE their own magnetic fields. •Wires that carry current EXPERIENCE Lorentz Forces due to external magnetic fields. •It should come as no surprise, then, that two current-carrying wires placed close together may apply MAGNETIC forces to each other.

•Wires with current I have moving charges •In the presence of an __________, those moving charges feel Lorentz forces too.

•Wires with current I have moving charges •In the presence of an external magnetic field B ⃗, those moving charges feel Lorentz forces too. F_B=ILB sin⁡(θ_IB )

Which sketch shows the voltage across the resistor over time?

•ΔV_R=I∙R does change because I eventually dies to zero Amps •So, ΔV_R gradually reaches 0 V once the capacitor is fully charged. •It should gradually approach 0 Volts in the same shape as the current because ΔV_R=I∙R

Can Resistivity of objects change? How?

-***-Resistivity is just a property of a material and it cannot change (ONLY impurities, TEMPERATURE and LENGTH/ WIDTH)**** -so that means that if you cool a metal down you can lower its resistivity rho because delta t will become negative if you cool it down lower than 20 degrees Celsius that makes it easier for current to get through -if you increase the temperature above 20 degrees Celsius you can increase the resistivity you can make it harder to get current through. -"resistivity (p) causes resistance (R)" -temperature increases and the lattice structure starts to get really unstable all these obstacles that inhibit the free flow of electrons like the nuclei they start to vibrate wildly with energy as the temperature goes up it gets chaotic -LONGER resistors take more time to pass through so RESISTANCE of an object INCREASES as it gets LONGER -cross-sectional area (Width) -- LOWER resistance in the WIDER case so the resistance of an object decreases as its cross-sectional are grows (more room to get through faster)

A cubic centimeter of ________ which is a ________ has a resistance of about 1 microΩ. A cubic centimeter of ________ which is a ________ has a resistance of about 1 quadtrillionΩ.

-A cubic centimeter of copper which is a conductor has a resistance of about 1 microΩ. -A cubic centimeter of rubber which is a insulator has a resistance of about 1 quadtrillionΩ. (1 quadtrillion ohms of resistance)

How do the light bulbs compare in terms of their relative brightness? Connected in series

-Current does not change from one side of the resistor to the other -Before Bulb A, the current is I -After Bulb A (but before Bulb B), the current is still I -After Bulb B, the current is still I -So both bulbs are equally bright -But the potential drops by ΔV_R=I∙R across each bulb

How to connect an ammeter so that it measures how much current is passing through a resistor? Why?

-put the ammeter in SERIES with that resistor because you want all of the current going through the resistor to also go through the ammeter that will tell you how much current is going through the resistor (you do NOT want to change the equivalent resistance of this circuit because then current will probably change) -AMMETERS have very LOW resistance that means that all of the resistor's current goes through the ammeter and it slows the current down by only the tiniest amount when you install it - IF the ammeter has a very high resistance well as soon as you put the ammeter in this circuit it's going to kill the current if the ammeter has a massive resistance the circuit will pretty much lose all of its current you'll be trying to send water through a brick wall and the whole circuit will see just a trickle of current

Examples of insulators? Explain resistivity in insulators

-rubber glass wood plastic -it's going to take a lot of energy to compel these charges to leave if you want them to migrate somewhere else and become part of a caravan of current you're gonna have to work for it can be done maybe a really really really high voltage across this metal extreme potential difference from one side of the other if you can make a really extreme electric field in there maybe you can push them -an insulator resistivities can be a billion to maybe 10 quadrillion ohm meters

a 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch that can close and once I close the switch, I will complete the circuit, at the moment, the switch is open and so no charge can move, now immediately after I close the switch and complete the circuit, what happens next?

-the capacitor begins to fill up it started out empty and it starts to fill up the light bulb was really bright and you'll notice that the current was moving pretty fast but as time has passed you can see several things have also changed now, now the capacitor is mostly full the light bulb went dim and the current slowed down -let's watch that one more time watch the current the brightness of the bulb and notice that the capacitor is mostly full this process happens over time it doesn't happen all at once and the capacitor goes from empty to full the currents seem to go from fast to slow to stopped all these things are related

What is the relationship between ρ (rho) and R

-they're making the resistance (R) lower by lowering the resistivity (ρ) -they're making the resistance (R) higher by increasing the resistivity (ρ) -now you could do that by changing its temperature, length of the material, cross-sectional area (width) and/or what type of material you're using (some objects just simply have a higher resistivity (insulators)) ****Resistivity (ρ) (landmines) causes (affects) Resistance (R) in objects**** -if you make rho bigger obviously r should get bigger

How to connect a voltmeter so that it measures the difference in potential from one side of a resistor to the other side? Why?

