PHYSICS - Electricity
What is an equipotential
A circle connecting all points at the same voltage - always perpendicular to the electric field lines
what is a multimeter?
A device that acts both as an ammeter (measuring current) and a voltmeter (measuring voltage)
What is the difference between electric potential (V) and electric potential energy (U)?
Electrical potential energy (U) = the energy present due to the electrostatic attraction between charged particles, much like the gravitational potential between a lifted object and the ground (another object) Electric potential = the difference in potential between two points in space. - can also be described as 'The potential energy per unit of charge (q)'
What is the charge of 1 electron or 1 proton?
Electron = - 1.6 x 10^-19 C Proton = + 1.6 x 10^-19 C
Give the formula for the electric force felt by a point charge placed in a certain electric field
F = q'E F = force (N) q' = test charge of an object (doesnt effect E (C) E = electric field (N/C)
Resistance is measured in?
Ohms, Ω
In electric field lines, how do you determine the strength of the charge at different points in the diagram?
The electric charge gets weaker the further apart the field lines get
Give the equation for the electrical potential energy generated by a capacitor (any shape)
U = 1/2 QV U = electrical potential energy (J) Q = charge (C) V = voltage (V)
Give the equation of Ohms law
V = IR V = potential difference, voltage (V) I = current (A) R = resistance (Ω)
a) define a field b) define an electric field
a) a distortion in space that creates a force on a charge b) the electrostatic force per unit charge
Give the formula for electric field due to a single charge
|E| = k(|q|/r²) E = electric field, a vector that points in the direction of the field (N/C or V/m) k = Coulomb's constant, 9 x 10^9 (N x m^2/C^2) q = the charge of an object (C) r = the distance between the field and the charge (m) NOTE - while E is abs, its still a vector (aka, you need to write your directions separately after the math, they wont come up from the math). Also, an electric field due to a single +ve charge points AWAY from the charge, and an electric field due to a single -ve charge points TOWARDS the charge (why? bc electric fields go from + places to - places)
Electric potential is high near _______ (+ve/-ve) charges and low near _______ (+ve/-ve) charges
+ve, -ve
In a battery, which way do the electrons flow? which way does current flow? What type of cell is a battery?
- electrons flow from the anode (-) to the cathode (+) - current flows from the cathode (+, longer battery line in circuit drawing) to the anode (-, shorter battery line in circuit drawing) --> think, Current, Cathode Batteries are galvanic cells
Describe the transition of energy types that occur within batteries
1. Start with chemical energy: the energy stored in bonds of atoms/molecules - released when chemical reactions break these bonds 2. Conversion to electric energy: movement of electrical charges 3. Conversion to the energy released by the device (ie kinetic energy, light, sound, heat etc)
What is the mass of 1 electron?
9 x 10^-31 kg
For circuits, Work = potential energy (aka W = ∆U). What potential energy formula do we equate work to when determining the work done by a) a capacitor b) a charge in a point in space
Any time you have a change in potential energy, work has been done. So you can equate ∆U = W in terms of their formulas. But cant equate ∆U to just anything. a) W = 1/2QV - technically, this refers to the work done AGAINST or BY the electric field between the 2 capacitor plates - note, if they ask about the work needed to insert a dielectric between 2 capacitor plates, need to do ∆U = (1/2Q₂V) - (1/2Q₁V). We usually assume U₁ = 0, but if given info that this isnt the case, we need to U₂ - U₁ (aka ∆U) b) W = Vq - from the formula V = U/q so U = Vq - be careful here, the work done is the work to MOVE a charge in space. However, it could be moved from one capacitor plate to the other, but were not talking about the work of the capacitor. Talking about the charge
Explain how attractive/repulsive forces between current in 2 different wires works
Attractive / repulsive forces between current in 2 wires = opposite of point charge trend - ie, 2 charges with opposite directions will attract (+ and -), and 2 charges with same direction will repel - however, 2 currents with opposite directions will repel, and 2 currents with same direction will attract
What is the voltage of a battery - the potential difference - a difference between?
Between the potentials of the cathode and the anode of the battery
What is the difference between electromotive force (EMF) and terminal voltage?
