Deck 23: Circuits

Question 1

When two or more different capacitors are connected in series across a potential source, which of the following statements must be true? (There could be more than one correct choice.)

A) The total voltage across the combination is the algebraic sum of the voltages across the individual capacitors.
B) Each capacitor carries the same amount of charge.
C) The equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
D) The potential difference across each capacitor is the same.
E) The capacitor with the largest capacitance has the most charge.

Answer 1

A, B, C

Question 2

Three identical capacitors are connected in series across a potential source (battery). If a charge of Q flows into this combination of capacitors, how much charge does each capacitor carry?

A) 3Q
B) Q
C) Q/3
D) Q/9

Answer 2

B

Question 3

A 5-µF, a 7-µF, and an unknown capacitor C_X are connected in parallel between points a and b as shown in the figure. What do you know about the equivalent capacitance C_ab between a and b? (There could be more than one correct choice.)

A) C_ab > 12 µF
B) C_ab > C_X
C) 5 µF < C_ab < 12 µF
D) C_ab < 5 µF
E) C_ab < C_X

Answer 3

A, B

Question 4

As more resistors are added in parallel across a constant voltage source, the power supplied by the source

A) increases.
B) decreases.
C) does not change.
D) increases for a time and then starts to decrease.

Question 5

Four unequal resistors are connected in series with each other. Which one of the following statements is correct about this combination?

A) The equivalent resistance is equal to that of any one of the resistors.
B) The equivalent resistance is equal to average of the four resistances.
C) The equivalent resistance is less than that of the smallest resistor.
D) The equivalent resistance is less than that of the largest resistor.
E) The equivalent resistance is more than the largest resistance.

Question 6

The lamps in a string of decorative lights are connected in parallel across a constant-voltage power source. What happens if one lamp burns out? (Assume negligible resistance in the wires leading to the lamps.)

A) The brightness of the lamps will not change appreciably.
B) The other lamps get brighter equally.
C) The other lamps get brighter, but some get brighter than others.
D) The other lamps get dimmer equally.
E) The other lamps get dimmer, but some get dimmer than others.

Question 7

A 5-µF, a 7-µF, and an unknown capacitor C_X are connected in series between points a and b. What do you know about the equivalent capacitance C_ab between a and b? (There could be more than one correct choice.)

A) C_ab > 12 µF
B) 5 µF < C_ab < 7 µF
C) 5 µF < C_ab < 12 µF
D) C_ab < 5 µF
E) C_ab < C_X

Question 8

When two or more different capacitors are connected in parallel across a potential source (battery), which of the following statements must be true? (There could be more than one correct choice.)

A) The potential difference across each capacitor is the same.
B) Each capacitor carries the same amount of charge.
C) The equivalent capacitance of the combination is less than the capacitance of any one of the capacitors.
D) The capacitor with the largest capacitance has the largest potential difference across it.
E) The capacitor with the largest capacitance has the most charge.

Question 9

Three identical capacitors are connected in parallel to a potential source (battery). If a charge of Q flows into this combination, how much charge does each capacitor carry?

A) 3Q
B) Q
C) Q/3
D) Q/9

Question 10

Suppose you have two capacitors and want to use them to store the maximum amount of energy by connecting them across a voltage source. You should connect them

A) in series across the source.
B) in parallel across the source.
C) It doesn't matter because the stored energy is the same either way.

Question 11

When different resistors are connected in parallel across an ideal battery, we can be certain that

A) the same current flows in each one.
B) the potential difference across each is the same.
C) the power dissipated in each is the same.
D) their equivalent resistance is greater than the resistance of any one of the individual resistances.
E) their equivalent resistance is equal to the average of the individual resistances.

Question 12

As more resistors are added in series to a constant voltage source, the power supplied by the source

A) increases.
B) decreases.
C) does not change.
D) increases for a time and then starts to decrease.

