Deck 28: Direct-Current Circuits

Question 1

At what rate is thermal energy being generated in the 2R-resistor when ε = 12 V and R = 3.0 Ω?

A) 12 W
B) 24 W
C) 6.0 W
D) 3.0 W
E) 1.5 W

Answer 1

6.0 W

Question 2

When a 20-V emf is placed across two resistors in series, a current of 2.0 A is present in each of the resistors. When the same emf is placed across the same two resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the two resistances?

A) 7.2 Ω
B) 7.6 Ω
C) 6.9 Ω
D) 8.0 Ω
E) 2.8 Ω

Answer 2

7.2 Ω

Question 3

Determine the magnitude and sense (direction) of the current in the 10-Ω resistor when I = 1.8 A.

A) 1.6 A right to left
B) 1.6 A left to right
C) 1.2 A right to left
D) 1.2 A left to right
E) 1.8 A left to right

Answer 3

1.6 A right to left

Question 4

What is the potential difference V_b − V_a shown in the circuit below.

A) −8.0 V
B) +8.0 V
C) −18 V
D) +18 V
E) −12 V

Question 5

Determine ε when I = 0.50 A and R = 12 Ω.

A) 12 V
B) 24 V
C) 30 V
D) 15 V
E) 6.0 V

Question 6

How much heat is produced in the 10-Ω resistor in 5.0 s when ε = 18 V?

A) 72 J
B) 32 J
C) 50 J
D) 18 J
E) 90 J

Question 7

At what rate is thermal energy generated in the 30-Ω resistor?

A) 20 W
B) 27 W
C) 60 W
D) 13 W
E) 30 W

Question 8

Determine the magnitude and sense (direction) of the current in the 500-Ω resistor when I = 30 mA.

A) 56 mA left to right
B) 56 mA right to left
C) 48 mA left to right
D) 48 mA right to left
E) 26 mA left to right

Question 9

Determine R when I = 0.20 A and ε = 18 V.

A) 50 Ω
B) 8.0 Ω
C) 10 Ω
D) 20 Ω
E) 30 Ω

Question 10

At what rate is thermal energy generated in the 20-Ω resistor when ε = 20 V?

A) 6.5 W
B) 1.6 W
C) 15 W
D) 26 W
E) 5.7 W

Question 11

What is the current in the 10-Ω resistor ?

A) 0.60 A
B) 3.0 A
C) 1.2 A
D) 2.4 A
E) 0.30 A

Question 12

A resistor of unknown resistance and a 15-Ω resistor are connected across a 20-V emf in such a way that a 2.0 A current is observed in the emf. What is the value of the unknown resistance?

A) 75 Ω
B) 12 Ω
C) 7.5 Ω
D) 30 Ω
E) 5.0 Ω

Question 13

Determine the potential difference V_a − V_b shown in the circuit below.

A) −5.0 V
B) +5.0 V
C) −10 V
D) +10 V
E) 0 V

Question 14

At what rate is thermal energy generated in the 5-Ω resistor when ε = 24 V?

A) 13 W
B) 3.2 W
C) 23 W
D) 39 W
E) 51 W

Question 15

If ε = 8.0 V, at what rate is that emf providing energy to the circuit shown below?

A) 8.4 W
B) 7.6 W
C) 5.6 W
D) 11 W
E) 2.0 W

Question 16

At what rate is power supplied by the 10-V emf shown below?

A) −10 W
B) +10 W
C) zero
D) +20 W
E) −20 W

Question 17

Determine the current in the 10-V emf.

A) 2.3 A
B) 2.7 A
C) 1.3 A
D) 0.30 A
E) 2.5 A

Question 18

What is the magnitude of the potential difference across the 20-Ω resistor?

A) 3.2 V
B) 7.8 V
C) 11 V
D) 5.0 V
E) 8.6 V

Question 19

What is the magnitude of the current in the 20-Ω resistor?

A) 0.75 A
B) 0.00 A
C) 0.25 A
D) 0.50 A
E) 1.00 A

Question 20

What is the current in the 15-Ω resistor when ε = 9.0 V?

A) 0.20 A
B) 0.30 A
C) 0.10 A
D) 0.26 A
E) 0.60 A

Question 21

If R = 3.0 kΩ, C = 5.0 mF, ε = 6.0 V, Q = 15 mC, and I = 4.0 mA, what is the potential difference V_b − V_a?

A) −3.0 V
B) +9.0 V
C) −15 V
D) +21 V
E) −6.0 V

Question 22

How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor?

A) 0.60
B) 0.46
C) 0.52
D) 0.40
E) 1.1

Question 23

How long will it take a charged 80-μF capacitor to lose 20% of its initial energy when it is allowed to discharge through a 45-Ω resistor?