-voltmeter and the resistor are connected during measurement in PARALLEL that's the only way to measure the difference in potential from one side to the other (to not change the equivalent resistance) -VOLTMETERS have a very HIGH RESISTANCE that means that almost no current goes through them at all instead it stays through the original resistor just like it was intended to this minimally disrupts the circuit -remember if you change the resistance of this circuit then you have also changed the potential difference across the resistor (if r changes then its voltage changes) you do NOT want to do that -If voltmeter had a very low resistance, you've completely re-routed where the current is going (most of the current would go through it and very little would ever go through the resistor and that's whose voltage you want to measure)

The graph shown below illustrates electric charge accumulating on the plates of a capacitor (it plateaus over time because the capacitor cannot accept more charge forever; eventually it fills up). Roughly how large is the average current (in A) in the circuit between 8 s and 9 s?

0 The rate at which the charge flows through this circuit and onto the capacitor plates is apparently zero by the end. The slope of the Q vs. t graph is flat, and since ΔQ = 0 C during the final second, there must be effectively no current flowing. This is expected: the current comes to a halt in the circuit once the capacitor can no longer accept more charge. The capacitor becomes a roadblock, and no extra amount of charge feels compelled to join the charged plates.

Suppose you place the terminals of a 1.5 V battery across a piece of metal and find that 6 A of current flows through it. What is the electrical resistance of this metal (in Ohms)?

0.25

Suppose the quantity τ is a constant (i.e., it doesn't change) and the quantity t is a variable (i.e., it can take on many values, and it does change). Which of the following is equivalent to the quantity e^(− t / τ)?

1 / (e^( t/τ ))

Suppose a R b u l b = 250 Ω light bulb is connected to a battery. To measure the voltage across this light bulb, a voltmeter is placed in parallel with the bulb. If the voltmeter has a resistance of R V M = 10 6 Ω, what is the equivalent resistance of this circuit with the voltmeter attached (in Ohms)?

249.938 Notice that this is almost exactly the original resistance before measurement took place, which is what you want. 1/(1/250 + 1/1000000) = 1/(0.004 + 0.000001) = 1/(0.004001) =249.938 (Parallel) If your answer is something that changes the resistance of this circuit significantly, then you calculated it wrong. ****Remember: the equivalent resistance should not change much during measurement.

A 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch that can close and I open the switch, to uncomplete the circuit. If I remove the battery while the capacitor is already full of charge, and now there's no battery in the circuit at all, so therefore, there's nothing keeping these ___________. The only thing that is keeping them on these plates right now ________.

A 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch that can close and I open the switch, to uncomplete the circuit. If I remove the battery while the capacitor is already full of charge, and now there's no battery in the circuit at all, so therefore, ***there's nothing keeping these charges of same sign on their respective plates* the only thing that is keeping them on these plates right now is the fact that **they do not have a conductive path to get back around*

A cylinder has a radius r and a diameter d = 2 r. Which of the following correctly shows its cross-sectional area (i.e., the area of a single circular slice)?

A=π⋅r^2 A=π⋅(d/2)^2

how should we add a new resistor between the points A and B if we want to increase the equivalent resistance of Circuit 1? All resistors connected in series

Any new resistor placed between points C and D will successfully increase the equivalent resistance. The equivalent resistance of a series of resistors looks like: R(series)=R1+R2+... Adding another term will never cause the overall sum to decrease. It will only make the equivalent resistance bigger. The reason for this is that the overall effective length of the resistors has increased, forcing current to travel through even more resistive material to reach the other side.

Any time you encounter a circuit element like battery or resistor, the _____________ can change across it. Both batteries and resistors act like ________ in _____________ in circuit. Whether you ___________ in _____________ as you trace your finger across it depends on ___________.

Any time you encounter a circuit element like battery or resistor, the potential can change across it. Both batteries and resistors act like cliffs or steps in electric potential in circuit. Whether you step up or down in potential as you trace your finger across it depends on the direction you go.

How do you know whether it's an increase in potential or a decrease when using Loop Rule across a battery? (How do you know whether it's a positive voltage or a negative voltage when using Loop Rule?)

As you TRACE around your FINGER through this loop, just depends on which direction you go. *BATTERY: (Positive and negative sides labelled) -If you went from its NEGATIVE terminal TO its POSITIVE terminal that must be an INCREASE in POTENTIAL simply because your finger first touched the minus terminal and second touched the plus terminal -If you first touch the positive terminal of the battery and second touch the negative that must mean you went from a side of higher potential to a side of lower potential that's a DROP in potential

Assuming one knew how to write voltage equations using Kirchhoff's Second Rule, which of the following loops could yield a correct voltage equation for the circuit shown below?