EMF doesnt account for internal resistance of the battery, while terminal voltage does. For an ideal battery, the observed terminal voltage is equal to the electromotive force: V=ℰ However, in real systems a battery uses chemical reactions to physically segregate positive and negative charges in a process that is not perfectly efficient. As a result, internal resistance (r) within the battery dissipates some of the electric potential energy as charges are transported as current (I) to the appropriate battery terminals. The voltage that is "lost" (Vloss) due to internal resistance WITHIN the battery is expressed by application of Ohm's law: Vloss=Ir Accordingly, the discrepancy between electromotive force and the observed terminal voltage is: V=ℰ−Vloss=ℰ−Ir V = ℰ - (I)(r) - V = terminal voltage - ℰ = emf - I = current WITHIN THE BATTERY - r = internal resistance WITHIN THE BATTERY
if A is +ve and to the left of B, which is -ve, if we ask "what is the effect of A on B" what does this mean? What is the direction of the pull?
If were looking at the effect of A on B, it means were talking about B. The direction is to the left, starting at B, towards A (B is where we start at bc thats what were talking about)
Where are the positive and negative charges on a battery in circuit notation?
In circuit notation, a battery is represented with 2 parallel lines, one of which is slightly longer than the other - the +ve charge will be at the longer line and the -ve charge will be at the shorter line - thus, we can say current starts flowing on the side of the longer line (since its opposite to electron flow)
Current runs _________ (in the same direction/in the opposite direction) as electrons
In the opposite direction
What does an increase in temperature do to resistance of a material?
Increases - bc when you increase the kinetic energy, the electrons are more likely to come into close proximity with one another and produce repulsive effects This can be demonstrated via the formula R = R₀ [1 + α(T - T₀)] - dont need to memorize the formula, but understand the takeaway that higher temp = higher resistance
If you have a resistor that is in series with a capacitor, what will decrease the strength of an electric field more - increasing circuit resistance (w/ a fixed current) or increasing distance between the plates?
Increasing the circuit resistance for a fixed current will decrease the electric field, but not by as much as does the length change. This is explained by a formula. Formula for electric field of a capacitor that is in series with a resistor (specifically!!)= E = (ε − IR)/d - E = electric field between capacitor plates - ε = emf - IR = voltage lost across the resistor thats in series with the capacitor (where I is the current across the resistor and R is the resistance of the resistor) - d = distance between the 2 plates Note - typically when we talk about terminal voltage and emf (Vterm = ε - IR) , were talking about IR as the lost voltage due to the internal resistance of the battery itself. But this can be applied to any resistor as well. Any added resistor in series with a capacitor will decrease the voltage available to the capacitor by IR, hence= ε-IR. And since V = Ed (where V would have to be the "terminal" voltage aka the voltage available for the capacitor), E = V/d so sub V for ε − IR and you get E = (ε − IR)/d
What does it mean if a charged particle is said to be "slowing down" if placed in an electric field?
It means that it is moving towards the charge it is repelled by NOTE - electric field lines move from + to - but if you place a charged particle in that field it doesnt necessarily have to move from + to -! Depends on the charge of the particle - an electron moves to the + side, but a proton would move to the - side because this is what charges the particles are attracted to - if the charged particle slows down, this means its moving to the side it is repelled by, instead of the side it is attracted to
Give the formula for power that relates to circuits
P = IV - P = power (W) - I = current (A) - V = voltage (V)
Give the formula for Coulomb's Law (aka formula for electrostatic force)
Same format as the gravitational force formula!! F = k( |q1q2|/r²) - F =magnitude of electrostatic force; the attraction/repulsion between two charged objects (N) - k = Coulomb's constant, 9 x 10^9 (N x m^2/C^2) - q1 and q2 = the respective charges of object 1 and object 2 (C) - r = the distance between the centres of charge (m) NOTE - in the case where there are only 2 charges, if the product of q1q2 is +ve, then the force is repulsive, and if its -ve, the force is attractive. Since there is an abs value on q1 and q2, you need to input this sign yourself after calculations. But in a multi charge setting where you need to add the F's together, +ve F means the charge youre looking at is going right, and -ve charge means going left. NOTE - in the way that the formula its written (q1 written before q2), F describes the force experienced by q1 due to q2. However, know that the force experienced by q2 due to q1 is equal in magnitude, but in the opposite direction
What is the net voltage of a circuit that has 2 batteries that have current flow in opposite directions (aka they oppose each other; cathodes face each other)
The net voltage is the difference between the voltage of each battery - the direction of flow is in the direction of the higher voltage battery (aka like that battery "wins")
The current produced by a cell is directly proportional to?
