Physics Concepts: Chapters 15, 16, 17 & 18
Two important differences between electric forces and gravitational forces:
1. electric forces can be either attractive or repulsive, but gravitational forces are always attractive 2. the electric force between charged elementary particles is far stronger than the gravitational force between the same particles
A student stands on a thick piece of insulating material, places her hand on top of a Van de Graaf generator, and then turns on the generator. Does she receive a shock?
She is not shocked. She becomes part of the dome of the Van de Graaff, and charges flow onto her body. They do not jump to her body via a spark, however, so she is not shocked.
16.2 If a negatively charged particle is placed at rest in an electric potential field that increases in the positive x direction, will the particle a) accelerate in the positive x direction b) accelerate in the negative x direction c) remain at rest
a
Why is it important to avoid sharp edges or points on conductors used in high-voltage equipment?
Sharp corners are where more charge would accumulate, creating larger electric fields. With high voltage equipment, these charges would have greater energy thus making it easier for them to jump off of the corner(s) onto a passing person.
All points on the surface of a charged conductor in electrostatic equilibrium are at the ______________ potential
same
18.1 True or False: While discharging, the terminal voltage of a battery can never be greater than the emf of the battery?
true
3. Figure shows equipotential contours in the region of space surrounding two charged conductors. Find (a) the work Wab electron volts done by the electric force on a proton that moves from point A to point B. Similarly, find (b) Wac (c) Wad, (d) Wae
(a) 0 A and B are on the same line W = -qEx equipotential is opposite direction of the field W = Fd Since displacement is perpendicular to the force then there is zero work being done. (b) -50.0 eV -qEx, so it will be negative 50 There is no potential in this equation W = -q deltaV (c) -90.0 eV we are going from zero to 90 (d) -90.0 eV
5. Two copper wires A and B have the same length and are connected across the same battery. If Rb = 2 R a, find (a) the ratio of their cross-sectional areas, Ab/Aa, (b) the ratio of their resistivities, pb/pa, and (c) the ratio of the currents in each wire, Ib/Ia
(a) 0.5 (b) 1 (c) 0,5
Four concentric spheres S1, S2, S3, S4 are arranged as in Figure and each charge in the figure has the same magnitude. What is the ratio of the electric flux through spheres S2, S3, and S4 to the flux through sphere S1: (a) 2/1= (b) 3/1= (c) 4/1=
(a) 1 (b) 2 (c) -1
5. A parallel-plate capacitor with capacitance C stores charge of the magnitude Q on plates of area A separated by distance d. The potential difference across the plates is V. If the capacitor is attached to a battery and the charge is doubled to 2Q, what are the ratios (a) C new/ C o and (b) V new /V o? A second capacitor is identical to the first capacitor except the plate area is doubled to 2A. If given a charge of Q, what are the ratios (c) C new/ C o and (d) V new/ V o? A third capacitor is identical to the first capacitor, except the distance between the plates is to the first capacitor, except the distance between the plates is doubled to 2d. If the third capacitor is then given a charge of Q o, what are the ratios (e) C new/ C o and (f) V new/ V o?
(a) 1 (b) 2 (c) 2 (d) 0.500 (e) 0.500 (f) 2
1. A proton is released from rest in a uniform electric field. Determine whether the following quantities increase, decrease, or remain unchanged as the proton moves. Indicate your answers with I, D, or U, respectively. (a) the electric potential at the proton's location (b) The proton's associated electric potential energy (c) Its kinetic energy (d) Its total energy
(a) Decreases the proton will move in the same direction as the electric field. electric fields go from high to low potentials. (b) D PE = -qE (change in x) if we increase location then we are increasing it negatively making it have a smaller potential energy. protons want to get rid of potential energy and turn it into kinetic energy. (c) I kinetic energy will increase since potential energy is decreasing. (d) U total energy will stay the same since it is conserved.
7. The following statements are related to household circuits and electrical safety. Determine whether each statement is true (T) or false (F). (a) Circuit breakers are wired in series with the outlets they protect. (b) A circuit breaker rated at 20 A provides a constant current of 20 to each outlet in the circuit. (c)Three-wire electrical cords help prevent dangerous electrical shocks by grounding the case of a device
(a) T this is to prevent injury fro occurring. if it is in parallel it could just skip the trap door. (b) F every time there is more than one path a circuit makes, a current will change. so it wont stay constant at 20 A (c) T it takes extra charge down to the ground
11. (a) Why is it dangerous to touch the terminals of a high-voltage capacitor even after the voltage source that charged the battery is disconnected from the capacitor? (b) What can be done to make the capacitor safe to handle after the voltage source has been removed?
(a) The capacitor often remains charged long after the voltage source is disconnected. This residual charge can be lethal. (b) The capacitor can be safely handled after discharging the plates by short-circuiting the device
1. Choose the words that make each statement correct. (i) When two or more resistors are connected in series, the equivalent resistance is always [(a) greater than; (b) less than] any individual resistance. (ii) When two or more resistors are connected in parallel, the equivalent resistance in always [(c) greater than; (d) less than] any individual resistance.
