Circuits and Electricity AP Physics
The Law of Conservation of Charge
If a certain amount of positive charge appears somewhere, an equal amount of negative charge must appear elsewhere so that the net charge doesn't change
Coulomb's Law
If two charged particles having charges q and q2 are a distance r apart, the particles exert force on each other of magnitude F10n2 = F2on1 = k|q1||q2|/(r^2) The forces are directed along the line joining the two particles, and the forces are repulsive for 2 like charges and attractive for 2 opposite charges
Kirchoff's Loop Law
If we add all of the potential differences around the loop formed by the circuit, the sum must be zero Can only be true if at least one of the potential differences ∆Vi is negative
Ohm's Law
Relationship between the potential difference across a conductor and the current passing through it that was deduced by George Ohm I = ∆V/R Limited to materials whose resistance R remains constant
Resistors
Represents a given amount of resistance in a circuit The measure of how the flow of electric current is opposed Examples include heating elements, circuit elements, sensor elements, etc.
Ideal Wire
Rwire = 0 ohms The potential difference ∆V between the ends of a connecting wire is zero, even if there is a current in it
Fundamental Charge
Symbolized by e, it is the magnitude of the charge of an electron or a proton; measured at e = 1.6 x 10^-19 C
Resistivity
Symbolized by p Characterizes the electrical properties of materials Materials that are good conductors have low resistivities and vice versa
Kirchoff's Junction Law
At any junction point, the sum of all the currents entering the junction must equal the sum of all currents leaving the junction
Equivalent Resistance
A different way of indicating "total" resistance In a series circuit, the different components are connected in a single, continuous loop
Circuit Diagram
A logical picture of what is connected to what in a circuit The actual circuit looks very different when built but will have the same logic connections
Resistance
A measure of how hard it is to push through a wire Symbolized by R A large resistance implies that it is hard to move charges through the wire, and vice versa
When two resistors, having resistance R1 and R2 are connected in parallel, the equivalent resistance of the combination is 5 ohms. Which of the following statements about the resistance is correct? A) Both R1 and R2 are greater than 5 ohms B) Both R1 and R2 are equal to 5 ohms C) Both R1 and R2 are less than 5 ohms D) One of the resistances is greater than 5 ohms and one of the resistances is less than 5 ohms
A) The equivalent resistance in parallel is smaller than the smallest resistance.
In the circuit shown above, what is the value of the potential difference between points X and Y if the 6-volt battery has no internal resistance? A) 2V B) 3V C) 4V D) 6V
A) The total resistance of the 3 and 6 in parallel is 2 making the total circuit resistance 6 and the total current E/R = 1 A. This 1 A will divide in the ratio of 2:1 through the 3 and 6 respectively so the 3 resistor receives 2/3 A making the potential difference IR = (2/3 A)(3 ) = 2 V.
Two conducting cylindrical wires are made out of the same material. Wire X has twice the length and twice the diameter of wire Y. What is the ratio Rx/Ry of their resistances? A) 1/2 B) 1 C) 2 D) 4
A) . R = L/A L/d2 where d is the diameter. Rx/Ry = Lx/dx 2 ÷ Ly/dy 2 = (2Ly)dy 2 /[Ly(2dy)
A lamp, a voltmeter V, an ammeter A, and a battery with zero internal resistance are connected as shown above. Connecting another lamp in parallel with the first lamp as shown by the dashed lines would: A) Increase the ammeter reading B) Decrease the ammeter reading C) Increase the voltmeter reading D) Decrease the voltmeter reading
A) Adding resistors in parallel decreases the total circuit resistance, this increasing the total current in the circuit.
A circuit is connected as shown. All light bulbs are identical. When the switch in the circuit is closed illuminating bulb #4, which of the other bulb(s) become brighter? A) Bulb 1 only B) Bulb 2 only C) Bulbs 2 and 3 D) Bulbs 1, 2, and 3
A) Closing the switch reduces the total resistance of the circuit, increasing the current in the main branch containing bulb 1
The batteries in each of the circuits shown above are identical and the wires have negligible resistance. In which circuit is the current furnished by the battery the greatest? A) A B) B C) C D) D
A) Current is greatest where resistance is least. The resistances are, in order, 1 , 2 , 4 , 2 and 6
How do the currents I1, I2, and I3 compare in the circuit diagram shown above? A) I1 > I2 > I3 B) I1 > I3 > I2 C) I2 > I1 > I2 D) I3 > I1 > I2
A) I1 is the main branch current and is the largest. It will split into I2 and I3and since I2 moves through the smaller resistor, it will be larger than I3.
The above circuit diagram shows a battery with an internal resistance of 4.0 ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes. What power is dissipated by the 4-ohm internal resistance of the battery? A) 0.36 W B) 1.2 W C) 3.2 W D) 3.6 W
A) P = I^2r
A variable resistor is connected across a constant voltage source. Which of the following graphs represents the power P dissipated by the resistor as a function of its resistance R? A) Downward Quadratic B) Straight Line Downward C) Upward Quadratic D) Logarithmic
A) P = V2 /R and if V is constant P 1/R
The electrical resistance of the part of the circuit shown between point X and point Y is: A) 4/3 ohms B) 2 ohms C) 4 ohms D) 6 ohms
A) Resistance of the 1 and 3 in series = 4 . This, in parallel with the 2 resistor gives (2 × 4) /(2 + 4) = 8/6 . Also notice the equivalent resistance must be less than 2 (the 2 resistor is in parallel and the total resistance in parallel is smaller than the smallest resistor) and there is only one choice smaller than 2 .
The total equivalent resistance between points X and Y in the circuit shown above is: A) 3 Ohms B) 4 Ohms C) 5 Ohms D) 6 Ohms
A) The resistance of the two 2 resistors in parallel is 1. Added to the 2 resistor in series with the pair gives 3
Two resistors, one with resistance R and the second with resistance 4R are placed in a circuit with a voltage V. If resistance R dissipated power P, what would be the power dissipated by the 4R resistance? A) 4P B) 2P C) 1/2P D) 1/4P
A) P = I2R and the current is the same through each resistor.