The surface area of the cathode and the anode
What is the difference between an electric field and a magnetic field
They are similar since theyre both produced by charges, but have their differences (below) Electric field - all charges, static and moving, create an electric field around them - produces no force on a magnet - electric field lines go from +ve charge to -ve charge Magnetic field - only moving charges produce magnetic fields - produces no force on a static electric charge - outside the magnet, the magnetic field lines go from the north pole to the south pole. Inside the magnet, the magnetic field lines go from south pole to north pole NOTE - all current creates a magnetic field
Give the equation for electric potential energy if an electric field is created by a point charge
U = k(q1q2)/r U = electric potential energy (not due to elevation as seen with gravitational potential energy, rather, due to repulsion forces. similar concept tho) k = Coulomb's constant, 9 x 10^9 (N x m^2/C^2) q1 and q2 = the charges of 2 objects (C) r = the distance between the 2 charges (m) - notice how r is NOT SQUARED HERE
Give the formula for electric potential energy of a charge in an electric field
U = qEd (just gravitational potential energy which is E = mgy) U = potential energy q = charge, NOT abs value E = electric field (magnitude only) d = displacement (measured from a zero point of your own choosing) Note - for this formula, the+ve y direction = opposite to the field direction. -ve y direction = in the same direction as the field
How much work is done on a charged particle moving through a magnetic field that is forced into a curved path?
ZERO - since the force felt by the charged particle is always 90 degrees to the velocity direction (and thus the displacement direction too), and the formula for work is W = Fdcosθ, since θ here is the angle between F and d which is 90, and cos90 = 0, W = 0
What is the net force that a dipole inside a capacitor feels?
Zero - since dipoles have a +ve and a -ve end, there is a force (via F = qE) coming out of either end of this dipole (ie, +ve dipole end has F pointing towards -ve plate, and -ve dipole end has F pointing towards + plate). These force are equal in magnitude at either end of the dipole, but have opposite signs. Thus, they cancel out and the net force is zero on the dipole NOTE - any dipole will have a net force of zero! This is no exception
What is the force felt on a charge moving to the right in a magnetic field that also points to the right?
Zero! - since both the velocity and the magnetic fields point to the right, θ in sinθ (the angle between these 2) is 0 and sinθ = 0. Thus, F = 0 because F = qvBsinθ NOTE - same case when the velocity and magnetic fields are in opposite directions because sin180 = 0
Define centre of charge
a point from which the charge generated by an object is said to originate
Explain the right hand rule for a) F = qvBsinθ b) F = ILBsinθ c) B = (µ₀I)/(2πr)
a) - thumb = points in the direction of the velocity (v) - fingers = point in the direction of the magnetic field (B) - palm = if the charge is positive, the direction of the force points out of the palm - back of the hand = if the charge is negative, the direction of the force points out of the back of the hand b) - thumb = points in the direction of current (I) - fingers = point in the direction of the magnetic field (B) - palm = if the charge is positive, the direction of the force points out of the palm (note that charge of interest is always +ve bc this formula is for current specifically, so there is no case where you'd need to reverse the direction of F) c) - thumb = points in the direction of current (I) - fingers, curled = curl around the wire to give the direction of the magnetic field (B). Visual explanation in pic
Compare what happens a) with no dielectric vs with a dielectric - battery is in for both cases b) no dielectric + battery in vs dielectric + battery taken out
a) No dielectric - Q is lower - C is lower - E is the same - V is the same (since V = Ed, and if E doesnt change, and d doesnt change then V doesnt change) - faster build up of charge on plates when charging (it holds less charge, so time needed to reach that charge is less) With dielectric - Q is higher - C is higher - E is the same - V is the same (since V = Ed, and if E doesnt change, and d doesnt change then V doesnt change) - slower build up of charge on the plates b) update
a) 1 eV = ______ J? b) how is eV proportional to ∆V and charge?