(i) a (ii) d in a series, equivalent resistance is greater than individual resistance in parallel, equivalent resistance is always less than individual resistance
Each of the following statements is related to conductors in electrostatic equilibrium. Choose the words that make each statement correct. (i) The net charge is always zero [(a) inside; (b) on] the surface of an isolated conductor. (ii) The electric field is always zero [(c) inside; (d) just outside] a perfect conductor. (iii) The charge density on the surface of an isolated, charged conductor is highest where the surface is [(e) sharpest; (f) smoothest].
(i) a - net charge is zero inside the surface of an isolated conductor. This is bc the electrons can move freely - they want to be as far away from each other as they can. (ii) c - electric field is zero inside a perfect conductor (the electric field is zero on the inside because all of the charges on the outside are canceling each other out) (iii) e - charge density on the surface of an isolated, charged conductor is highest where the surface is highest where the surface is sharpest. This is because all the electrons want to go there since it appears as if there aren't many on the sharp point.
3. Choose the words that make each statement correct. (i) To properly measure current through a device, the [(a) ammeter; (b) voltmeter] must be connected [(c) in series with; (d) in parallel with] the device. (ii) to properly measure the voltage across a device, the [(e) ammeter; (f) voltmeter] must be connected [(g) in series with; (h) in parallel with] the device
(i) a, c ammeter measures current in a series (ii) f, h voltmeter measures voltage in parallel.
7. Choose the words that make each statement correct. (i) After being released from rest in a uniform electric field, a proton will move [(a) in the same direction as; (b) opposite the direction of] the electric field to regions of [(c) higher; (d) lower] electric potential. (ii) After being released from rest in a uniform electric field, an electron will move [(e) in the same direction as; (f) opposite the direction of] the electric field to regions of [(g) higher; (h) lower] electric potential.
(i) a, d (ii) f, g
A short circuit is a circuit containing a path of very low resistance in parallel with some other part of the circuit. Discuss the effect of a short circuit on the portion of the circuit it parallels. Use a lamp with a frayed line cord as an example.
A short circuit can develop when the last bit of insulation frays away between the two conductors in a lamp cord. Then the two conductors touch each other, creating a low resistance path in parallel with the lamp. The lamp will immediately go out, carrying no current and presenting no danger. A very large current will be produced in the power source, the house wiring, and the wire in the lamp cord up to and through the short. The circuit breaker will interrupt the circuit quickly but no before considerable heating and sparking is produced in the short-circuit path. if the line frays and attaches to the other end then the charge will skip the lightbulb and choose to go through the path of least resistance
7. Newspaper articles often have statements such as "10,000 volts of electricity surged through the victim's body." What is wrong with this statement?
A voltage is not something that "surges through a completed circuit. A voltage is a potential difference that is applied across a device or a circuit. It would be more correct to say "1 ampere of electricity surged through the victim's body." Although this amount of current would have disastrous results on the human body, a value of 1 (ampere) doesn't sound as exciting for a newspaper article as 10,000 (volts). Another possibility is to write "10,000 volts of electricity were applied across the victim's body", which still doesn't sound quite as exciting.
If electrical power is transmitted over long distances, the resistance of the wires becomes significant. Why? Which mode of transmission would result in less energy loss: high current and low voltage or low current and high voltage? Discuss.
A wire or cable in a transmission line is thick and made of material with very low resistivity. Only when its length is very large does its resistance become significant. To transmit power over a long distance it is most efficient to use low current at high voltage. when in long distances resistance is high bc of R = rho l/A if you want to keep the resistance low then you would want to use a high current and low voltage?
If you are given three different capacitors C1, C2, and C3, how many different combinations of capacitance can you produce, using all capacitors in your circuits?
All three in series. All three in parallel. C1 and C2 in parallel, with C3 in series. C1 and C3 in parallel, with C2 in series. C2 and C3 in parallel, with C1 in series. C1 and C2 in series, with C3 in parallel. C1 and C3 in series, with C2 in parallel. C2 and C3 in series, with C1 in parallel. Other combinations can be made if only two capacitors are used
There is an old admonition given to experimenters to "keep one hand in the pocket" when working around high voltages. Why is this warning a good idea?
An electrical shock occurs when your body serves as a conductor between two points having a difference in potential. The concept behind the admonition is to avoid simultaneously touching points that are at different potentials.
18.2 Why does a battery get warm while in use?
Because of the battery's internal resistance, power is delivered to the battery material, raising its temperature.
Why is it dangerous to turn on a light when you are in a bathtub?
Because water is a good conductor, if you should become part of a short circuit when fumbling with any electrical circuit while in a bathtub, the current would follow a pathway through you, the water, and to ground. Electrocution would be the result.