Both the navy blue loop and the pink loop would work, and so too would their opposite orientations *"Any" means "any." I can't say it more clearly than that.*

Conventional current always flows in the direction of _________________ potential. If we trace across a resistor with the flow of current, the potential must have ________________ going across it.

Conventional current always flows in the direction of decreasing potential. If we trace across a resistor with the flow of current, the potential must have dropped going across it.

To help me understand how electrical resistance in an object relates to various other quantities, I created a conceptual analogy called "Track and Field." Current, Resistivity, Cross-Sectional Area of Resistor, Length of Resistor, Resistor, Impurities, atomic nuclei, other electrons

Current - Runners Resistivity - Density/Spacing/Height Cross-Sectional Area of Resistor - # of racing lanes (This is the room the current has to spread out. The larger the area, the more spread out) Length of Resistor- Trach distance Resistor - Race track with hurdles (This is the object that resists the flow of electrons) Impurities, atomic nuclei, other electrons - Hurdles

True/false: If you increase the voltage across an object by a factor of two, you will reduce the current flowing through that object by a factor of two .

False If you reduce the voltage across an object by a factor of two, you will reduce the current flowing through that object by a factor of two.

What is Kirchhoff's first rule: Junction Rule?

In a Junction: Σ I (in) = Σ I (out) it says that when currents encounter a fork in the road they have to split into two separate currents anytime they meet a junction the current going into that junction 4.6 amps has to be equal to all the currents coming out 3.6 and 1.0. -It also says that separate currents must Rejoin 1 amp going in, 3.6 amps going in, 4.6 amps coming out so whenever current split off any time current split off the sum of all of the currents going into that junction must be equal to the sum of all the currents coming out of it that applies to any time that there are branches in a circuit in fact as long as the current is steady that's the only time you will see the current be different is when it branches off or rejoins --**everything going into the junction has to be equal to everything coming out

What is Kirchhoff's second rule: Loop Rule? Equation?

In a Loop: Σ ΔV = 0V loop rule involves drawing a loop around any part of any circuit and keeping track of all the places where the voltage goes up or down and when you do this you will find that any closed loop traced around a circuit comes back to wherever it started that's how you know it's a closed loop and the sum of all of the changes in potential up or down in that closed loop give you exactly zero volts. -it basically says that if you go up or down in elevation you didn't change as long as you come back to where you started -**if you can draw any closed loop in any direction any orientation anywhere in any part of a circuit and you come back to where you started your overall change in potential must be zero volts**

In an old-fashioned incandescent light bulb, current flows through the filament. As current moves through the filament, high energy charges endure collisions with the atoms that make up the filament. This causes ["an increase", "a decrease"] in temperature, which ["decreases", "increases"] the resistivity of the wire. That causes the overall resistance of the light bulb to ["increase", "decrease"] , which means the current moving through the bulb will now move even ["faster", "slower"] . All of this happens in the first instant after turning the bulb on, but the ultimate result is that the bulb very quickly becomes just slightly ["brighter", "dimmer"] .

In an old-fashioned incandescent light bulb, current flows through the filament. As current moves through the filament, high energy charges endure collisions with the atoms that make up the filament. This causes ["an increase"] in temperature, which ["increases"] the resistivity of the wire. That causes the overall resistance of the light bulb to ["increase"] , which means the current moving through the bulb will now move even ["slower"] . All of this happens in the first instant after turning the bulb on, but the ultimate result is that the bulb very quickly becomes just slightly ["dimmer"] .

A 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch that can close and I closed the switch, completed the circuit. We connect the voltmeter across the resistor/light bulb and the voltage changes over time. How does Kirchhoff's second rule (loop rule) apply?

Kirchhoff's second rule says trace across the capacitor from the positive plate to the negative plate that'll be a drop trace across the resistor while there's current flowing through it that'll be a drop and trace from the minus terminal the battery going left towards the plus terminal of the battery and that'll be a jump up of course those must sum to zero volts if you return to where you started. What's interesting about this relationship is that if you add one of those terms to the other side say add the potential difference across the battery to the other side you will find that the voltage across the cap and the voltage across the resistor always add up to that of the battery at any moment in time this is always true because I never specified exactly which moment in time I was doing this tracing so it must be true for any of those times and you'll find that if you make this graph as the voltage across the capacitor grows the voltage across the resistor dies but there's sum always adds up to that of the battery. Kirchhoff's second rule guarantees it time may elapse the current may die the voltage across the resistor may die the charge on the cap may grow its voltage the difference in potential from the positive plate to the negative plate may also grow but the sum of delta vc and delta vr is always the same number when it's charging it always sums to that of the battery now in the case of discharging

Suppose a R (bulb) = 250 Ω light bulb is connected to a battery. To measure the current flowing through this light bulb, an ammeter is placed in series with the bulb. If the ammeter has a resistance of R(AM) = 10 − 3 Ω, what is the equivalent resistance of this circuit with the ammeter attached (in Ohms)?