a) 1.6 x 10^-19 J b) If charge is of just 1 electron or proton (ie, -1 or +1, NOT the charge in coloumbs aka 1.6 x 10-19), then the ∆V will be equal to the value in eV - aka if ∆V = 5, eV = 5 But if the particle is charged, need to account for this too - aka if we have an alpha particle with a charge of +2e thats moving through a ∆V of 1, then eV = 2 eV NOTE - so you literally just multiply the charge of the particle with the ∆V value to get the eV value. This is because V = U/q so U = qV. So 1 eV is LITERALLY the charge of 1 electron x 1 V. And since 1 electron has a charge of 1.6 x 10^-19 Q, this makes sense.
a) When is an electric dipole created? a) Whats the formula for dipole moment? b) the further apart 2 charges, the ________ the dipole get
a) Created by two opposite charges with equal magnitude b) p = qd p = dipole moment q = charge (C) d = distance between the 2 equal and opposite charges b) stronger! yes sounds counterintuitive but it makes sense with the formula above
a) Give the formula of the force on a charged particle moving through a magnetic field b) Give the formula of the force on a current-carrying wire in a magnetic field c) Give the strength of magnetic field caused by a current carrying wire
a) F = qvBsinθ F = force (N), also known as the Lorentz force - direction is perpendicular to both the velocity and the magnetic field - is actually a centripetal force as the charged particle will start spinning once it goes into the magnetic field (recall Fc = (mv²)/r...Lorentz force is equal to this too. Ie qvBsinθ = (mv²)/r ) q = charge (C) v = velocity (m/s) - notice how for a charge to feel a force in a magnetic field, it needs to be moving! B = the magnetic field (T, for tesla) - the magnetic field could point in any direction, but if it points into the page this is denoted with an 'X' (think tail of arrow!), and if it points out of the page this is denoted with a dot (think tip of arrow!) θ = the angle between the v and B b) F = ILBsinθ - F = force (N) - I = current (A) (replaces velocity in the original formula, since current is just the flow of positive charge) - L = length of the wire exposed to magnetic field (m) - B = magnetic field (T) - θ = angle between I and B Note -a current-carrying wire feels a force as it enters an external magnetic field. However, any force you feel, you can also create (like Fg vs. FN for eg). Similarly, a current carrying wire can also CAUSE its own magnetic field, and some other wire may able to feel this too (as an external field). This is what formula c) describes c) B = (µ₀I)/(2πr) - B = magnetic field (T) - µ₀ = a constant ('permeability of free space') - I = current (A) - r = distance from the particular part of magnetic field youre examining to the wire (aka the field gets weaker the further you get from the wire)
a) Electric potential flows from ______ (high/low) potential to _______ (high/low) potential b) charges want to travel in the direction of ____ electric potential energy? c) charges want to travel in the direction of _____ electric potential?
a) High, low b) decreasing (ie, from high to low) - note, but only when the particle can. This is what it wants to do. If its forced to go in the opposite direction, this will increase its potential energy, which it doesnt want c) depends on the sign of the charge!! Look at pic
a) how do you find total current in a series system? b) how do you find total current in a parallel system? c) how do you find total voltage for a series system? d) how do you find total voltage for a parallel system? e) how do you find total resistance of resistors in series? f) how do you find total resistance of resistors in parallel? g) how do you find total capacitance for a series system? h) how do you find total capacitance for a parallel system?