Question 13

You obtain a 100-W light bulb and a 50-W light bulb. Instead of connecting them in the normal way, you devise a circuit that places them in series across normal household voltage. If each one is an incandescent bulb of fixed resistance, which statement about these bulbs is correct?

A) Both bulbs glow with the same brightness, but less than their normal brightness.
B) Both bulbs glow with the same brightness, but more than their normal brightness.
C) The 100-W bulb glows brighter than the 50-W bulb.
D) The 50-W bulb glows more brightly than the 100-W bulb.

Question 14

Draw a circuit consisting of a battery connected to two resistors, R₁ and R₂, in series with each other and a capacitor C connected across the resistors.

Question 15

Draw a circuit with two batteries, a resistor between them, and a capacitor in parallel with the resistor. The batteries are connected negative pole to positive pole.

Question 16

Four unequal resistors are connected in a parallel with each other. Which one of the following statements is correct about this combination?

A) The equivalent resistance is less than that of the smallest resistor.
B) The equivalent resistance is equal to the average of the four resistances.
C) The equivalent resistance is midway between the largest and smallest resistance.
D) The equivalent resistance is more than the largest resistance.
E) None of the other choices is correct.

Question 17

Draw a circuit with a battery connected to four resistors, R₁, R₂, R₃, and R₄, as follows. Resistors R₁ and R₂ are connected in parallel with each other, resistors R₃ and R₄ are connected in parallel with each other, and both parallel sets of resistors are connected in series with each other across the battery.

Question 18

A 9-V battery is hooked up to two resistors in series using wires of negligible resistance. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Which statements about this circuit are true? (There could be more than one correct choice.)

A) The current is exactly the same at points A, B, C, and D.
B) The current at A is greater than the current at B, which is equal to the current at C, which is greater than the current at D.
C) The current at A is greater than the current at B, which is greater than the current at C, which is greater than the current at D.
D) The potential at B is equal to the potential at C.
E) The potential at D is equal to the potential at C.

Question 19

When unequal resistors are connected in parallel in a circuit,

A) the same current always runs through each resistor.
B) the potential drop is always the same across each resistor.
C) the largest resistance has the largest current through it.
D) the power generated in each resistor is the same.

Question 20

When unequal resistors are connected in series across an ideal battery,

A) the same power is dissipated in each one.
B) the potential difference across each is the same.
C) the current flowing in each is the same.
D) the equivalent resistance of the circuit is less than that of the smallest resistor.
E) the equivalent resistance of the circuit is equal to the average of all the resistances.

Question 21

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t?

Question 22

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

Question 23

A resistor is made out of a wire having a length L. When the ends of the wire are attached across the terminals of an ideal battery having a constant voltage V₀ across its terminals, a current I flows through the wire. If the wire were cut in half, making two wires of length L/2, and both wires were attached across the terminals of the battery (the right ends of both wires attached to one terminal, and the left ends attached to the other terminal), how much current would the battery put out?

A) 4I
B) 2I
C) I
D) I/2
E) I/4

Question 24

Identical light bulbs can be attached to identical ideal batteries in three different ways (A, B, orC), as shown in the figure. The ranking (from lowest to highest) of the total power produced by the battery is

A) B, A, C
B) A, B, C
C) C, B, A
D) A, C, B

Question 25

For the circuit shown in the figure, write the Kirchhoff loop equation for the entire outside loop. Notice the directions of the currents!

Question 26

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

Question 27

In the circuit shown in the figure, the resistor R has a variable resistance. As R is decreased, what happens to the currents?

A) I₁ remains unchanged and I₂ increases.
B) I₁ decreases and I₂ decreases.
C) I₁ decreases and I₂ increases.
D) I₁ increases and I₂ decreases.
E) I₁ increases and I₂ increases.

Question 28

Kirchhoff's junction rule is a statement of

A) the law of conservation of momentum.
B) the law of conservation of charge.
C) the law of conservation of energy.
D) the law of conservation of angular momentum.
E) Newton's second law.