A 9-volt battery is connected to four resistors to form a simple circuit as shown below: What would be the potential at point B with respect to point D? A) +2 V B) +4 V D) +5 V D) +7 V
A) The 2 A will divide equally between the two branches with 1 A going through each branch. From B to D we have - (1 A)(2 ) = -2 V, with B at the higher potential
A 9-volt battery is connected to four resistors to form a simple circuit as shown below: What would be the current at point E in the circuit? A) 2 amp B) 4 amp C) 5 amp D) 7 amp
A) . ACD = 9 , ABD = 9 so the total resistance is 4.5 making the total current E/R = 2 A
Four positive point charges are arranged as shown in the accompanying diagram. The force between charges 1 and 3 is 6.0 N; the force between charges 2 and 3 is 5.0 N; and the force between charges 3 and 4 is 3.0 N. The magnitude of the total force on charge 3 is most nearly: A) 6.3 N B) 8.0 N C) 10.0 N D) 11 N E) 14 N
A) . Vector addition. Since all the charges are positive, the forces due to charges 2 and 4 point in opposite directions, making the magnitude of the net force along the x axis 2 N. Combine this with a net force along the y axis of 6 N using the Pythagorean theorem
Five identical lightbulbs, each with resistance of 10 ohms, are connected in a simple electrical circuit with a switch and a 10 volt battery as shown in the diagram below: Which bulb (or bulbs) could burn out without causing other bulbs in the circuit to also go out? A) only bulb D B) only bulbs C or D C) only bulb E D) only bulbs A or E
A) A and E failing in the main branch would cause the entire circuit to fail. B and C would affect each other.
A charge of +Q is located on the x-axis at x = -1 meter and a charge of -2Q is held at x = +1 meter, as shown in the diagram above. At what position on the x-axis will a test charge of +q experience a zero net electrostatic force? A) -(3 + sqrt(8)) m B) -1/3 m C) 1/3 m D) (3 + sqrt(8)) m
A) Any charge will experience a net force of zero where the electric field is zero. This must be where the fields from each charge point in opposite directions and also closer to the smaller charge, which is to the left of the +Q charge (the answer will be to the left of -1 m). Let the distances to the +Q and the -2Q charge be x and (X + 2), respectively. This gives E1 = E2 and kQ/x2 = k(2Q)/(x + 2)2 . Solve for x and add the extra 1 m to the origin.
A positive point charge exerts a force of magnitude F on a negative point charge placed a distance x away. If the distance between the two point charges is halved, what is the magnitude of the new force that the positive point charge exerts on the negative point charge? A) 4F B) 2F C) F/2 D) F/4
A) F 1/r2
The positive point charges repel each other with force 0.36 N when their separation in 1.5 m. What force do they exert on each other when their separation is 1.0 m? A) 0.81 N B) 0.36 N C) 0.24 N D) 0.16 N
A) F 1/r2
Two identical electrical point charges Q, separated by a distance d produce an electrical force of F on one another. If the distance is decreased to a distance of 0.40d, what is the strength of the resulting force? A) 6.3 F B) 2.5 F C) 0.40 F D) 0.16 F
A) F 1/r2 ; if r × 0.4 then F ÷ 0.42
Two point objects each carrying charge 10 Q are separated by a distance d. The force between them is F. If half the charge on one object is transferred to the other object while at the same time the distance between them is doubled, what is the new force between the two objects? A) 0.19 F B) ).25 F C) 4.0 F D) No change in F
A) F q1q2/r2 ; the original force F 100Q2 /d2 . The new charges are 15Q and 5Q making the new force F 75Q2 /(2d)2 = 19Q2
Suppose that an electron could orbit a proton in a circular orbit of constant radius R. Assuming that the proton is stationary and only electrostatic forces act on the particles, which of the following represents the kinetic energy of the two-particle system? A) (1/8•pi•e)•(e^2/R) B) - (1/8•pi•e)•(e^2/R) C) (1/4•pi•e)•(e^2/R^2) D) -(1/4•pi•e)•(e^2/R^2)
A) FE = FC and q1 = q2 = e so we have ke2 /R2 = mv2 /R and we multiply both sides by ½ R so the right side becomes ½ mv2 (the kinetic energy). Choices C and E could have been eliminated because they are negative, and kinetic energy cannot be negative. Choices A & D are dimensionally incorrect (D has the units of a force, not energy, and A has the units of electric potential)
An electroscope is given a positive charge, causing its foil leaves to separate. When an object is brought near the top plate of the electroscope, the foils separate even further. We could conclude: A) That the object is positively charged B) That the object is electrically neutral C) That the object is negatively charged D) Only that the object is charged
A) If the leaves are positive, further separation means they are becoming more positive, which implies electrons are leaving the leaves, attracted to the top plate of the electroscope. This will occur if the object is positively charged.
Wire Y is made of the same material but has twice the diameter and half the length of wire X. If wire X has a resistance of R then wire Y would have a resistance of: A) R/8 B) R C) 2R D) 8R
A) R L/A = L/d2 . If d × 2, R ÷ 4 and if L ÷ 2, R ÷ 2 making the net effect R ÷ 8
In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance. Closing which of the switches will produce the greatest voltage across R3? A) S1 only B) S2 only C) S1 and S2 only D) S1 and S3 only
A) S1 must be closed to have any current. The greatest voltage will occur with the greatest current through R3 but closing S2 or S3 will draw current away from R3.
An electric circuit consists of a 12 V battery, an ideal 10 A fuse, and three 2 ohm resistors connected as shown above. What would be the reading on a voltmeter connected across points A and C? A) 12 V B) 6 V C) 3 V D) 2 V
A) Starting at A and summing potential differences counterclockwise to point C gives 12 V
Given 4 identical resistors of resistance R, which of the following circuits would have an equivalent resistance of 4/3 R? A) Three in parallel and one in series B) Two in series which are in parallel with two other resistors C) Two in series and two in series are both in parallel with each other D) Two in series are in parallel with one, all of which are in series with one resistor
A) The resistances are, respectively, 4/3 R, 2/5 R, R, and 5/3 R
An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. With the switch open, what would be the potential difference across the 15 ohm resistor? A) 30 V B) 60 V C) 70 V D) 110 V
A) V = IR
Multiple correct: Forces between two objects which are inversely proportional to the square of the distance between the objects include which of the following? Select two answers: A) Gravitational force between two celestial bodies B) Electrostatic force between two electrons C) Nuclear force between two neutrons D) Magnetic force between two magnets
A, B) Fg = Gm1m2/r2 and FE = kq1q2/r2 . The nuclear force does not have a similar relationship
Consider the compound circuit shown above. The three bulbs 1, 2, and 3 - represented as resistors in the diagram - are identical. Which of the following statements are true? Select two correct answers: A) Bulb 3 is brighter than bulb 1 or 2 B) Bulb 3 has more current passing through it than bulb 1 or 2 C) Bulb 3 has the same voltage drop across it than bulb 1 D) Bulb 2 has the same voltage drop across it than bulb 2
A, B) The current through bulb 3 is twice the current through 1 and 2 since the branch with bulb 3 is half the resistance of the upper branch. The potential difference is the same across each branch, but bulbs 1 and 2 must divide the potential difference between them.