13. Rank the electric potentials at the four points shown in figure from largest to smallest
D>C>B>A
A spherical surface surrounds a point charge q. Describe what happens to the total flux through the surface if (a) the charge is tripled, (b) the volume of the sphere is doubled, (c) the surface is changed to a cube, (d) the charge is moved to another location inside the surface, and (e) the charge is moved outside the surface.
EA = sigma = Q inside/free space a. if you increase q by 3, then E will increase by 3 b. 4 pi R ^2 therefore if we decrease E c. d. If charge is moved to another location inside the surface, then the Q will stay the same, so E stays the same e. Q represents the charge on the inside and if you move it then the Q will decrease
Positive charges and electric potential
If a positive charge is given some initial velocity in the direction of high potential, it can move in that direction, but will slow and finally turn around just like a ball tossed upwards in a gravity field.
Negative charges and electric potential
If released from rest, they accelerate from regions of low potential toward regions of high potential. Work must be done on negative charges to make them go in the direction of lower electric potential. the exact opposite.
In fair weather, there is an electric field at the surface of the Earth, pointing down into the ground. What is the sign of the electric charge on the ground in this situation?
If the field is pointing towards the ground, the ground must have a negative charge. (Electric fields point away from positive charges, toward negative charges.) we are talking about the sky to the ground
9. Explain why, under static conditions, all points in a conductor must be at the same electric potential.
If two points on a conducting object were at different potentials, then free charges in the object would move, and we would not have static conditions in contradiction to the initial assumption. (Free positive charges would migrate from locations of higher to locations of lower potential. Free electrons would rapidly move from locations of lower to locations of higher potential.) All of the charges would continue to move until the potential became equal everywhere in the conductor a) There is no electric field within the conductor, so it takes no energy to move charges around inside it. Thus the potential energy won't change. So the electric potential difference is zero. b) If you move a charge along the surface of the conductor where there might be an electric field, the field must be perpendicular to the surface. Thus it still takes no energy to move the charge and hence no change in electric potential.
11. When is more power delivered to a lightbulb, immediately after it is turned on and the flow of the filament is increasing or after it has been on for a few seconds and the flow is steady?
Immediately after it is turned on and the glow of the filament is increasing Once the switch is closed, the line voltage is applied across the bulb. As the voltage is applied across the cold filament when it is first turned on, the resistance of the filament is low, the current is high, and a relatively large amount of power is delivered to the bulb. As the filament warms, its resistance rises and the current decreases. As a result, the power delivered to the bulb decreases. The large current spike at the beginning of the bulb's operation is the reason that lightbulbs often fail just after they are turned on.
1. We have seen that an electric field must exist inside a conductor that carries a current. How is that possible in view of the fact that in electrostatics we concluded that the electric field must be zero inside a conductor?
In the electrostatic case in which charges are stationary, the electric field inside a conductor must be zero. A non-zero field would produce a current (by interacting with the free electrons in the conductor), which would violate the condition of static equilibrium. In this chapter, we deal with conductors that carry current, a non-electrostatic situation. The current arises because of a potential difference applied between the ends of the conductor, which produces an internal electric field. In the previous chapters we said it didn't for electrostatic cases - but now we want a current running through it so there can be.
15. Is it always possible to reduce a combination of capacitors to one equivalent capacitor with the rules developed in this topic? Explain.
Not all connections are simple combinations of series and parallel circuits. As an example of such a complex circuit, consider the network of five capacitors, C1, C2, C3, C4, and C5 shown in the figure in the next column This combination cannot be reduced to a simple equivalent by the techniques of combining series and parallel capacitors
The plates of a capacitor are connected to a battery. (a) What happens to the charge on the plates if the connecting wires are removed from the battery? (b) What happens to the charge if the wires are removed from the battery and connected to each other?
Nothing happens to the charge if the wires are disconnected. If the wires are connected to each other, charges in the single conductor which now exists move between the wires and the plates until the entire conductor is at a single potential and the capacitor is discharged
If a suspended object A is attracted to a charged object B, can we conclude that A is charged? Explain.
Object A could either be uncharged or oppositely charged to object B. If it is uncharged, there will be a shift in the electron cloud to be attracted to object B. One might think that both objects need to be charged, and oppositely charged at that, but that's not quite the case. Bringing a charged object close to a neutral object can attract charges of opposite sign in the neutral object, and at the same time repel charges of like sign. Since the charges of opposite sign in the neutral object are now closer to the charged object than the charges of like sign, there is a net attractive force! Note that it doesn't matter what sign of charge is on the charged object. The force between a charged object and a neutral object, when it exists, is always attractive. The slight separation of charges in the neutral object caused by the charged object is called an "induced charge."