Question 29

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in parallel with the first one, the time constant of the new RC circuit will be

A) the same as before.
B) twice as large as before.
C) three times a large as before.
D) one-half as large as before.
E) one-fourth as large as before.

Question 30

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the resistor as a function of time t?

Question 31

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about the circuit?

A) The capacitor charges to its maximum value in one time constant.
B) The capacitor charges to its maximum value in two time constants.
C) The potential difference across the resistor is always equal to the potential difference across the capacitor.
D) Current flows through the circuit even after the capacitor is essentially fully charged.
E) Once the capacitor is essentially fully charged, there is no current in the circuit.

Question 32

A resistor, an uncharged capacitor, a dc voltage source, and an open switch are all connected in series. The switch is closed at time t = 0 s. Which one of the following is a correct statement about this circuit?

A) The charge on the capacitor after four time constants is about 98% of the maximum value.
B) The charge on the capacitor after one time constant is 50% of its maximum value.
C) The charge on the capacitor after one time constant is 1/e of its maximum value.
D) The voltage on the capacitor after one time constant is 1/e of the maximum value.
E) The voltage on this capacitor after one time constant is 100% of its maximum value.

Question 33

Identical ideal batteries are connected in different arrangements to the same light bulb, as shown in the figure. For which arrangement will the bulb shine the brightest?

A) A
B) B
C) C

Question 34

Kirchhoff's loop rule is a statement of

A) the law of conservation of momentum.
B) the law of conservation of charge.
C) the law of conservation of energy.
D) the law of conservation of angular momentum.
E) Newton's second law.

Question 35

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

Question 36

A 9-V battery is hooked up to two resistors in series. One has a resistance of 5 Ω, and the other has a resistance of 10 Ω. Several locations along the circuit are marked with letters, as shown in the figure. Through which resistor is energy being dissipated at the higher rate?

A) the 10-Ω resistor
B) the 5-Ω resistor
C) Energy is being dissipated by both resistors at the same rate.

Question 37

For the circuit shown in the figure, write the Kirchhoff current equation for the node labeled A. Notice the directions of the currents!

Question 38

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the charge Q on the capacitor as a function of time t?

Question 39

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the current I through the resistor as a function of time t?

Question 40

A capacitor C is connected in series with a resistor R across a battery and an open switch. If a second capacitor of capacitance 2C is connected in series with the first one, the time constant of the new RC circuit will be

A) the same as before.
B) larger than before.
C) smaller than before.
D) variable.

Question 41

A system of four capacitors is connected across a 90-V voltage source as shown in the figure. What is the equivalent capacitance of this system?

A) 1.5 μF
B) 15 μF
C) 3.6 μF
D) 3.3 μF

Question 42

A 5.0-μF capacitor and a 7.0-μF capacitor are connected in series across an 8.0-V potential source. What is the potential difference across the 5.0-μF capacitor?

A) 0 V
B) 8.0 V
C) 2.7 V
D) 3.6 V
E) 4.7 V

Question 43

A network of capacitors is mostly inside a sealed box, but one capacitor C_X is sticking out, as shown in the figure. When you connect a multimeter across points a and b, it reads 27.0 µF. What is C_X?

A) 27.0 µF
B) 23.0 µF
C) 4.0 µF
D) 2.4 µF
E) 2.2 µF

Question 44

A potential difference of V = 100 V is applied across two capacitors in series, as shown in the figure. If = and the voltage drop across it is 75 V, what is the capacitance of C₂?

A) 30 μF
B) 2.5 μF
C) 7.5 μF
D) 3.3 μF

Question 45

Two capacitors are connected as shown in the figure, with C₁ = 4.0 µF and C₂ = 7.0 µF. If a voltage source V = 90 V is applied across the combination, find the potential difference across C₁.

A) 57 V
B) 36 V
C) 60 V
D) 9.0 V

Question 46

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time t = 0 s, the switch is closed. Which of the graphs below best describes the potential difference V across the capacitor as a function of time t?