Multiple Correct: Which two arrangements of resistors shown above have the same resistance between the terminals? Select two answers: I is a series circuit with two 1 ohm resistors II is a series circuit with two 2 ohm resistors III is a parallel circuit with two 2 ohm resistors IV is a parallel circuit with two 4 ohm resistors A) I B) II C) III D) IV
A, D) The resistances are as follows: I: 2, II: 4, III: 1, IV: 2
The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which is the greatest resistance? A) Wire with length l and current A B) Wire with length 2l and current A C) Wire with length l and current 2A D) Wire with length 2l and one current 2A and one current A
B) R = L/A. Greatest resistance is the longest, narrowest resistor.
A wire of length L and radius r has a resistance R. What is the resistance of a second wire made from the same material that has a length L/2 and a radius r/2? A) 4R B) 2R C) R D) R/4
B) . R = L/A. If L ÷ 2, R ÷ 2 and is r ÷ 2 then A ÷ 4 and R × 4 making the net effect R ÷ 2 × 4
The circuit in the figure above contains two identical lightbulbs in series with a battery. At first both bulbs glow with equal brightness. When switch S is closed, which of the following occurs to the bulbs? BULB 1 BULB 2 A) Goes out Gets Brighter B) Gets brighter Goes out C) Gets brighter Gets slightly dimmer D) Gets slightly dimmer Gets brighter
B) Closing the switch reduces the resistance in the right side from 20 to 15 , making the total circuit resistance decrease from 35 to 30 , a slight decrease, causing a slight increase in current. For the current to double, the total resistance must be cut in half.
When the switch S is open in the circuit shown to the left, the reading on the ammeter A is 2.0 A. When the switch is closed, the reading on the ammeter is: A) Doubled B) Increased slightly but not doubled C) Decreased slightly but not halved D) Halved
B) Closing the switch reduces the resistance in the right side from 20 to 15 , making the total circuit resistance decrease from 35 to 30 , a slight decrease, causing a slight increase in current. For the current to double, the total resistance must be cut in half.
The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance. A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right. What is the emf of the battery/ A) 0.025 V B) 2.5 V C) 6.25 V D) 40 V
B) P = IE
Kirchoff's loop rule for circuit analysis is an expression of which of the following? A) Conservation of Charge B) Conservation of Energy C) Ampere's Law D) Ohm's law
B) The loop rule involves the potential and energy supplied by the battery and it's use around a circuit loop
An immersion heater of resistance R converts electrical energy into thermal energy that is transferred to the liquid in which the heater is immersed. If the current in the heater is I, the thermal energy transferred to the liquid in time t is: A) IRt B) I^2Rt C) IRt^2 D) IR/t
B) W = Pt = I2Rt
In the diagram above, resistors R1 and R2 are shown in two different connections to the same source of emf that has no internal resistance. How does the power dissipated by the resistors in these two cases compare? A) It is greater for the series connection B) It is greater for the parallel connection C) It is different for each connection, but one must know the values of R1 and R2 to know which is greater D) It is difficult for each connection, but one must know the value of emf to know which is greater
B) With more current drawn from the battery for the parallel connection, more power is dissipated in this connection. While the resistors in series share the voltage of the battery, the resistors in parallel have the full potential difference of the battery across them.
A positively charged object is brought near but not in contact with the top of an uncharged gold leaf electroscope. The experimenter then briefly touches the electroscope with a finger. The finger is removed, followed by the removal of the positively charged object. What happens to the leaves of the electroscope when a negative charge is now brought near but not in contact with the top of the electroscope? A) They remain uncharged B) They move farther apart C) They ove closer together D) They remain negatively charged but unmoved
B) The process described is charging by induction which gives the electroscope in this case a net negative charge. Bringing a negative charge near the top of the electroscope will cause electrons to repel to the leaves. Since the leaves are already negative, this will cause them to separate further.
In the electric circuit shown above, the current through the 2.0 ohm resistor is 3.0 amps. Approximately what is the emf of the battery? A) 51 V B) 42 V C) 36 V D) 24 V
B) . Using ratios, the currents in the 6 and 3 resistors are 1 A and 2 A. They have three times and 3/2 times the resistance of the 2 resistor so they will have 1/3 and 2/3 the current. The total current is then 6 A giving a potential drop of 36 V across the 6 resistor in the main branch and adding any one of the branches below with the loop rule gives 36 V + 6 V = 42 V for the battery
A circular ring made of an insulating material is cut in half. One half is given a charge -q uniformly distributed along its arc. The other half is given a charge +q also uniformly distributed along its arc. The two halves are then rejoined with insulation at the junctions J, as shown above. If there is no change in the charge then rejoined with insulation at the junction J, as shown above. If there is no change in the charge distributions, what is the direction of the net electrostatic force on an electron located at the center of the circle? A) Toward the top of the page B) Toward the bottom of the page C) To the right D) To the left
B) By symmetry, the force on an electron at the center from the top half will be straight down and the force from the bottom half will also be straight down
B1, B2, B3, and B4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. All voltmeters are connected so that they display positive voltages. Assume that the voltmeters do not affect the circuit. If B2 were to burn out, opening the circuit, which voltmeter(s) would read zero volts? A) None would read zero B) Only V2 C) Only V3 and V4 D) Only V2, V4, and V5
B) Even though B2 burns out, the circuit is still operating elsewhere as there are still closed paths.