a) I total = I1 = I2 = I3... b) I total = I1 + I2 + I3... c) Vtotal = V1 + V2 + V3... d) V total = V1 = V2 = V3... e) Rtotal = R1 + R2 + R3... f) 1/Rtotal = 1/R1 + 1/R2 + 1/R3... g) 1/Ctotal = 1/C1 + 1/C2 + 1/C3... h) Ctotal = C1 + C2 + C3... Note - notice how current and voltage have exactly opposite rules, and resistance and capacitance have exactly opposite rules
Explain Kirchoff's... a) first law b) second law
a) Junction rule for current: the sum of current at a junction is equal to 0 (aka current going into junction = current leaving junction (split up) b) Loop rule for voltage: the sum of voltage change within a loop is equal to 0 (aka any increase in potential within a loop will be compensated by decreases in potential)
a) Field lines go from _______ (positive/negative) to _______ (positive/negative) b) electrons go from _______ (positive/negative) to _______ (positive/negative)
a) Positive, negative b) Negative, positive
a) Give the formula for resistance b) Give the formula for conductivity
a) R = p (L/A) - R = resistance of a resistor or wire (Ω) - p = resistivity (how resistant the wire or resistor is to electron flow) - L = length of resistor or wire (m) - A = cross sectional area, aka πr² (m²) Note - technically this formula can be used to find resistance of ANY material, but most often its for a wire or resistor b) conductivity = 1/resistivity
When the electric field begins to build up between plates of a capacitor, the dipoles in the dielectric are rotated to point in the direction of the electric field. a) what causes this to happen b) what is the resulting effect of this on the capacitor
a) Recall that because each dipole end experiences a force of equal magnitude but opposite direction, the dipole feels no net force - however, it does experience torque, and its the torque that causes the dipoles to rotate and align with the external electric field (align meaning going from randomly oriented to parallel with the electric field lines) - however, the + end of the dipoles will be closer to the -ve plate and the - end of the dipoles will be closer to the +ve plate (because of electrostatic attraction) b) Once the dipoles are reoriented, they create a small electric field of their own, pointing in the opposite direction of the electric field of the plates - this causes the net electric field to be weaker with a dielectric because now there are also a bunch of small electric fields that oppose the direction of the original electric field (aka net electric field decreases) - recall that V = Ed and C = Q/V. Can combine these as Q/C = Ed - Since E decreases initially due to the dielectric dipoles, Q increases to bring E back up - and since V (aka Q/C) must stay constant across a dielectric (just a rule), if Q increases then C increases ULTIMATE RESULT: capacitance of the capacitor increases with the addition of a dielectric, which is why we add them in the first place
Define current and give the formula
a) The flow of (imaginary) positive charge (A, amps) per unit of time b) I = ∆Q/∆t I = current (A) Q = charge (C) t = time (s) NOTE - said to be the flow of "positive charge" because current direction is opposite to the flow of electrons, and thus, in the same direction as the flow of protons
a) What is the charge of a Cl- ion? b) what is the charge of a carbon nucleus?
a) The same as an electron (-1.6 x 10^-19) because the CHARGE is -1 bc there are 17 P and 18e-. b) A carbon "nucleus" is just referring to the protons that are present in carbon. Since Carbon has 6 protons, you need to do 6x(1.6 x 10^-19) to find the charge
For capacitors, a) describe how charging works b) describe how you can manipulate capacitance values b) describe the graphs of Q/t, V/t and I/t during charging and discharging
a) When capacitor is charging, easiest to understand by thing of electron flow. Before charging starts, plate1 has equal number of + and - charge, and so does plate2 (both are neutral). During charging, electrons leave the -ve terminal and deposit on plate1. As -ve charge increases on plate1, the -ve charges on plate2 are repelled back towards the +ve terminal, leaving only +ve charge on plate2. b) Capacitance = fixed for a capacitor. Can only change capacitance by changing properties of the capacitor - this means, changing Q or V does not change C (in C = Q/V), instead, manipulating Q would manipulate V such that the ratio stays the same (and vice versa) - however, if you were to create a new capacitor with any of the following below, this would increase the capacitance compared to the old capacitor= 1. Increase surface area of the plates (C = (Aε₀)/d) 2. Decrease distance between plates (C = (Aε₀)/d) 3. Add a dielectric (C = (kAε₀)/d) c) pic
Define and give examples of a) conductor b) insulator
a) a material that allows charge to move (note that all the charge will be on the conductors surface, not the inside. inside has no electric field) - eg copper, any metal, dirty water b) a material that does not allow charge to move, rather it holds the charge in place (note that there can be a charge/electric field inside an insulator, eg with a dielectric b/w 2 capacitor plates) - eg glass, rubber, pure water
a) what is a dielectric? b) What is the dielectric constant, k (in capacitors) c) how does the capacitance formula for a parallel plate capacitor change if you add a dielectric? d) give the value of the dielectric constant, k for a vacuum, and for air
a) an insulator that you place in the empty space between the positive and negative plates in a parallel capacitor (aka now the dielectric fills the space) - the insulator works to amplify the capacitance of the capacitor b) A constant based on the material of the dielectric - note, this is not coulombs constant! Dont confuse the 2, they both have the letter k c) The capacitance is amplified by the amount of the dielectric constant (which is typically greater than 1) - old formula was C = (Aε₀)/d - with a dielectric, the formula is C = (kAε₀)/d d) both have a value of 1. All other substances will be greater than 1
a) gravitation force is _________ (attractive, repulsive, either) b) electric force is ________ (attractive, repulsive, either)
a) attractive b) either
a) how does resistance increase? b) how does capacitance increase?