Question 47

Three capacitors of equal capacitance are arranged as shown in the figure, with a voltage source across the combination. If the voltage drop across C₁ is what is the voltage drop across

A) 20 V
B) 10.0 V
C) 40 V
D) 30 V

Question 48

A 5.0-μF and a 12.0-μF capacitor are connected in series, and the series arrangement is connected in parallel to a capacitor. How much capacitance would a single capacitor need to replace this combination of three capacitors?

A) 33 μF
B) 13 μF
C) 16 μF
D) 38 μF

Question 49

A 1.0-µF capacitor and a 2.0-µF capacitor are connected together, and then that combination is connected across a 3.0-V potential source (a battery). What is the potential difference across the 2.0-µF capacitor if the capacitors are connected (a) in series or (b) in parallel?

Question 50

A 5.0-μF, a 14-μF, and a 21-μF capacitor are connected in series. How much capacitance would a single capacitor need to have to replace the three capacitors?

A) 40 μF
B) 3.6 μF
C) 2.0 μF
D) 3.1 μF

Question 51

You have three capacitors with capacitances of 4.00 μF, 7.00 μF, and 9.00 μF. What is the equivalent capacitance if they are connected (a) in series and (b) in parallel?

Question 52

Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points A and B?

A) 12 μF
B) 4.0 μC
C) 7.1 μF
D) 1.7 μF
E) 8.0 μF

Question 53

A system of four capacitors is connected across a 90-V voltage source as shown in the figure.
(a) What is the potential difference across the plates of the 6.0-µF capacitor?
(b) What is the charge on the 3.0-µF capacitor?

Question 54

Three capacitors of capacitance 5.00 μF, 10.0 μF, and 50.0 μF are connected in series across a 12.0-V potential difference (a battery).
(a) How much charge is stored in the 5.00-μF capacitor?
(b) What is the potential difference across the 10.0-µF capacitor?

Question 55

A 2.0-μF capacitor and a 4.0-μF capacitor are connected in series across an 8.0-V potential source. What is the charge on the 2.0-μF capacitor?

A) 2.0 μC
B) 4.0 μC
C) 12 μC
D) 11 μC
E) 25 μC

Question 56

A system of four capacitors is connected across a 90-V voltage source as shown in the figure.
(a) What is the charge on the 4.0-µF capacitor?
(b) What is the charge on the 2.0-µF capacitor?

Question 57

A network of capacitors is connected across a potential difference V₀ as shown in the figure.
(a) What should V₀ be so that the 60.0-µF capacitor will have 18.0 µC of charge on each of its plates?
(b) Under the conditions of part (a), how much total energy is stored in this network of capacitors?

Question 58

A 4.0-µF capacitor and an 8.0-µF capacitor are connected together. What is the equivalent capacitance of the combination if they are connected (a) in series or (b) in parallel?

Question 59

Four 16-μF capacitors are connected in combination. What is the equivalent capacitance of this combination if they are connected
(a) in series?
(b) in parallel?
(c) such that two of them are in parallel with each other and that combination is in series with the remaining two capacitors?

Question 60

A 5.0-μF, a 14-μF, and a capacitor are connected in parallel. How much capacitance would a single capacitor need to have to replace the three capacitors?

A) 40 μF
B)
C) 5.0 μF
D) 14 μF

Question 61

What is the equivalent resistance between points A and B of the network shown in the figure?

Question 62

A combination of a 2.0-Ω resistor in series with 4.0-Ω resistor is connected in parallel with a 3.0-Ω resistor. What is the equivalent resistance of this system?

A) 2.0 Ω
B) 3.0 Ω
C) 4.0 Ω
D) 9.0 Ω

Question 63

A group of 1.0-μF, 2.0-μF, and 3.0-μF capacitors is connected in parallel across a 24-V potential difference (a battery). How much energy is stored in this three-capacitor combination when the capacitors are fully charged?

A) 1.7 mJ
B) 2.1 mJ
C) 4.8 mJ
D) 7.1 mJ

Question 64

The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. What is the final potential difference across capacitor Z?