A student wants to make a brighter light bulb. He decides to modify the filament. How should the filament of a light bulb be modified in order to make the light bulb produce more light at a given voltage? A) Increase the resistivity only B) Increase the diameter only C) Decrease the diameter only D) The length only
B) For more light at a given voltage, more current is required, which requires less resistance. R = L/A
Consider a simple circuit containing a battery and three light bulbs. Bulb A is wired in parallel with bulb B and this combination is wired in series with bulb C. What would happen to the brightness of the other two bulbs if bulb A were to burn out? A) Both would get brighter B) Bulb B would get brighter and bulb C would get dimmer C) Bulb B would get dimmer and bulb C would get brighter D) Only bulb B would get brighter
B) If A were to burn out, the total resistance of the parallel part of the circuit increases, causing less current from the battery and less current through bulb A. However, A and B split the voltage from the battery in a loop and with less current through bulb A, A will have a smaller share of voltage, increasing the potential difference (and the current) through bulb B.
Three resistors - R1, R2, and R3 - are connected in series to a battery. Suppose R1 carries a current of 2.0 A, R2 has a resistance of 3 ohms, and R3 dissipates 6.0 W of power. What is the voltage across R3? A) 1.0 V B) 3.0 V C) 6.0 V D) 12 V
B) In series, they all have the same current, 2 A. P3 = I3V3
Two isolated charges, +q and -2q, are 2 centimeters apart. If F is the magnitude of the force acting on charge -2Q, what are the magnitude and direction of the force acting on the charge +q? MAGNITUDE DIRECTION A) 2F Away from charge -2q B) F Toward charge -2q C) F Away from charge -2q D) 2F Toward charge -2q
B) Newton's third law
An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. How much current flows through a 4 ohm resistor that is dissipating 36 watts of power? A) 2.25 amps B) 3.0 amps C) 4.24 amps D) 9.0 amps
B) P = I^2R
A fixed voltage is applied across the length of a tungsten wire. An increase in the power dissipated by the wire would result if which of the following could be increased? A) The resistivity of the tungsten B) The cross-sectional area of the wire C) The length of the wire D) The temperature of the wire
B) P = V2 /R and R = L/A giving P = V2A/L
Five identical lightbulbs, each with resistance of 10 ohms, are connected in a simple electrical circuit with a switch and a 10 volt battery as shown in the diagram below: The steady current in the above circuit would be closest to which of the following values? A) 0.2 amp B) 0.37 amp C) 0.5 amp D) 2.0 amp
B) Resistance of bulbs B & C = 20 combined with D in parallel gives 6.7 for the right side. Combined with A & E in series gives a total resistance of 26.7 . E = IR
A point charge +q is placed midway between two point charges +3q and -q separated by a distance 2d. If Coulomb's constant is k, the magnitude of the force on the charge +q is: A) 2•(kq^2/d^2) B) 4•(kq^2/d^2) C) 6•(kq^2/d^2) D) 9•(kq^2/d^2)
B) The distance between the +q charge and each charge is d. The force on the +q charge from each charge is in the same direction, making the net force kq2 /d2 + k(3q2)/d2
A charged rod is placed between two insulated conducting spheres as shown. The spheres have no net charge. Region II has the same polarity as Region: A) I only B) III only C) IV only D) I and IV only
B) The rod will attract the same charge from each sphere to the side closer to the rod.
Which of the following wiring diagrams could be used to experimentally determine R using Ohm's Law? Assume an ideal voltmeter and an ideal ammeter. A) V and A in series B) V and A in series on separate resistors C) V and P in parallel D) V and P in series on only one circuit
B) Voltmeters must be placed in parallel and ammeters must be placed in series.
In the circuit above the voltmeter V draws negligible current and the internal resistance of the battery is 1.0 ohms. The reading of the voltmeter is: A) 10.5 V B) 10.8 V C) 11.6 V D) 12.0 V
B) With a total resistance of 10 , the total current is 1.2 A. The terminal voltage VT = E - Ir
Multiple Correct: A positively charged conductor attracts a second object. Which of the following statements could be true? Select two answers: A) The second object is a conductor with positive net charge B) The second object is a conductor with zero net charge C) The second object is an insulator with zero net charge D) The second object is an insulator with positive net charge
B, C) Charged objects attract object with an opposite charge, but also neutral objects by separation of charges.
What is the current I1 in the circuit diagram shown above? A) 1.0 mA B) 2.0 mA C) 3.0 mA D) 6.0 mA
C) Resistance of the 2000 and 6000 in parallel = 1500 , adding the 2500 in series gives a total circuit resistance of 4000 . Itotal = I1 =
In the circuit shown above, the equivalent resistance of the three resistors is: A) 15 ohms B) 20 ohms C) 50 ohms D) 115 ohms
C) The equivalent resistance of the 20 and the 60 in parallel is 15 , added to the 35 resistor in series gives 15 + 35 = 50
Two concentric circular loops of radii b and 2b, made of the same type of wire, lie in the plane of the page, as shown above. The total resistance of the wire loop of radius b is R. What is the resistance of the wire loop of radius 2b? A) R/4 B) R/2 C) 2R D) 4R
C) . The larger loop, with twice the radius, has twice the circumference (length) and R = L/A
Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above: Rank the current through the bulbs: A) L = M > K = N B) L > M > K > N C) N > K > L = M D) N > L = M > K
C) N is in the main branch, with the most current. The current then divides into the two branches, with K receiving twice the current as L and M. The L/M branch has twice the resistance of the K branch. L and M in series have the same current.