Notice that this is almost exactly the original resistance before measurement took place, which is what you want. 250 + 10^-3 =250.001 R1+R2 (Series) If your answer is something that changes the resistance of this circuit significantly, then you calculated it wrong. ****Remember: the equivalent resistance should not change much during measurement.

Ohm's Law tells us about the ________________ across a resistor

One of the most studied misconceptions in Physics Education Research: "Current is used up" WRONG! -**Ohm's Law tells us about the potential difference across a resistor, ΔV_R** -It tells us how much the potential drops from the high potential side to the low potential side of the resistor: ΔV_R=I∙R -But the current is the same immediately before and after the resistor - it's slowed down everywhere in the circuit -It's the potential that changes from one side of the resistor to the other side

Explain current in a parallel combination resistor?

R(Parallel)= 1/((1/R1)+(1/R2)+...) parallel, they're not longer, now they're wider. the wider the cross-sectional area through which a current can spread out when it moves through an object, the less resistance it should encounter and we saw that when the cross-sectional area increases the overall resistance of something decreases. now having some amount of cross-sectional area is great but if you want lower resistance, spread several of them out side by side and when you do that, it effectively makes one very wide resistor where you have a lot more cross-sectional area available now current that moves through now has more room spread out since there's more room available for the current to spread out. Adding resistors in parallel will reduce the equivalent resistance R=ρ⋅(L/A)

The graph shown below illustrates electric charge accumulating on the plates of a capacitor (it plateaus over time because the capacitor cannot accept more charge forever; eventually it fills up). On average, about how much current flows through this circuit in the first one second?

The average current flowing through this circuit is I= (ΔQ/Δt). -charge on the capacitor grew from Q=0 C at t = 0 s up to Q = 0.0015 C after t = 1 s had elapsed. Therefore, the charged flowed onto this capacitor at an average rate of: I= (0.00150-0C)/(1s-0s) = 0.0015.2 C/s This is the average slope (or average "rate of change") of the accumulated charge.

A circuit with just a battery, switch, and resistor in series (Each circuit has an identical battery of voltage E). What is the correct behavior of the circuit of its current once the switch ("S") is closed.

The current will start high, and stay high forever. Without a capacitor to accumulate charge, why would the current ever change?

A circuit with just a battery, switch, resistor, and capacitor in series (Each circuit has an identical battery of voltage E). What is the correct behavior of the circuit of its current once the switch ("S") is closed. Assume the capacitor is previously empty.

The current will start high, drop quickly at first, and then gradually reach 0A

Two circuits shown below contain identical resistors, each with resistance R. How should we add a new resistor between the points A and B if we want to increase the equivalent resistance of Circuit 1? All resistors connected in parallel.

The equivalent resistance of a parallel set of resistors looks like: R(Parallel)= 1/((1/R1)+(1/R2)+...) Adding another term to the denominator will never cause the overall fraction to increase. It will only make the equivalent resistance smaller. The reason for this is that the overall effective cross-sectional area has increased, allowing current to spread out more easily as it moves through the resistors.

Two identical bulbs A and B are connected in series to a battery. Which bulb is brighter?

They are the same brightness.

Suppose the quantity τ is a constant (i.e., it doesn't change) and the quantity t is a variable (i.e., it can take on many values, and it does change). Which graphs most resembles the function y = e^(− t / τ)?

This is called "exponential decay." If you watched the Pre-Lecture 12 video, you may have some guesses as to which physical quantities decay exponentially in an RC circuit.

What is Ohm's Law? Unit?