A) 0.92 ms
B) 0.64 ms
C) 0.40 ms
D) 0.19 ms
E) 0.80 ms

Question 24

If R = 4.0 kΩ, C = 3.0 mF, ε = 15 V, Q = 12 mC, and I = 2.0 mA, what is the potential difference V_b − V_a?

A) +3.0 V
B) −19 V
C) −3.0 V
D) +27 V
E) +21 V

Question 25

At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 μF, ε = 30 V, and R = 5.0 kΩ, at what rate is energy being stored in the capacitor when I = 2.0 mA?

A) 32 mW
B) 40 mW
C) 44 mW
D) 36 mW
E) 80 mW

Question 26

If ε ₁ = 4.0 V, ε ₂ = 12.0 V, R₁ = 4 Ω, R₂ = 12 Ω, C = 3 μF, Q = 18 μC, and I = 2.5 A, what is the potential difference V_a − V_b?

A) −30 V
B) 30 V
C) 5.0 V
D) −5.0 V
E) −1.0 V

Question 27

If the current in the 4.0-Ω resistor is 1.4 A, what is the magnitude of the potential difference, V_A − V_B?

A) 69 V
B) 55 V
C) 62 V
D) 48 V
E) 31 V

Question 28

If Q = 400 μC and the potential difference V_A − V_B = −10 V in the circuit segment shown below, what is the current in the resistor?

A) 1.0 mA right to left
B) 1.0 mA left to right
C) 3.5 mA right to left
D) 3.5 mA left to right
E) None of the above

Question 29

Determine the potential difference, V_A − V_B, in the circuit segment shown below when I = 2.0 mA and Q = 50 μC.

A) −40 V
B) +40 V
C) +20 V
D) −20 V
E) −10 V

Question 30

In an RC circuit, how many time constants must elapse if an initially uncharged capacitor is to reach 80% of its final potential difference?

A) 2.2
B) 1.9
C) 1.6
D) 3.0
E) 5.0

Question 31

What is the potential difference V_B − V_A when I = 0.50 A in the circuit segment shown below?

A) +28 V
B) +2.0 V
C) −28 V
D) −2.0 V
E) +18 V

Question 32

If R = 2.0 kΩ, C = 4.0 mF, ε = 8.0 V, Q = 20 mC, and I = 3.0 mA, what is the potential difference V_b − V_a?

A) +7.0 V
B) +19 V
C) +9.0 V
D) −3.0 V
E) −14 V

Question 33

In an RC circuit, what fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants?

A) 0.84
B) 0.90
C) 0.75
D) 0.60
E) 0.03

Question 34

If I = 2.0 A in the circuit segment shown below, what is the potential difference V_B − V_A?

A) +10 V
B) −20 V
C) −10 V
D) +20 V
E) +30 V

Question 35

Determine the resistance R when I = 1.5 A.

A) 40 Ω
B) 8.0 Ω
C) 85 Ω
D) 28 Ω
E) 32 Ω

Question 36

If I = 0.40 A in the circuit segment shown below, what is the potential difference V_a − V_b?

A) 31 V
B) 28 V
C) 25 V
D) 34 V
E) 10 V

Question 37

At t = 0 the switch S is closed with the capacitor uncharged. If C = 50 μF, ε = 20 V, and R = 4.0 kΩ, what is the charge on the capacitor when I = 2.0 mA?

A) 360 μC
B) 480 μC
C) 240 μC
D) 600 μC
E) 400 μC

Question 38

What is the potential difference V_B − V_A when the I = 1.5 A in the circuit segment below?

A) +22 V
B) −22 V
C) −38 V
D) +38 V
E) +2.0 V

Question 39

If Q = 350 μC and I = 4.0 mA in the circuit segment shown below, determine the potential difference, V_A − V_B.

A) −30 V
B) +80 V
C) +40 V
D) −40 V
E) +10 V

Question 40

If R = 3.0 kΩ, C = 6.0 nF, ε ₁ = 10.0 V, Q = 18 nC, ε ₂ = 6.0 V, and I = 5.0 mA, what is the potential difference V_b − V_a?

A) −13 V
B) +28 V
C) +13 V
D) −28 V
E) +2.0 V

Question 41

At t = 0 the switch S is closed with the capacitor uncharged. If C = 30 μF, ε = 50 V, and R = 10 kΩ, what is the potential difference across the capacitor when I = 2.0 mA?

A) 20 V
B) 15 V
C) 25 V
D) 30 V
E) 45 V

Question 42

What is the equivalent resistance between points A and B in the figure when R = 18 Ω?