The power dissipated in a wire carrying a constant electric current I may be written as a function of the length l of the wire, the diameter d of the wire, and the resistivity p of the material in the wire. In this expression, the power dissipated is directly proportional to which of the following? A) I only B) d only C) I and p only D) d and p only
C) P = I2R and R = L/A giving P L/d2
A hair dryer is rated at 1200 W, 120 V. Its effective internal resistance is: A) 0.1 ohms B) 10 ohms C) 12 ohms D) 120 ohms
C) P = V2 /R
The five resistors shown below have the lengths and cross-sectional areas indicated and are made of material with the same resistivity. Which resistor has the least resistance? A) Wire of length l and current A B) Wire of length l and one current 2A and one current A C) Wire of length l and current 2A Wire of length 2l and one current 2A and one current A
C) R = L/A. Least resistance is the widest, shortest resistor
Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above: In order of decreasing brightness (starting with the brightest), the bulbs are: A) L = M > K = N B) L > M > K > N C) N > K > L = M D) N > L = M > K
C) See above. Current is related to brightness (P = I2R)
A 9 volt battery is connected to four resistors to form a simple circuit as shown above: What would be the potential at point B with respect to point C in the above circuit? A) +7 V B) +3 V C) -3 V D) -7 V
C) The resistance in each of the two paths is 9 , making the current in each branch 1 A. From point A, the potential drop across the 7 resistor is then 7 V and across the 4 resistor is 4 V, making point B 3 V lower than point C
A 30-ohm resistor and a 60-ohm resistor are connected as shown above to a battery of emf 20 volts and internal resistance r. The current in the circuit is 0.8 ampere. What is the value of r? A) 0.22 ohms B) 4.5 ohms C) 5 ohms D) 16 ohms
C) Total resistance = E/I = 25 . Resistance of the 30 and 60 resistors in parallel = 20 adding the internal resistance in series with the external circuit gives Rtotal = 20 + r = 25
Given the simple electrical circuit above, if the current in all three resistors is equal, which of the following statements must be true? A) X, Y, and Z all have equal resistance B) X and Y have equal resistance C) X and Y added together have the same resistance as Z D) X and Y each have more resistance than Z
C) For the currents in the branches to be equal, each branch must have the same resistance.
A cylindrical graphite resistor has length L and cross-sectional area A. It is to be placed into a circuit, but it first must be cut in half so that the new length is 1/2L. What is the ratio of the new resistivity to the old resistivity of the cylindrical resistor? A) 4 B) 2 C) 1 D) 1/2
C) Resistivity is dependent on the material. Not to be confused with resistance
An electric circuit consists of a 12 V battery, an ideal 10 A fuse, and three 2 ohm resistors connected as shown above. What would be the reading on an ammeter inserted at point B? A) 9 A B) 6 A C) 3 A D) 2 A
C) The branch with two 2 resistors has a total resistance of 4 and a potential difference of 12 V. V = IR
Two initially uncharged conductors, 1 and 2, are mounted on insulating stands and are in contact, as shown above. A negatively charged rod is brought near but does not touch them. With the rod held in place, conductor 2 is moved to the right by pushing its stand, so that the conductors are separated. Which of the following is now true of conductor 2? A) It is uncharged B) It is positively charged C) It is negatively charged D) It is charged, but its sign cannot be predicted
C) While spheres 1 and 2 are in contact, electrons will repel away from the rod out of sphere 1 into sphere 2.
Three metal spheres A, B, and C are mounted on insulating stands. The spheres are touching one another, as shown in the diagram below. A strong positively charged object is brought near sphere A and a strong negative charge is brought near sphere C. While the charged objects remain near spheres A and C, sphere B is removed by means of its insulating stand. After the charged objects are removed, sphere B is first touched to sphere A and then to sphere C. The resulting charge on B would be of what relative amount and sign? A) The same sign but 1/2 the magnitude as originally on sphere A B) The opposite sign but 1/2 the magnitude as originally on sphere A C) The opposite sign but 1/4 the magnitude as originally on sphere A D) The same sign but 1/2 the magnitude as originally on sphere C
C) . Initially, when B is removed, A and C are equally and oppositely charged and B is neutral. Touching B to A gives B ½ the charge of A (split equally). The charge on B is then ½ that of C and oppositely charged. When B and C touch, the total charge between them is ½ the charge of C and the same sign as C. Each sphere then has ¼ of the charge of C after contact is made. This makes the end result that the charge on sphere B is ¼ the original charge of A and the same sign as sphere C, which is opposite that of A
In the circuit diagram to the left, all of the bulbs are identical. Which bulb will be the brightest? A) A B) B C) C D) D
C) Bulb C in the main branch receiving the total current will be the brightest
The three lightbulbs in the circuit above are identical, and the battery has zero internal resistance. When switch S is closed to cause bulb 1 to light, which of the other two bulbs increase(s) in brightness? A) Neither bulb B) Bulb 2 only C) Bulb 3 only D) Both bulbs
C) Closing the switch adds another parallel branch, increasing the total current delivered by the battery. Bulb 3 will get brighter. Bulb 2, in its own loop with bulb 3 and the battery will then lose some of its share of the potential difference from the battery and will get dimmer.
An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. With the switch open, what must be the voltage supplied by the battery? A) 30 V B) 60 V C) 70 V D) 110 V
C) E = IRtotal where Rtotal = 35
Each member of a family of six owns a computer rated at 500 watts in a 120 V circuit. If all computers are plugged into a single circuit protected by a 20 ampere fuse, what is the maximum number of the computers can be operating at the same time? A) 2 B) 3 C) 4 D) 5 or more
C) Each computer draws I = P/V = 4.17 A. 4 computers will draw 16.7 A, while 5 will draw over 20 A.
Three different resistors, R1, R2, and R3 are connected in parallel to a battery. Suppose R1 has 2 V across it, R2 = 4 ohms, and R3 dissipates 6 W. What is the current in R3? A) 0.5 A B) 2 A C) 3 A D) 12 A
C) In parallel, all the resistors have the same voltage (2 V). P3 = I3V3
A person rubs a neutral comb through their hair and the comb becomes negatively charged. Which of the following is the best explanation for this phenomenon? A) The hair gains protons from the comb B) The hair gains protons from the comb while giving electrons to the comb C) The hair loses electrons to the comb D) The comb loses protons to the person's hand while also gaining electrons from the hair
C) Only electrons are transferred in static charging processes.
Wire I and wire Ii are made of the same material. Wire II has twice the diameter and twice the length of wire I. If wire I has resistance R, wire II has resistance: A) R/8 B) R/4 C) R/2 D) R
C) R = L/A L/d2 where d is the diameter. RII/RI = LII/dII2 ÷ LI/dI2 = (2LI)dI2 /[LI(2dI) 2] = ½
In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance. Closing which of the switches will produce the greatest power dissipation in R2? A) S1 only B) S2 only C) S1 and S2 only D) S1 and S3 only
C) S1 must be closed to have any current. Closing S2 will allow current in R2 but closing R3 would short circuit R2.
For the circuit shown, a shorting wire of negligible resistance is added to the circuit between points A and B. When this shorting wire is aded, bulb 3 goes out. Which bulbs (all identical) in the circuit brighten? A) Only bulb 2 B) Only bulb 4 C) Only bulbs 1 and 4 D) Bulbs 1, 2, and 4
C) Shorting bulb 3 decreases the resistance in the right branch, increasing the current through bulb 4 and decreasing the total circuit resistance. This increases the total current in the main branch containing bulb 1.