a) by increasing the length of the wire b) by increasing the cross sectional area
a) describe charging by induction b) describe grounding
a) if a charged object is brought close to (but not touching) a neutral conductor, the charges in the neutral conductor (which has equal amounts of +ve and -ve charge) are induced to move (opposites attract and likes repel) b) if a conductor is touching the ground/touching another conductor touching the ground), then if you charge by induction like in a) the repelled charges in the neutral conductor get to run away to the ground and youre left with a charged conductor (if you remove the original charged object, then the repelled charges in the ground will come back up bc theyre not repelled anymore) NOTE - the earth is like an unlimited store of positive charge. So like lightning, the clouds are -vely charged and the ground is +vely charged. Thus, the lightning CURRENT goes from the ground up to the clouds (ie flow of +ve charge), but the ELECTRICITY goes from the clouds to the ground
a) Give the formula to calculate the dielectric constant based on permittivity parameters b) what is permittivity c) what is permeability
a) k = ε/ε₀ - k = dielectric constant - ε = permittivity of a material - ε₀ = permittivity of free space (vacuum) b) The resistance encountered when forming an electric field in a medium - can think of it like the ability of a material to transmit (or 'permit') the formation of an electric field c) the ability of the material to allow the magnetic lines of force to pass through it (ie how permeable the material is in letting lines of force thru it) - used in the equation B = 𝜇₀I/2πr where 𝜇₀ is the permeability of free space (vacuum)
State the direction for the lines of force for a) electric fields b) gravitational fields c) magnetic fields d) what does the distance between the lines represent
a) positive charge to negative charge b) towards the mass creating the field c) outside the magnet, the magnetic field lines go from the north pole to the south pole. Inside the magnet, the magnetic field lines go from south pole to north pole d) the strength of the field. the closer the lines, the stronger the field NOTE - notice that both mass and charge can create fields! - electric field is created by charge - gravitational field is created by mass - magnetic field is created by charge
a) What is a capacitor? b) give the 2 formulas for capacitance of a parallel plate capacitor (with no dielectric)
a) something that temporarily stores energy in a circuit, in the form of separated charge (generating an electric field between the separated charges) - eg = the paddles in a defibrillator (they are separated by a distance, and store charge this way. one paddle will have a +ve charge, and the other has a -ve charge. When you place them both on someones chest, you connect the whole circuit and so current flows (hopefully through the heart) b) 1. C = Q/V C = capacitance (F) Q = charge (C) on the plate -note that since capacitors have 2 plates where positive charge is built up on one, and -ve charge is on the other, Q represents the charge on one of the plates. The other plate will have the exact same magnitude of charge, but in the opposite sign. So dont add up the charges of both plates to give you Q, Q just refers to the charges on ONE of the plates but the charge on the other plate would be the exactly the same just diff sign V = voltage (V) 2. C = (Aε₀)/d - C = capacitance (F) - A = total plate area of both plates (m²) - ε₀ = permittivity of free space (vacuum) - d = distance between the plates (m)
a) Give the general formula for electric potential (also called potential difference, or voltage) a) Give the formula for electric potential due to a constant (aka uniform) electric field b) give the formula for electric potential due to a single charge
a) ∆V = U/q ∆V = electric potential, a scalar (V) U = electric potential energy (J) q = charge (C) a) ∆V = Ed ∆V = electric potential, a scalar (V) E = magnitude of uniform electric field (V/m or N/C) d = distance between charges or points (m) NOTE - distance must be measured parallel to the electric field direction and just like the formula U = qEy, the +ve y direction MUST be in the opposite direction of the field direction, and the -ve y direction must be in the same direction as the field b) ∆V = kq/r ∆V = electric potential, a scalar (V) k = Coulomb's constant, 9 x 10^9 (N x m^2/C^2) q = charge (C) r = distance (m)
what does it mean if something is polarized?
when something has a direction to it