Positive charge Q is located at the center of a hollow, conducting spherical shell. (a) Is the induced charge Qinner on the inner surface of the shell positive or negative? Answer P for positive, or N for negative. (b) Is the induced charge Qouter on the outer surface of the shell positive or negative? Answer P or N. (c) Determine the ratio Qinner/Q and (d) ratio Qouter/Q.
On a conductive sphere electrons are on the outside. The net charge will be what is on the inside surface and the outside surface added together (-Qoutside + Qinside = net charge) (a) Negative; because there is a positive charge on the inside, there will be an induced negative charged on the outside to cancel out and make zero. The inner surface of the outside shell is negative (b) Positive; because of the inner surface of the outer shell is negative, the outer surface will oppose that and be positive. (c) -1 (-1/+1) this is the inner surface of the outershell over the center. (d) 1 (+1/+1) this is the outer surface over the center
Rank the potential energies of the four systems of particles shown in figure from largest to smallest. Include equalities if appropriate.
PE = k q1q1/r a is the greatest because Q is greater than r and the signs are the same b and d would be the same because we have a q squared on both and they cancel out. c is the smallest.
11. Suppose a parachutist lands on a high-voltage wire and grabs the wire as she prepares to be rescued. Will she be electrocuted? If the wire then breaks, should she continue to hold onto the wire as she falls to the ground?
She will not be electrocuted if she holds onto only one high voltage wire, because she is not completing a circuit. There is no potential difference across her body as long as she clings to only one wire. However, she should release the wire immediately once it breaks, because she will become part of a closed circuit when she reaches the ground or comes into contact with another object.
Two lightbulbs are each connected to a voltage of 120 V. One has a power of 25 W and the other 100 W. (a) Which lightbulb has the higher resistance? (b) Which lightbulb carries more current?
The 25 watt one has the higher resistance and the other one therefore draws more current, as long as they are connected in parallel. P = I^2V I= square root of (P/V) = 25/120 = 0.46 A I = square root of (100/210) = 0.91 A Therefore, there is more current in the 100 watt bulb or V = IR R = V/I = 120/0.46 = 260.97 Ohms R = V/I = 120/0.91 = 131.87 Therefore, there is a higher resistance with the 25 watt bulb (a) The 25 W bulb has the higher resistance. Because R=(change in V)squared/P, and both operate from 120V, the bulb dissipating the least power has the higher resistance. (b) When the voltage is constant, the current and power are directly proportional to each other, P=(change in V)I=(constant)I. This, the higher power bulb (100W) carries more current.
9. Why is it possible for a bird to sit on a high-voltage wire without being electrocuted?
The bird is resting on a wire of fixed potential. In order to be electrocuted, a large potential difference is required between the bird's feet. The potential difference between the bird's feet is too small to harm the bird.
Two sets of Christmas lights are available. For set A, when one bulb is removed, the remaining bulbs remain illuminated. For set B, when one bulb is removed, the remaining bulbs do not operate. Explain the difference in wiring for the two sets.
The bulbs of set A are wired in parallel. The bulbs of set B are wired in series, so removing one bulb produces an open circuit with infinite resistance and zero current.
If you were asked to design a capacitor in which small size and large capacitance were required, what would be the two most important factors in your design?
The plates should be close together, have a large surface area, and have a dielectric between them. (C = A/d --> if the area is bigger and distance is smaller than the C is bigger)
9. What could happen to the drift velocity of the electron in a wire and to the current in the wire if the electrons could move through it freely without resistance?
The drift velocity might increase steadily as time goes on, because collisions between electrons and atoms in the wire would be essentially nonexistent and the conduction electrons would move with constant acceleration. The current would rise steadily without bound also, because I is proportional to the drift velocity
A charged comb often attracts small bits of dry paper that then fly away when they touch the comb. Explain why that occurs.
The dry paper is initially neutral. The comb attracts the paper because its electric field causes the molecules of the paper to become polarized - the paper as a whole cannot be polarized because it is an insulator. Each molecule is polarized so that its unlike-charged side is closer to the charged comb than its like-charged side, so the molecule experiences a net attractive force toward the comb. Once the paper comes in contact with the comb, like charge can be transferred, the like-charged paper is then repelled by the like-charged comb. The charge in the comb induces dipoles in the paper. The dipoles are attracted to the charge on the comb. When the paper touches the comb, some charge is transferred from the comb making the paper now charged with charges of the same sign. Thus they now repel and fly away from the comb.
There are great similarities between electric and gravitational fields. A room can be electrically shielded so that there are no electric fields in the room by surrounding it with a conductor. Can a room be gravitationally shielded? Explain.
The electric shielding effect of conductors depends on the fact that there are two kinds of charge; positive and negative. As a result, charges can move within the conductor so that the combination of positive and negative charges establishes an electric field that exactly cancels the external field within the conductor and any cavities inside the conductor. There is only one type of gravitation charge, however, because there is no negative mass. As a result, gravitational shielding is not possible. A room cannot be gravitationally shielded because mass is always positive or zero, never negative.