For the circuit shown, when a shorting wire (no resistance) connects the point labeled A and B, which of the numbered light bulbs become brighter? Assume that all four bulbs are identical and have resistance R: A) Bulb 2 only B) Bulb 3 only C) Bulb 1 and 3 only D) Bulbs 1, 2, and 3
C) Shorting bulb 4 decreases the resistance in the right branch, increasing the current through bulb 3 and in the main branch containing bulb 1.
A battery, an ammeter, three resistors, and a switch are connected to form the simple circuit shown above. When the switch is closed what would happen to the potential difference across the 15 ohm resistor? A) It would equal the potential difference across the 20 ohm resistor B) It would be twice the potential difference across the 30 ohm resistor C) It would equal the potential difference across the 30 ohm resistor D) It would be half the potential difference across the 30 ohm resistor
C) The 15 resistor would be in parallel with the 30 resistor when the switch is closed.
If F is the magnitude of the force on the test charge due to only one of the other charges, what is the magnitude of the net force acting on the test charge due to both of these charges? A) F/sqrt(2) B) F C) sqrt(2)F D) 2
C) The two vectors, each of magnitude F, point at right angles to each other so the resultant field is √2F
Two 1000 ohm resistors are connected in series to a 120-volt electrical source. A voltmeter with a resistance of 1000 ohms is connected across the last resistor as shown. What would be the reading on the voltmeter? A) 80 V B) 60 V C) 40 V D) 30 V
C) The voltmeter is essentially another resistor. The voltmeter in parallel with the 100 resistor acts as a 500 resistor, which will half ½ the voltage of the 100 resistor on the left. Thus the 120 V will split into 80 V for the 1000 resistor and 40 V for the voltmeter combination.
Two metal spheres that are initially uncharged are mounted on insulating stands, as shown above. A negatively charged rubber rod is brought close to, but does not make contact with, Sphere X. Sphere Y is then brought close to X on the side opposite to the rubber rod. Y is allowed to touch X and then is removed some distance away. The rubber rod is then moved far away from X and Y. What are the final charges on the spheres? SPHERE X SPHERE Y A) Negative Negative B) Negative Positive C) Positive Negative D) Positive Positive
C) While spheres X and Y are in contact, electrons will repel away from the rod out of sphere X into sphere Y.
For the circuit shown, the ammeter reading is initially I. The switch in the circuit then is closed. Consequently: A) The ammeter reading decreases B) The potential difference between E and F increases C) The potential difference between E and F stays the same D) Bulb #3 lights up more brightly
C) Wire CD shorts out bulb #3 so it will never light. Closing the switch merely adds bulb #2 in parallel to bulb #1, which does not change the potential difference across bulb #1.
B1, B2, B3, and B4 are identical light bulbs. There are six voltmeters connected to the circuit as shown. All voltmeters are connected so that they display positive voltages. Assume that the voltmeters do not affect the circuit. If B2 were to burn out, opening the circuit, what would happen to the reading V1? Let V be its original reading when all bulbs are functioning and let V be the reading when B2 is burnt out. A) V > 2V B) 2V > V > V C) V > V > V/2 D) V/2 > V
C) With B2 burning out, the total resistance of the circuit increases as it is now a series circuit. This decreases the current in the main branch, decreasing V1. For V1 to be halved, the current must be halved which means the total resistance must be doubled, which by inspection did not happen in this case (total before = 5/3 R, total after = 3 R)
An ideal battery, an ideal ammeter, a switch and three resistors are connected as shown. With the switch open as shown in the diagram the ammeter reads 2.0 amperes. When the switch is closed, what would be the current in the circuit? A) 1.1 A B) 2.0 A C) 2.3 A D) 3.0 A
C) With the switch closed, the resistance of the 15 and the 30 in parallel is 10 , making the total circuit resistance 30 and E = IR
The batteries in each of the circuits shown above are identical and the wires have negligible resistance. In which circuit is the equivalent resistance connected to the battery the greatest? A) A B) B C) C D) D
D)
If the ammeter in the circuit above reads zero, what is the resistance R? A) 1.5 ohms B) 4 ohms C) 5 ohms D) 6 ohms
D) For the ammeter to read zero means the junctions at the ends of the ammeter have the same potential. For this to be true, the potential drops across the 1 and the 2 resistor must be equal, which means the current through the 1 resistor must be twice that of the 2 resistor. This means the resistance of the upper branch (1 and 3 ) must be ½ that of the lower branch (2 and R) giving 1 + 3 = ½ (2
A cylindrical resistor has length L and radius r. This piece of material is then drawn so that it is a cylinder with new length 2L. What happens to the resistance of this material because of this process? A) The resistance is quartered B) The resistance is halved C) The resistance is doubled D) The resistance is quadrupled
D) Since the volume of material drawn into a new shape in unchanged, when the length is doubled, the area is halved. R = L/A
The operating efficiency of a 0.5 A, 120 V electric motor that lifts a 9 kg mass against gravity at an average velocity of 0.5 m/s is most nearly: A) 13% B) 25% C) 53% D) 75%
D) The motor uses P = IV = 60 W of power but only delivers P = Fv = mgv = 45 W of power. The efficiency is "what you get" ÷ "what you are paying for" = 45/60
When there is a steady current in the circuit, the amount of charge passing a point per unit of time is: A) The same everywhere in the circuit B) Greater in the 1 ohm resistor than the 2 ohm resistor C) Greater at point X than at point Y D) Greater in the 2 ohm resistor than in the 3 ohm resistor
D) The upper branch, with twice the resistance of the lower branch, will have ½ the current of the lower branch.
A narrow beam of protons produces a current of 1.6 x 10^-3 A. There are 10^9 protons in each meter along the beam. Of the following, which is the best estimate of the average speed speed of the proton in the beam? A) 10^-15 m/s B) 10^-12 m/s C) 10^-7 m/s D) 10^7 m/s
D) Dimensional analysis: 1.6 × 10-3 A = 1.6 × 10-3 C/s ÷ 1.6 × 10-19 C/proton = 1016 protons/sec ÷ 109 protons/meter = 107 m/s
Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above: Bulb K burns out. Which of the following statements is true? A) All the light bulbs go out B) Bulb N becomes brighter C) The brightness of bulb N remains the same D) Bulb N becomes dimmer but does not go out
D) If K burns out, the circuit becomes a series circuit with the three resistors, N, M and L all in series, reducing the current through bulb N.