V=IR -true mostly for metals, conducting objects -the difference in potential across a resistor that voltage that you put across that object is directly proportional to how much current will flow through it -if you double the voltage across an object you double the current that will flow through it and he called this constant and proportionality resistance the bigger this quantity are the less current you get for the same voltage -if an object is more resistive the same voltage will make current flow through it more slowly -metric unit for resistance an ohm (omega) -it tells us how difficult it would be to move electric charge through an object

a 100 volt battery connected to a capacitor and a light bulb (________) and the battery, also have a switch that i can close and once i close the switch, i will complete the circuit. At the moment, the switch is open and so no ____________ can move, now if I close the switch, I complete the circuit.

a 100 volt battery connected to a capacitor and a light bulb (RESISTOR) and the battery, also have a switch that I can close and once I close the switch, I will complete the circuit, at the moment, the switch is open and so no CHARGE can move now immediately after i close the switch and complete the circuit

What are the two different ways of calculating current?

average (calculate) and instantaneous (only understand since calc-based) average current is what you would measure over some sizable duration of time maybe two seconds maybe five minutes maybe an hour. Average current not so sizable finite duration of time how much current flowed between now and later on average. An instantaneous current is what you would measure over an extremely short duration of time like at a single moment like right now how much current is flowing right now nanosecond scale zero time elapsed at this one moment how much time has elapsed none how fast is the current going that's your instantaneous current

What are RC circuits? Example?

circuits that involve resistors and capacitors -it's a resistor that you can dial to whatever setting you want and this is called an rc circuit it's one that features both an r and a c a resistor and a capacitor and they're in series with each other -rc circuits are used in all kinds of different applications especially audio and speaker output in fact pretty much anything that you want to turn on and then turn off gradually at a chosen time will happen with an rc circuit (another example windshield wipers)

current flows to ___________ potential

current flows to lower potential

If you trace a resistor with the direction of current (it travels the same direction as current) the potential (increases/decreases)

decreases

Suppose the quantity τ is a constant (i.e., it doesn't change) and the quantity t is a variable (i.e., it can take on many values, and it does change). What happens to the quantity e (− t/τ) as t → 0?

e^(− t / τ) → 1

If you trace a resistor against the direction of current (it travels in the opposite direction as current) the potential (increases/decreases)

increases

How do you know whether it's an increase in potential or a decrease when using Loop Rule across a resistor? (How do you know whether it's a positive voltage or a negative voltage when using Loop Rule?)

it's fundamental it comes from ohm's law all we know is that the potential drops across a resistor in the direction that the current flows through it but you know the current could flow in either direction -conventional current meaning made of positive charges they're going to find their way downhill whichever way they seem to be going across a resistor they are showing you where lower potential is located -if you find the current coming at you as you trace through it, you probably went to the higher potential side of the resistor -If you're going WITH the current that means you must have found the LOW potential side, that's a DROP in POTENTIAL -the current shows me which way is downhill

A 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch. If I remove the battery while the capacitor is already full of charge, and now there's no battery in the circuit at all. I close the switch, what occurs next?

only thing that is keeping the same charges on these plates right now is the fact that they do not have a conductive path to get back around but when i close the switch they will the only barrier between their return home from the minus plate back onto the positive plate that compels them is the single light bulb that's in the way once the switch is closed, they have no choice but to march through the filament of the light bulb on their way back around as they leave this cramped uncomfortable hateful negative plate that all these electrons inhabit unwillingly so with no battery to keep them on once the switch is closed the capacitor will kick the electrons off of the negative plate they themselves will kick each other off and they will gladly rejoin the positive charges on the other so here's what happens -when i close the switch you'll see the capacitor is fully charged but it begins to release it the bulb is bright and the current is pretty high but as time passes the capacitor begins to lose all of its charge again because it can the bulb goes dim and the current appears to come to a stop -when you give them a conductive path to get back to the positive plate they will take it but they do have to go through the light bulb to get there eventually the capacitor begins to drain itself of all its stored charge until it has none left -there is no excess negative charge on the minus plate and there is no excess positive charge on the plus plate with no more stored charge on the plates there's nothing else to kick off -no charges move everyone reaches electrostatic equilibrium and all current comes to a stop and the bulb goes dark

What is real current made of?

real currents are made of electrons that move through wires i'm talking to the microscopic level wires are made of atoms. atoms have their own electrons and their own protons and they exert coulomb forces on everyone else that's in that wire and everyone else that moves through it including the electrons that make up a moving current so what happens is electrons do kind of a dance they bounce around like pinball anything in the way every single atom every single valence electron that isn't moving every single valence electron that is moving inner shell electrons anything that could possibly exert coulomb forces electrons that make up the currents that move through wires they bounce off of all of them and what it looks like is a mess electrons in a wire. every step in any direction is the result of a random collision with something nearby

What is a resistor?

resistor is just a fancy name for a wire or an appliance a light bulb, your skin, any object through which you'd like to send current -electrical resistance, a quantity that impedes/obstructs the flow of current

How to combine resistors? Equation?

resistors combine in a way that is opposite to capacitors -series resistors add directly R(series)=R1+R2+... -parallel resistors add inversely R(Parallel)= 1/((1/R1)+(1/R2)+...)