13. Embodied in Kirchhoff's rules are two conservation laws. What are they?
The junction rule is a statement of conservation of charge. It says that the amount of charge that enters a junction in some time interval must equal the charge that leaves the junction in that time interval. The loop rule is a statement of conservation of energy. it says that the increases and decreases in potential around a closed loop in a circuit must add to zero.
A ski resort consists of a few chairlifts and several interconnected downhill runs on the side of a mountain, with a lodge at the bottom. The lifts are analogous to batteries, and the runs are analogous to resistors. Describe how two runs can be in series. Describe how three runs can be in parallel. Sketch a junction of one lift and two runs. One of the skiers is carrying an altimeter. State Kirchhoff's junction rule and Kirchhoff's loop rule for ski resorts.
The lift is the source that is pumping people (aka electrons) up the hill (aka the circuit). Once they ski back down this creates a circuit.
Explain why a dielectric increases the maximum operating voltage of a capacitor even though the physical size of the capacitor doesn't change.
The material of the dielectric may be able to withstand a larger electric field than air can withstand before breaking down to pass a spark between the capacitor plates.
3. Suppose the energy transferred to a dead battery during charging is W. The recharged battery is then used until fully discharged again. Is the total energy transferred out of the battery during use also W?
The total amount of energy delivered by the battery will be less than W. Recall that a battery can be considered an ideal, resistance-less battery in series with the internal resistance. When the battery is being charged, the energy delivered to it includes the energy necessary to charge the ideal battery, plus the energy that goes into raising the temperature of the battery due to I^2r heating in the internal resistance. This latter energy is not available during discharge of the battery, when part of the reduced available energy again transforms into internal energy in the internal resistance, further reducing the available energy below W.
Why should a ground wire be connected to the metal support rod for a television antenna?
This gives any electrical charge that gets to the antenna a path to follow other than into your TV. For example, a lightning bolt.
A student who grew up in a tropical country and is studying in the United States may have no experience with static electricity sparks and shocks until his or her first American Winter. Explain.
Tropical countries are very humid. Water is a good conductor of electricity. Static Electricity - sharp points are more concentrated with charge
If more electric field lines leave a Gaussian surface than enter it, what can you conclude about about the net charge enclosed by that surface?
You can only conclude that the net charge inside the Gaussian surface is positive. Electric fields point towards negative charge and move away from positive charge.
15.4 A circular ring of charge of radius b has a total charge q uniformly distributed around it. Find the magnitude of the electric field in the center of the ring. a) 0 b) kq/b^2 c) kq^2/b^2 d) kq^2/b e) none of these answers is correct
a
15.6 Rank the magnitudes of the electric field at points A, B, and C in Figure with the largest magnitude first. a) A, B, C b) A, C, B c) C, A, B d) The answer can't be determined by visual inspection.
a
16.11 Consider a parallel-plate capacitor with a dielectric material between the plates. If the temperature of the dielectric increases, does the capacitance a) decrease b) increase c) remain the same
a
5. Electric current I enters a node with three resistors connected in parallel. Which one of the following is correct? (a) I=I and I2=I3=0 (b) I2>I1 and I2>I3, (c) V1<V2<V3 (d) I1>I2>I3>0
d
17.7 A voltage V is applied across the ends of Nichrome heater wire having a cross-sectional area A and length L. The same voltage is applied across the ends of a second Nichrome heater wire having a cross sectional area A and length 2L. Which wire gets hotter? a) the shorter wire does b) the longer wire does c) more information is needed
a
17.8 For the two resistors shown in Figure, rank the currents at points a through f from largest to smallest. a) Ia = Ib > Ie = If > Ic = Id b) Ia = Ib > Ic = Id > Ie = If c) Ie = If > Ic = Id > Ia = Ib
a
17.9 Two resistors, A and B, are connected in a series circuit with a batter. The resistance of A is twice that of B. Which resistor dissipates more power? a) Resistor A does b) Resistor B does c) More info is needed
a
18.4 The circuit in Figure consists of two resistors, a switch, an ammeter, and a battery. When the switch is closed, power P is delivered to resistor R. When the switch is opened, which of the following statements is true about the power P delivered to R? a) Po<Pc b) Po=Pc c) Po>Pc
a
18.5 In Figure, the current is measure with the ammeter on the right side of the circuit diagram. When the switch is closed does the reading on the ammeter a) increase b) decrease c) remain the same
a
16.7 An electron initially at rest accelerates through a potential difference of 1V, gaining kinetic energy KEe whereas a proton, also initially at rest, accelerates through a potential difference of -1V, gaining kinetic energy KEp. Which of the following relationships holds? a) KEe=KEp b) KEe<KEp c) KEe>KEp d) the answer cannot be determined
a the kinetic energy is the same even though the masses and velocities are different for both the proton and electron qV = PE they have the same magnitude of electric potential. When at rest they both have the same potential energy and that is equivalent to the kinetic energy
Power P = IV is delivered to a resistor of resistance R. If the resistance is doubled, while the voltage is adjusted such that the current is constant, what are the ratios (a) Pnew/Po and (b) V new/ V o? If, instead the resistance is held constant while P new = 2 P, what are the ratios (c) V new/ V o and (d) I new/ I o?