Four identical light bulbs K, L, M, and N are connected in the electrical circuit shown above: Bulb M burns out. Which of the following statements is true? A) All of the light bulbs go out B) Bulb N goes out but at least one other bulb remains lit C) The brightness of bulb N remains the same D) Bulb N becomes dimmer but does not go out
D) If M burns out, the circuit becomes a series circuit with the two resistors, N and K in series, with bulb L going out as well since it is in series with bulb M.
The batteries in each of the circuits shown above are identical and the wires have negligible resistance. Which circuit dissipates the least power? A) A B) B C) C D) D
D) Least power is for the greatest resistance (P = E 2
A wire of resistance R dissipates power P when a current I passes through it. The wire is replaced by another wire with resistance 3R. The power dissipated by the new wire when the same current passes through it is: A) P/9 B) P/3 C) 3P D) 6P
D) P = I2R
When lighted, a 100-watt light bulb operating on a 110-volt household circuit has a resistance closes to: A) 10^-2 ohms B) 10^-1 ohms C) 10 ohms D) 100 ohms
D) P = V2 /R
In the circuit shown above, the value of r for which the current I is 0.5 ampere is: A) 1 Ohm B) 5 Ohm C) 10 Ohm D) 20 Ohm
D) The resistance of the two resistors in parallel is r/2. The total circuit resistance is then 10 + ½ r, which is equivalent to E/I = (10 V)/(0.5 A) = 20 = 10
Which of the following combinations of 4 ohms resistors would dissipate 24 W when connected to a 12 V battery? A) A series circuit with two resistors B) Parallel circuit with three resistors on their own wires C) Parallel circuit with three resistors on two wires D) Parallel circuit with two resistors and series circuit with one resistor
D) To dissipate 24 W means R = V2 /P = 6 . The resistances, in order, are: 8 , 4/3 , 8/3 , 12 and 6
The above circuit diagram shows a battery with an internal resistance of 4.0 ohms connected to a 16-ohm and a 20-ohm resistor in series. The current in the 20-ohm resistor is 0.3 amperes. What is the emf of the battery? A) 1.2 V B) 6.0 V C) 10.8 V D) 12.0 V
D) Total circuit resistance (including internal resistance) = 40 ; total current = 0.3 A. E = IR
Two uniformly charged non-conducting spheres on insulating bases are placed on an air table. Sphere A has a charge +3Q coulombs and sphere B has a charge +Q coulombs. Which of the following correctly illustrates the magnitude and direction of the electrostatic forces between the spheres when they are released? A) A and B to the right B) A (smaller) to left B (longer) to right C) A and B to the left D) A (equal) to left B (equal) to right
D) Newton's third law requires the forces be equal and opposite. This eliminates choices A, B and C. Since they both positive, the force is repulsive.
When a single resistor is connected to a battery, a total power P is dissipated in the current. How much total power is dissipated in a circuit if n identical resistors are connected in series using the same battery? Assume the internal resistance of the battery is zero: A) n^2P B) nP C) P D) P/n
D) P = E 2 /R. Total resistance of n resistors in series is nR making the power P = E 2 /nR = P/n
Two identical conducting spheres are charged to +2Q and -Q respectively, and are separated by a distance d (much greater than the radii of the spheres) as shown above. The magnitude of the force of attraction on the left sphere is F1. After the two spheres are made to touch and then are re-separated by distance d, the magnitude of the force on the left sphere are made to touch and then are re-separated by distance d, the magnitude of the force on the left sphere is F2. Which of the following relationships is correct? A) 2F1 = F2 B) F1 = F2 C) F1 = 2F2 D) F1 = 8F2
D) The net charge on the two spheres is +Q so when they touch and separate, the charge on each sphere (divided equally) is ½ Q. F Q1Q2 so before contact F (2Q)(Q) = 2Q2 and after contact F (½ Q)(½ Q) = ¼ Q2 or 1/8 of the original force
When two charged point-like objects are separated by a distance R, the force between them is F. If the distance between them is quadrupled, the force between them is: A) 16 F B) 4 F C) F/4 D) F/16
D) . F 1/r2 ; if r × 4, F ÷ 16
Sphere X of mass M and charge +q hangs from a string as shown above. Sphere Y has an equal charge +q and is fixed in place a distance d directly below sphere X. If sphere X is in equilibrium, the tension in the string is most nearly: A) Mg B) Mg - kq/d C) Mg + kq^2/d^2 D) Mg - kq^2/d^2
D) . F = 0 so we have T + k(q)(q)/d2 - Mg = 0 giving T = Mg - kq2
Two identical spheres carry identical electric charges. If the spheres are set a distance d apart they repel one another with a force F. A third sphere, identical to the other two but initially uncharged is then touched to one sphere and then to the other before being removed. What would be the resulting force between the original two spheres? A) 3/4 F B) 5/8 F C) 1/2 F D) 3/8 F
D) Assuming C remains constant and UC = ½ CV2 , for UC to double V must increase by √2
A length of wire of resistance R is connected across a battery with zero internal resistance. The wire is then cut in half and the two halves are connected in parallel. When the combination is reconnected across the battery, what happens to the resultant power dissipated and the current drawn from the battery? POWER CURRENT A) Doubles Doubles B) Quadruples Doubles C) Doubles Quadruples D) Quadruples Quadruples
D) Before cutting the resistance is R. After cutting we have two wires of resistance ½ R which in parallel is an equivalent resistance of ¼ R. P = V2 /R and I = V/R
The diagram above represents a simple electrical circuit composed of 5 identical lightbulbs and 2 flashlight cells. Which bulb (or bulbs) would you expect to be the brightest? A) V only B) V and W only C) V and Z only D) V, W, and Z only
D) Bulbs in the main branch have the most current through them and are the brightest.