What do resistors do?

resistors slow down the flow of charge

Explain resistivity in metals (conductors)

solid metals like iron or copper they tend to be made of a tightly packed lattice of atoms a very well organized structure and in between the atomic nuclei is a free-flowing sea of valence electrons that can become part of a current if you turn one on if you apply a voltage (difference in potential) across this metal it'll cause there to be an electric field in this region and if you do that all of these freely flowing electrons in and around this metal lattice will suddenly become part of a current already available they're just waiting for an electric field to tell them where to go otherwise they just hang out around all the nuclei -resistivity in metals is very very very low (like 10 to the minus 8 ohm meters and that's the unit of resistivity)

Symbol for resistor

squiggly line OR in real life they actually look like they have little colored bands they look like little cylinders with colored bands and the colored bands are supposed to indicate their resistance

the voltage across the resistor starts high and gradually decays down to zero and the reason that's not a surprise is because you already know that the current dies and whenever the current dies, the voltage across any resistor dies that's what ohm's law tells us but again notice the rate at which the voltage decayed it was steep at the beginning but by the end it becomes a very slow death did you notice how quickly it took us from 100 volts down to one and now look how long it's taken to go from one to zero. let's see this measured over time, we start with a very high voltage about a hundred volts and then you see it quickly start to decay down to closer towards zero and then slowly more and more slowly we get closer and closer to zero volts but the process that we got to that level got slower and slower over time, and according to Kirchhoff's second rule which you know is the loop rule if you trace your finger around this circuit, you'll arrive at the following conclusion the drop in potential across the capacitor, the drop in potential across the resistor and the jump up in potential across the battery if you trace around this circuit clockwise must all add up to zero volts

Usually the goal in Kirchhoff questions is to understand _______________ through a certain region, a certain wire, a certain branch a certain resistor you could always just stick an ___________in the circuit and then you will know

usually the goal in Kirchhoff questions is to understand *how much current is flowing* through a certain region, a certain wire, a certain branch a certain resistor -you could always just stick an *ammeter in the circuit (voltmeter will simply spit out exactly what the potential difference across every object OR use ΔV=I∙R)

A 100 volt battery connected to a capacitor and a light bulb and the battery, also have a switch that can close and I closed the switch, completed the circuit. We connect the voltmeter across the plates of the capacitor and how does its voltage changes over time?

why don't we connect the voltmeter across the plates of the capacitor and let's watch how its voltage changes over time we can read it right off the voltmeter evidently as the capacitor begins to fill up with charge the voltage across it goes up and that's not a surprise based on the way that we define capacitance its voltage should grow proportional to the amount of charges on it that's the entire reason that it has a voltage the reason the difference in potential exists across its plates is because one of those plates has a lot of positive charge which makes a high potential and the other plate has a very negative charge which makes a low potential but did you notice that the rate that the voltage grows actually decays it still becomes a larger voltage but it happens more and more slowly by the second -let's see that again, when you close the switch very bright bulb a lot of current and the voltage across the cap is growing very quickly but you notice now even as i'm saying this it's growing more and more and more slowly the time it took to reach 99 volts was pretty short but look how long it's taking to reach 100 apparently this process slows down more and more by the second in fact we can watch it, if you watch the voltage across the capacitor graft you'll see that it grows quickly at first but then it starts to plateau and the more time passes the flatter this curve becomes until it's barely growing at all

A wire 100 m long and 2 mm in diameter is connected to a battery with a potential difference of 14 V, and the current is found to be 18 A. Assume the wire is at room temperature. What is the overall resistance of this wire? What material is the wire made of?

üIf we knew its resistivity ρ in Ω∙m, we'd be able to look up what the object is made of via the resistivity table üBut we probably don't have much hope of learning its resistivity until we at least know what its overall resistance is. üAccording to Ohm's Law, R=(ΔV_R)/I=(14 V)/(18 A)≈0.8 Ω What material is the wire made of? üIts resistance looked like R=ρ⋅(L/A), as all resistors do. üNow that we know R, if we rearrange that equation, we can determine its resistivity, and that will tell us what kind of material it is. ρ=(R∙A)/L=(((ΔV_R)/I)∙A)/L=(((14 V)/(18 A))∙π((2×〖10〗^(-3) m)/2)^2)/(100 m) ≈▭(2.4×〖10〗^(-8) Ω∙m) üIt must be gold.

Suppose that the electrical resistance of dry skin is about 106 kΩ. Which of the following voltages would put you in serious/potentially life-threatening danger due to electric shock during prolonged contact?