a) 2:1 b)2:1 c) square root of 2:1 bc of P = V^2/R d) 2P = I^2 R Square root of 2:1 if P goes up by 2, then the whole I squared goes up by two. Since it is squared we have to square root it to get the factor of two
16.9 A parallel-plate capacitor is disconnected from a battery, and the plates are pulled a small distance farther apart. Do the following quantities increase, decrease, or stay the same? a) C b) Q c) E between the plates d) V e) PEc
a) C decreases b) Q stays the same c) E stays the same d) V increases e) The energy stored increases
16.10 A fully charged parallel-plates capacitor remains connected to a battery while a dielectric is slid between the plates. Do the following quantities increase, decrease, or stay the same? a) C b) Q c) E between the plates d) V e) PEc
a) C increases b) Q increases c) E stays the same d) V remains the same e) The energy stored increases
A 12-V battery is connected across a device with variable resistance. As the resistance of the device increase, determine whether the following quantities increase, decrease, or remain unchanged. Indicate your answers with I, D or U respectively. (a) The current through the device. (b) The voltage across the device. (c) The power consumed by the device
a) decrease - they inversely proportional b) increase - they are directly proportional (V = IR) c) unchanged - (P=IV) if current (I) is decreasing and voltage is increasing then power will stay the same.
An uncharged series RC circuit is to be connected across a battery. For each of the following changes, determine whether the time for the capacitor to reach 90% of its final charge would increase, decrease, or remain unchanged. Indicate your answers with "I", "D", or "U" respectively. (a) the RC time constant is doubled. (b) The battery voltage is doubled (c) A second resistor is added in series with the original resistor.
a) if you double the RC, then the time for the capacitor to reach 90% will decrease b)
An electron is released from rest in a uniform electric field. Determine whether the following quantities increase, decrease or remain unchanged as the electron moves. Indicate your answers with I, D, or U. (a) The electric potential at the electron's location (b) The electron's associated electric potential energy (c) It's kinetic energy (d) Its total energy
a) the electric potential will increase since an electron goes the opposite way as the proton. b) It's electric potential energy will decrease since it is going in the opposite direction as the electric field lines. c) It's kinetic energy will decrease since potential energy is increasing d) its total energy is staying the same.
In an analogy between traffic flow and electrical current, (a) what would correspond to the charge Q? (b) What would correspond to the current I?
a)the number of cars b)the rate at which cars pass a given point
The fundamental charge is e=1.6 x 10^-19 C. Identify whether each of the following statements is true or false. (a) It's possible to transfer electric charge to an object so that its net electric charge is 7.5 times the fundamental electric charge, e. (b) All protons have a charge of +e. (c) Electrons in a conductor have a charge of -e while electrons in an insulator have no charge.
a. false; yes it is possible to transfer electric charge but you can't transfer a fraction of a charge. you cannot divide an electron. b. protons and electrons have the same charge except opposite. So yes. true c. false. in a conductor you have a lot of free electrons. In an insulator, electrons are bound.
Two uncharged, conducting spheres are separated by a distance d. When charge -Q is moved from sphere A to sphere B, the Coulomb force between them has magnitude Fo. (a) Is the Coulomb force attractive or repulsive? (b) If an additional charge -Q is moved from A to B, what is the ratio of the new Coulomb force to the original Coulomb force, Fnew/Fo? (c) If sphere B is neutralized so it has no net charge, what is the ratio of the new to the original Coulomb force, Fnew/Fo?
a. they both start out neutral and so when you take a negative charge from A and put on B, A will be + and B will be -. This will cause them to have an attractive force between sphere A and B. b. so if we take another charge it will make +2Q and -2q. The first one is is just 1q^2 and the second one is 4Q^2 so it is going 4:1. (F = kQq/r^2) c. If they take out a charge then it will be 0:1 aka it is just zero. F = kQq/d^2
15.2 Object A has a charge of +2 uC and object B has a charge of +6 uC. Which statement is true? a) Fab = -3Fba b) Fab = -Fba c) 3Fab = -Fba
b
15.8 Suppose the electric field of 15.7 is tilted 60 degrees away from the positive z direction. Calculate the magnitude of the flux through the same area. a) 0 b) 10.0 Nm^2/C c) 20.0 Nm^2/C d) more info is needed
b
16.1 If an electron is released from rest in a uniform electric field, does the electric potential energy of the charge-field system a) increase b) decrease c) remain the same
b
16.3 Figure is a graph of an electric potential as a function of position. If a positively charged particle is placed at point A, what will its subsequent motion be? Will it.. a) go to the right b) go to the left c) remain at point A d) oscillate around point B
b
18.3 In figure, the current is measure with the ammeter at the bottom of the circuit. When the switch is opened, does the reading on the ammeter a) increase b) decrease c) not change
b
18.6 When the switch is open in Figure power Po is delivered to the resistor R1. When the switch is closed, which of the following is true about the power Pc delivered to R1? a) Pc < Po b) Pc = Po c) Pc > Po
b
What happens when a charged insulator is placed near an uncharged metallic object? (a) They repel each other. (b) They attracted each other. (c) They may attract or repel each other, depending on whether the charge on the insulator is positive or negative. (d) They exert no electrostatic force on each other. (e) The charged insulator always spontaneously discharges.