Two small spheres have equal charges q and are separated by a distance d. The force exerted on each sphere by the other has magnitude F. If the charge on each sphere is doubled and d is halved, the force on each sphere has magnitude: A) F B) 2F C) 8F D) 16F
D) FE q1q2/r2 ; if q1 and q2 × 2; F × 4 and if r ÷ 2, F × 4 making the net effect F × 4 × 4
Four resistors, R1, R2, R3 and R4, are connected in the circuit diagram above. When the switch is closed, current flows in the circuit. If no current flows through the ammeter when it is connected as shown, what would be the value of R3? A) (R1+R4)/(R1+R2)•(R3+R4) B) (R1+R2)•(R4)/(R2+R4) C) (R1+R2)/(R4) D) (R1)•(R4/R2)
D) For no current to flow, the potential drop across R1 must equal the potential drop across R2. For this to occur I1R1 = I2R2. Since the two branches also have the same potential difference as a whole (they are in parallel) we also have I1(R1 + R3) = I2(R2 + R4). Solve for R3
Two small hollow metal spheres hung on insulating threads attract one another as shown. It is known that a positively charged rod will attract ball A. Which of the statements can be correctly concluded about the charge on the balls? A) Ball A has a positively charge B) Ball B has a negative charge C) Ball A and Ball B have opposite charges D) Ball A is neutral
D) If a positive rod attracts ball A, it is either negative or neutral. For ball B to also attract ball A means ball B can be charged positive or negative (if ball A is neutral) or neutral (if ball A is positive)
When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown above, the leaves spring apart (1). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is: A) Positive in both I and III B) Negative in both I and III C) Positive in I, negative in III D) Negative in I, positive in III
D) In I, charge separation occurs (negative charges repel to the leaves). The whole process describes charging by induction, where the electrons leave the electroscope to ground (the finger) and once contact with ground is broken, the electroscope is left with a positive charge (III)
Suppose you are given a constant voltage source V and three resistors R1, R2, and R3 with R1 > R2 > R3. If you wish to heat water in a pail which of the following combinations of resistors will give the most rapid heating? A) Three resistors in a series circuit B) Req alone C) R1 and R2 parallel and R3 series D) All resistors in a parallel circuit
D) Most rapid heating requires the largest power dissipation. This occurs with the resistors in parallel.
The diagram below shows five identical resistors connected in a combination series and parallel circuit to a voltage source: Which resistor(s) have the greatest rate of energy dissipation? A) J only B) M only C) N only D) J and N only
D) P = I^2R
Two cables can be used to wire a circuit. Cable A has a lower resistivity, a larger diameter, and a different length than cable B. Which cable should be used to minimize heat loss if the same current is maintained in either cable? A) Cable A B) Cable B C) The heat loss is the same for both D) It cannot be determined without knowing the length of each cable
D) R = pL/A
If all of the resistors in the simple circuit to the left have the same resistance, which would dissipate the greatest power? A) resistor A B) resistor B C) resistor C D) resistor D
D) Resistor D is in a branch by itself while resistors A, B and C are in series, drawing less current than resistor D.
The diagram below shows five identical resistors connected in a combination series and parallel circuit to a voltage source: Through which resistor(s) would there be the greatest current? A) J only B) M only C) N only D) J and N only
D) Resistors J and N are in the main branch and therefore receive the largest current.
In the circuit above, the resistors all have the same resistance. The battery, wires, and ammeter have negligible resistance. A closed switch also has negligible resistance. Closing which of the switches will produce the greatest reading on the ammeter? A) S2 only B) S3 only C) S1 and S2 only D) S1 and S3 only
D) S1 must be closed to have any current. Closing S3 will short circuit R3, leaving only resistor R1, which is the lowest possible resistance.
A solid conducting sphere is given a positive charge Q. How is the charge Q distributed in or on the sphere? A) It is concentrated at the center of the sphere B) It is uniformly distributed throughout the sphere C) Its density increases radially outward from the center D) It is uniformly distributed on the surface of the sphere only
D) Since charge is free to move around on/in a conductor, excess charges will repel each other to the outer surface
In the circuit shown above, a constant current device is connected to some identical light bulbs. After the switch S in the circuit is closed, which statement is correct about the circuit? A) Bulb #2 becomes brighter B) Bulb #1 becomes dimmer C) All three bulbs become equally brighter D) The voltage between points C and D is decreased
D) Since there is constant current, bulb 1 remains unchanged and bulbs 2 and three must now split the current. With half the current through bulb 2, the potential difference between A and B is also halved.
A 9 volt battery is connected to four resistors to form a simple circuit as shown above: How would the current through the 2 ohm resistor compare to the current through the 4 ohm resistor? A) One-fourth as large B) Four times as large C) Twice as large D) Equally as large
D) The equivalent resistance through path ACD is equal to the equivalent resistance through path ABD, making the current through the two branches equal
As shown above, two particles, each of charge +Q, are fixed at opposite corners of a square that lies in the plane of the page. A positive test charge +q is placed at a third corner. What is the direction of the force on the test charge due to the two other charges? A) Pointing 45º to the right B) Pointing directly to the right C) Pointing down 45º to right D) Pointing down 45º to left
D) The force vectors from the two +Q charges point down and to the left (away from the charges) so the resultant force points down and left
Complete Circuit
Once a charge reaches the positive terminal, it is able to flow downhill through the wire as a current flow until it reaches the negative terminal The charge escalator then lifts the charge back to the positive terminal where it can loop all over again
Coulomb
The SI unit for charge; represented by the symbol q (or Q sometimes)
Grounded
The excess charge is balanced by the transfer of electrons between the charged object and a ground
Current
The flow of electrical charge carriers, usually electrons or electron-deficient atoms Flows from relatively positive points to relatively negative points
Insulators
The materials on or in which charges retain immobile; ex: glass and plastic
Conductors
The materials through or along which charge easily moves; ex: metallic materials
EMF
The potential difference established by a device, such as a battery, that can actively separate charge Symbolized by E with a unit of volts
Ionization
The process of removing an electron from the electron cloud of an atom
Power
The rate at which energy is transferred from the battery to the moving charges is: Pbattery = rate of energy transfer = ∆V/∆t = (∆q/∆t)E Power is defined as P = IE In units of W
Charge Polarization
The slight separation of the positive and negative charge in a neutral object when a charged object is brought near
Potential Difference
The work done when a coulomb of charge passes between the points Found through ∆V = Vb - Va = 0 Created by separating positive charge from negative charge
Series
When two bulbs are connected and are connected directly to each other with no junction in between
Parallel
When two bulbs are connected in a circuit but they are now connected at both ends