üLet's conservatively say anything above 10 mA (0.01 A) is too dangerous for us to safely endure through our skin or across our body. -If dry skin (e.g., across our hands) has a resistance of about R_skin=106e3 Ω, then, according to Ohm's Law, we should avoid contacting voltages higher than: ΔV_danger=I_danger⋅R_skin =(0.01 A)(106 ×10^3 Ω) ≈1000 V =That means that 3 kV and 40 kV are certainly potential differences too large to place across our skin, lest we be harmed (or worse) by the current it would compel.

Suppose each light bulb has a resistance of R = 10 Ω, and suppose we measure the current flowing through the battery to be I = 0.6 A. In series

üOhm's Law says that the difference in potential from one side of each resistor to the other side must be ΔV_R=I⋅R üSince the top light bulb has a resistance of R=10 Ω and the current passing through it is I=0.6 A, the potential must drop by ΔV_R=(10 Ω)(0.6 A)=6 V across the bulb (shown as red to orange) üThe same information is true for the second light bulb, and it too will have a voltage of 6 V across it for the same reasons (shown as orange to blue). üSince the potential must drop from red to orange to blue in two increments of 6 V each, the entire drop in potential from red to blue must be 12 V total. üTherefore, the battery must have a voltage of 12 V across its two terminals.

How much current flows through the battery in this circuit?

üOhm's Law tell us that ΔV_(R_eq )=I_1∙R_equiv üThe voltage across any resistor is always ΔV_R=I∙R) üAnd we already saw that ΔV_(R_equiv )=ΔV_Battery based on our circuit design üSo the current running through this circuit must be: ΔV_Battery=I_1∙R_equiv→I_1=(ΔV_Battery)/R_equiv =(60 V)/(22 Ω)=▭(2.73 A) •We know that the current flowing through this circuit must be I_1=(ΔV_Battery)/R_eq =2.73 A •But how much goes through just R2? •Or how much goes through R3? •Thankfully, another 19th century German physicist answered this question.

Calculate the equivalent resistance of this circuit: When the switch is closed at Point a.

üThe orange box (R), the purple box (R_purple), and the blue box (R) are all in series with each other. üThe purple box has a parallel set inside it, so R_purple=1/(1/R+1/R)=1/(2/R)=R/2 üTherefore, the entire circuit is: R_equiv=R+R_purple+R =R+0.5⋅R+R =▭2.5R

Click on all of the locations where the electric potential increases while traveling around the clockwise blue loop.

üThe potential only increases in one location traveling clockwise around the blue loop. üThe positive terminal of the battery is 60 V higher than the negative terminal, and we encounter them going from - to +. No other increases in potential occur along this path.

If we make a wire out of each of these materials, and connect each wire to an identical 3 V battery, in which wire will we measure the lowest current at 20 ºC?

üThe resistivities of most metals (provided you're above extremely cold temperatures like 50 K, but below the melting point) look roughly like ρ=ρ_0⋅(1+α⋅ΔT), where ΔT=T-20 °C. üAt exactly T=20 °C, ρ=ρ_0⋅(1+α⋅0)=ρ_0, which isn't a coincidence or an accident - we defined ρ_0 on purpose to be the resistivity of an object at room temperature. üThe wire that will give us the LOWEST current will be the one with the HIGHEST room TEMPERATURE RESISTIVITY, because that will cause it to have the HIGHEST resistance. üOf the choices listed in the table, that means lead.

The resistivity of common metals is roughly linear with increases in temperature, as ρ=ρ_0⋅(1+α⋅ΔT).What is the resistivity of platinum on a hot day in south Florida (35 ºC) in Ω•m?

üThe resistivity of platinum, like most metals, will look like ρ=ρ_0⋅(1+α⋅ΔT), where ΔT=T-20 °C. üAt exactly T=35 °C, ρ=ρ_0⋅(1+α⋅(35 °C-20 °C)) üSince platinum has a room temperature resistivity of ρ_0=11×〖10〗^(-8) Ω⋅m and a temperature coefficient of α=3.92×〖10〗^(-3) 1/(°C), then its resistivity on a hot day must be: ρ=(11×〖10〗^(-8) Ω⋅m)⋅(1+(3.92×〖10〗^(-3) 1/(°C))⋅(35 °C-20 °C)) =▭(1.16×〖10〗^(-7) Ω⋅m)

The resistivity of common metals is roughly linear with increases in temperature, as ρ=ρ_0⋅(1+α⋅ΔT).What is the ratio of the resistivity of silver when cooled down to -10 ºC compared to room temperature?