b
17.5 All electric devices are required to have identifying plates that specify their electrical characteristics. The plate on a certain steam iron states that the iron carries a current of 6.00 A when connected to a source of 1.20 x 10^2 V. What is the resistance of the steam iron? a) 0.050 ohms b) 20.0 ohms c) 36.0 ohms
b 120/6 = 20
17.6 Suppose an electrical wire is replaced with one having every linear dimension doubled. Does the wire now have a) more resistance b) less resistance c) the same resistance than before
b ????
15.1 A suspended object A is attracted to a neutral wall. It's also attracted to a positively charged object B. Which of the following is true about object A? a) it is uncharged b) It has a negative charge c) It has a positive charge d) It may be either charged or uncharged
b if it is attracted to a neutral wall AND a positively charged object then it must have a negative net charge.
15.10 For a closed surface through which the net flux is zero, each of the following four statements could be true. Which of the statements MUST be true? (There may be more than one) a) there are no charges inside the surface b) the net charge inside the surface is zero c) the electric field is zero everywhere on the surface d) the number of electric field lines entering the surface equals the number leaving the surface
b & d
17.2 Suppose a current-carrying wire has a cross-sectional area that gradually becomes smaller along the wire so that the wire has the shape of a very long, truncated cone. How does the drift speed vary along the wire? a) It slows down as the cross section becomes smaller b) It speeds up as the cross section becomes smaller c) It doesn't change d) More information is needed
b (I = nqvA as A decreases v increases)
15.3 A test charge of +3 uC is at a point P where the electric field due to other charges is directed to the right and has a magnitude of 4 x 10^6 N/C. If the test charge is replaced with a charge of -3 uC, the electric field at P a) has the same magnitude as before, but changes direction b) increases in magnitude and changes direction c) remains the same d) decreases in magnitude and changes direction
c
15.7 Calculate the magnitude of the flux of a constant electric field of 5.00 N/C in the z direction through a rectangle with area 4.00 m^2 in the xy-plane. a) 0 b) 10.0 N m^2/C c) 20.0 N m^2/C d) More information is needed
c
16.8 A capacitor is designed so that one plate is large and the other is small. If the plates are connected to a batter, a) the large plate has a greater charge than the small plate b) the large plate has less charge than the small plate c) the plates have equal, but opposite, charge
c
18.9 The switch is closed in Figure. After a long time compared with the time constant of the circuit, what will the current be in the 2 Ohm resistor? a) 4A b) 3A c) 2A d) 1A e) More information is needed
c
17.10 The diameter of wire A is greater than the diameter of wire B, but their lengths and resistivities are identical. For a given voltage difference across the ends, what is the relationship between Pa and Pb, the dissipated power for wires A and B, respectively? a) Pa = Pb b) Pa < Pb c) Pa > Pb
c P = I^2R
16.6 A spherical balloon contains a positively charged particle at its center. As the balloon is inflated to a larger volume while the charged particle remains at the center, which of the following are true? a) the electric potential at the surface of the balloon increases b) the magnitude of the electric field at the surface of the balloon increases c) the electric flux through the balloon remains the same d) none of these
c as the area increases the E (electric field magnitude) decreases since it is getting farther away from the charge in the middle. They will even out and stay the same as the original electric flux as r gets bigger the electric field will decrease in magnitude because of E = kQq/r^2
15.5 A "free" electron and a "free" proton are placed in an identical electric field. Which of the following statements are true? a) Each particle is acted upon by the same electric force and has the same acceleration. b) The electric force on the proton is greater in magnitude than the electric force on the electron, but in the opposite direction. c) The electric force on the proton is equal in magnitude to the electric force on the electron, but in the opposite direction. d) the magnitude of the acceleration of the electron is greater than that of the proton e) both particles have the same acceleration
c & d - an electron weighs less (F/m = a)