A) 100 V
B) 600 V
C) 55 V
D) 38 V
E) 29 V

Question 65

Two 4.0-Ω resistors are connected in parallel, and this combination is connected in series with 3.0 Ω. What is the equivalent resistance of this system?

A) 1.2 Ω
B) 5.0 Ω
C) 7.0 Ω
D) 11 Ω

Question 66

What resistance must be connected in parallel with a 633-Ω resistor to produce an equivalent resistance of 205 Ω?

Question 67

A 2.0-Ω resistor is in series with a parallel combination of 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What is the equivalent resistance of this system?

A) 24 Ω
B) 4.0 Ω
C) 1.8 Ω
D) 2.7 Ω

Question 68

Three 2.0-Ω resistors are connected to form the sides of an equilateral triangle ABC as shown in the figure. What is the equivalent resistance between any two points, AB, BC, or AC, of this circuit?

A) 2.0 Ω
B) 6.0 Ω
C) 4.3 Ω
D) 3.3 Ω
E) 1.3 Ω

Question 69

The capacitive network shown in the figure is assembled with initially uncharged capacitors. Assume that all the quantities in the figure are accurate to two significant figures. The switch S in the network is kept open throughout. What is the total energy stored in the seven capacitors?

A) 48 mJ
B) 72 mJ
C) 96 mJ
D) 120 mJ
E) 144 mJ

Question 70

The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. How much charge is finally stored in capacitor Y?

A) 110 µC
B) 54 µC
C) 81 µC
D) 140 µC
E) 160 µC

Question 71

The network shown is assembled with uncharged capacitors X , Y, and Z, with C_X = 4.0 μF, C_Y = 6.0 μF, and C_Z = 5.0 μF. The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. What is the final potential difference across capacitor X?

A) 120 V
B) 82 V
C) 75 V
D) 67 V
E) 60 V

Question 72

A 9.00-µF and a 12.0-µF capacitor are connected together, and this combination is connected across a 25.0-V potential difference. How much electric energy is stored in the combination if they are connected (a) in parallel or (b) in series?

Question 73

Five 2.0-Ω resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points a and b?

A) 1.0 Ω
B) 10.0 Ω
C) 2.0 Ω
D) 6.0 Ω
E) 0.40 Ω

Question 74

Two resistors in series are equivalent to 9.0 Ω, and in parallel they are equivalent to 2.0 Ω. What are the resistances of these two resistors?

Question 75

The resistors in the circuit shown in the figure each have a resistance of What is the equivalent resistance between points a and b of this combination?

A) 700 Ω
B) 2800 Ω
C) 175 Ω
D) 1400 Ω

Question 76

What different resistances can be obtained by using two 2.0-Ω resistors and one 4.0-Ω resistor? You must use all three of them in each possible combination.

Question 77

What is the equivalent resistance in the circuit shown in the figure?

A) 80 Ω
B) 55 Ω
C) 50 Ω
D) 35 Ω

Question 78

Three capacitors are arranged as shown in the figure, with a voltage source connected across the combination. C₁ has a capacitance of has a capacitance of and has a capacitance of Find the potential drop across the entire arrangement if the potential drop across C₂ is

A) 1500 V
B) 1000 V
C) 470 V
D) 430 V

Question 79

The network shown is assembled with uncharged capacitors X , Y, and Z, with and The switches S₁ and S₂ are initially open, and a potential difference V_ab = 120 V is applied between points a and b. After the network is assembled, switch S₁ is then closed, but switch S₂ is kept open. How much energy is finally stored in capacitor X?

A) 29 mJ
B) 0.48 mJ
C) 0.24 mJ
D) 58 mJ
E) 0.96 mJ

Question 80

Each of the resistors shown in the figure has a resistance of What is the equivalent resistance between points a and b of this combination?

A) 450.0 Ω
B) 720.0 Ω
C) 540.0 Ω
D) 180.0 Ω