üThe resistivity of silver will look like ρ=ρ_0⋅(1+α⋅ΔT), where ΔT=T-20 °C. üAt T=-10 °C, ρ_(-10)=ρ_0⋅(1+α⋅(-10 °C-20 °C)) üSince silver has a temperature coefficient of α=3.8×〖10〗^(-3) 1/(°C), then the ratio of its current resistivity to that at room temperature (ρ_0) must look like: ρ_(-10)/ρ_20 =(ρ_0 (1+α⋅(-10 °C-20 °C)))/ρ_0 =1+(3.8×〖10〗^(-3) 1/(°C))⋅(-30 °C)=▭0.89

What is the equivalent resistance of a circuit segment?

üThe strategy here is to notice that the 20 Ω is in series with a set of three rows of parallel resistors üThe three rows of parallel resistors can be consolidated first (Note: the last parallel row has a series set in it) üThe three rows of parallel resistors give us: R_purple=1/(1/120+1/40+1/(50+5)) Ω =19.4 Ω üTherefore, the entire segment is: R_equiv=20 Ω+19.4 Ω =▭(39.4 Ω)

A battery with voltage Δ V B a t t e r y and a resistor with resistance R make up part of a circuit. The current running through this wire segment is I. What is the following equation showing you about the change in electric potential as you trace your finger from Point A to Point B? ΔV(AtoB)=-ΔV(Battery)+I∙R

ΔV(AtoB)= -ΔV(Battery)+I∙R Going from the positive terminal of the battery to the negative terminal should represent a drop in potential. Passing through the resistor against the flow of current, which will be falling toward lower potential, must mean we have encountered an increase in potential.

What is equation for resistivity? Explain

ρ=ρ_0 ⋅ (1+α⋅ΔT) - α is constant (LOOK UP) (can be affected by temp., but keep constant at room temp.) (resistivity coefficient alpha at 20 degrees celsius) Unit:1/°C - ρ_0 is just whatever the resistivity of the metal would be at 20 degrees (GIVEN) -if your current temperature is 20°C and you're comparing that to 20°C then ΔT is 0 degrees --if you plug in 0°C for ΔT you should find that its resistivity is just whatever that baseline resistivity ρ_0 is equal to -as temperature goes up, so too does resistivity

Add resistors in parallel [always, sometimes, never] increases resistance?

•Add resistors in parallel: üOnly makes the resistors effectively "wider" which decreases resistance R_parallel=1/(1/R_1 +1/R_2 +...)

Kirchhoff's Rules - What to do if you don't even know which way the currents are going to go in a circuit?

•Draw and label currents as best as you can! Don't worry if you guess their directions wrong. •You'll just get a minus sign in your final numerical answer for the current if you guess their direction wrong (e.g., I_4=-2.3 A). •That just means the current was backwards from what you thought, but you'll have the magnitude correct!

•How do I know whether a resistor or battery represents a drop (down) or jump (up) in potential?

•For a battery: it's easy. Just look to see which terminal of the battery your finger traces across first; if you go from - to +, you went up in V. • For a resistor: use the directions of the currents as a guide. ("Conventional") Current always flows towards lower potential.

What will happen if you stick a 9 V battery on your tongue? What kind of current will pass through you? The electrical resistance of the human tongue is about 7 ohms

•Human tongue has a resistance of about 7 kΩ. How much current will you receive from a 9 V battery? -According to Ohm's Law, you'll receive about: I=(ΔV_R)/R =(9 V)/(7000 Ω) =0.0013 A=▭(1.3 mA) üThis is akin to a light tingle, maybe a slight shock -Virtually no pain (maybe slightly more sensation on your tongue than on dry skin due to saliva and its conductivity).

What are the most tangible and accessible example of a resistor? Explain how work?

•Objects that resist the flow of current, anything made of matter through which you might try to move charge (e.g., wires, appliances) are called "resistors" •The most tangible and accessible example of a resistor is a single light bulb •Light bulbs "slow current down" in a circuit by using the energy of the moving electrons to light the bulb thanks to their repeated, violent collisions with the atoms in the filament •More current moving through a bulb means brighter light •Less current moving through a bulb causes dimmer light. •More light bulbs can mean more overall resistance in a circuit and therefore less current moving through the wires.

What look of wire would have the LARGEST overall resistance

•The first object appears to have a large resistivity (R↑), and a long length (R↑), but it has a big cross-sectional area (R↓). •The second object has a high resistivity (R↑), a long length (R↑), and a small cross-sectional area (R↑) •The third object has a small resistivity (R↓), so that ruins its chances. •The fourth object has a small length (R↓) and a large cross-sectional area (R↓), so that means it's probably not a large resistance either.

•We know that Ohm's Law tells us the voltage across any resistor is ________ •This can help us understand __________ through a single resistor

•We know that Ohm's Law tells us the voltage across any resistor is ΔV_R=I∙R •This can help us understand current through a single resistor

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