17.3 Look at the four circuits shown in Figure and select those that will light the bulb.
c and d
15.9 Find the electric flux through the surface in Figure. Assume all charges in the shaded area are inside the surface. a) -(3C)/e b) (3C)/e c) 0 d) -(6C)/e
d
16.4 If a negatively charged particle is placed at point B in Figure and given a very small kick to the right, what will its subsequent motion be? Will it a) go to the right and not return b) go to the left c) remain at point A d) oscillate around point B
d
16.5 Consider a collection of charges in a given region and suppose all other charges are distant and have negligible effect. Further, the electric potential is taken to be zero at infinity. If the electric potential at a given point in the region is zero, which of the following statements must be true? a) the electric field is zero at no net charge in the region b) the electric potential energy is a minimum at that point c) there is no net charge in the region d) some charges in the region are positive, and some are negative e) the charges have the same sign and are symmetrically arranged around the give point
d
17.1 Consider positive and negative charges all moving horizontally with the same speed through the four regions in Figure. Rank the magnitudes of the currents in these four regions from lowest to highest a) Id, Ia, Ic, Ib b) Ia, Ic, Ib, Id c) Ic, Ia, Id, Ib d) Id, Ib, Ic, Ia e) Ia, Ib, Ic, Id f) none
d
17.4 In Figure does the resistance of the diode a) increase b) decrease as the positive voltage V increases
decrease
A glass object receives a positive charge of +3 nC by rubbing it with a silk cloth. In the rubbing process, have protons been added to the object or have electrons been removed from it?
electrons have been removed from the glass object. Negative charge has been removed from the initially neutral rod, resulting in a net positive charge on the rod. The protons cannot be removed from the rod; protons are not mobile because they are within the nuclei of the atoms of the rod. protons do not move - electrons move. if the object, ends up with a positive charge, then it is missing electrons. if it is missing electrons, then it must have been removed form the object during the rubbing process.
Consider point A in Figure located an arbitrary distance from two point charges in otherwise empty space. (a) Is it possible for an electric field to exist at point A in empty space? (b) Does charge exist at this point? (c) Does a force exist at this point?
field lines go whichever way the charges will make them want to go. because they are two positively charged points they will go in opposite directions. a) yes it is possible for point A to exist in that empty space. The field is everywhere. b) in this diagram, no. a charge does not exist at this point. c) we have an electric field there, but NO charge. E = F/q this is because we have an electric field with no charge. Aka F = qE. At point A there is no charge, therefore q=0 and so F=0. Electric field times zero charge equals zero force. No charge exists at point A. All of the charge is at q1 or q2. No force exists there since there is nothing on which to exert a force. But yes, an electric field does exist there. The electric field embodies the capability to exert a force. And certainly if a charge was placed as A, the other two would exert a force on it. So the electric field does exist there.
An air-filled parallel-plate capacitor with capacitance C stores charge Q on plates separated by distance d. The potential difference across the plates is V and the energy stored is PE. If the capacitor is disconnected from its voltage source and the space between the plates is then filled with a dielectric of constant k = 2.00, evaluate the ratios (a) C new/ C o (b) V new/ V o and (c) PE cnew/PE co
if connected to a battery C = eA/d if distance increases, capacitance will decrease Q = CV so then if capacitance decreases the overall charge will increase if not connected to a battery. since it is air filled, the k is going to be 1 SO, a) 2:1 because of the new k b) 1:2 because if charge stays the same, C increases, V will decrease by 2 c) PE= .5CV^2 since v increases by exponent 2 and C decreases by half, you get four/two so the ratio is 2:1
electron volt
is defined as the kinetic energy that an electron gains when accelerated through a potential difference of 1V
By convention, for a closed surface, the flux lines passing into the interior of the volume are _______________ and those passing out of the interior of the volume are _____________.
negative, positive this has to do with electric flux
18.7 Suppose you have three identical lightbulbs, some wire, and a battery. You connect one lightbulb to the battery and take note of its brightness. You add a second lightbulb, connecting it in parallel with the previous lightbulbs, and again take note of the brightness. Repeat the process with the third lightbulb, connecting it in paralel with the other two. As the lightbulbs are added, what happens to a) the brightness of the lightbulbs? b) the individual currents in the lightbulbs? c) the power delivered by the battery? d) the lifetime of the battery?
parallel: a) unchanged b) unchanged c) increase d) decrease
No net work is required to move a charge between two points that are at the _____________ electric potential.
same
18.8 If the lightbulbs above are connected one by one in series instead of parallel, what happens to a) the brightness of the lightbulbs? b) the individual currents in the lightbulbs? c) the power delivered by the battery? d) the lifetime of the battery?
series: a) decrease b) decrease c) decrease d) increase
If q is negative...
the electric field at P points radially inwards towards q.
If q is positive...
the electric field at P points radially outwards from q.
Resistors in a series
the equivalent resistance of a series combination of resistors is the algebraic sum of the individual resistances and is always greater than any individual resistance.
Resistors in parallel
the inverse of the equivalent resistance of two or more resistors connected in parallel is the sum of the inverses of the individual resistances and is always less than the smallest resistance in the group