A) 48 Ω
B) 64 Ω
C) 80 Ω
D) 96 Ω
E) 110 Ω

Question 43

If R₁ = 3.0 Ω, R₂ = 6.0 Ω, R₃ = 12 Ω, and I = 0.50 A, at what rate is heat being generated in R₁?

A) 20 W
B) 17 W
C) 12 W
D) 31 W
E) 6.0 W

Question 44

If 480 C pass through a 4.0-Ω resistor in 10 min, what is the potential difference across the resistor?

A) 3.6 V
B) 2.8 V
C) 2.4 V
D) 3.2 V
E) 5.0 V

Question 45

When a capacitor is fully charged, the current through the capacitor in a direct-current circuit is

A) zero.
B) at its maximum value.
C) equal to the current in a resistive circuit in parallel with the capacitor circuit.
D) greater than the current in a resistor that is farther from the battery than the capacitor.
E) zero if it is the only capacitor, but maximum if there is another capacitor in series with it.

Question 46

What is the equivalent resistance between points a and b?

A) 14 Ω
B) 8.0 Ω
C) 6.0 Ω
D) 25 Ω
E) 40 Ω

Question 47

What is the equivalent resistance between points a and b when R = 30 Ω?

A) 27 Ω
B) 21 Ω
C) 24 Ω
D) 18 Ω
E) 7.5 Ω

Question 48

What is the equivalent resistance between points a and b when R = 13 Ω?

A) 29 Ω
B) 23 Ω
C) 26 Ω
D) 20 Ω
E) 4.6 Ω

Question 49

What is the equivalent resistance between points A and B in the figure when R = 20 Ω?

A) 77 Ω
B) 63 Ω
C) 70 Ω
D) 84 Ω
E) 140 Ω

Question 50

If R₁ = 10 Ω, R₂ = 15 Ω, R₃ = 20 Ω, and I = 0.50 A, at what rate is heat being generated in these resistors?

A) 29 W
B) 16 W
C) 22 W
D) 11 W
E) 1.1 W

Question 51

A 10-V battery is connected to a 15-Ω resistor and an unknown resistor R, as shown. The current in the circuit is 0.40 A. How much heat is produced in the 15-Ω resistor in 2.0 min?

A) 0.40 kJ
B) 0.19 kJ
C) 0.29 kJ
D) 0.72 kJ
E) 0.80 kJ

Question 52

The circuit below contains three 100-W light bulbs. The emf ε = 110 V. Which light bulb(s) is(are) brightest?

A) A
B) B
C) C
D) B and C
E) All three are equally bright.

Question 53

A capacitor in a single-loop RC circuit is charged to 85% of its final potential difference in 2.4 s. What is the time constant for this circuit?

A) 1.5 s
B) 1.3 s
C) 1.7 s
D) 1.9 s
E) 2.9 s

Question 54

At t = 0 the switch S is closed with the capacitor uncharged. If C = 40 μF, ε = 50 V, and R = 5.0 kΩ, how much energy is stored by the capacitor when I = 2.0 mA?

A) 20 mJ
B) 28 mJ
C) 32 mJ
D) 36 mJ
E) 40 mJ

Question 55

The circuit below contains three 100-watt light bulbs. The emf ε = 110 V. Which light bulb(s) is(are) the brightest?

A) A
B) B
C) C
D) B and C
E) All three are equally bright.

Question 56

In a loop in a closed circuit, the sum of the currents entering a junction equals the sum of the currents leaving a junction because

A) the potential of the nearest battery is the potential at the junction.
B) there are no transformations of energy from one type to another in a circuit loop.
C) capacitors tend to maintain current through them at a constant value.
D) current is used up after it leaves a junction.
E) charge is neither created nor destroyed at a junction.

Question 57

A certain brand of hot dog cooker applies a potential difference (120 V) to opposite ends of the hot dog and cooks by means of the joule heat produced. If 60 kJ is needed to cook each hot dog, what current is needed to cook four hot dogs simultaneously in 3.0 min?

A) 11 A
B) 2.8 A
C) 8.3 A
D) 2.1 A
E) 3.6 A

Question 58

The algebraic sum of the changes of potential around any closed circuit loop is

A) zero.
B) maximum.
C) zero only if there are no sources of emf in the loop.
D) maximum if there are no sources of emf in the loop.
E) equal to the sum of the currents in the branches of the loop.

Question 59

What is the equivalent resistance between points a and b when R = 12 Ω?

A) 20 Ω
B) 16 Ω
C) 24 Ω
D) 28 Ω
E) 6.0 Ω

Question 60

What is the equivalent resistance between points A and B in the figure when R = 10 Ω?

A) 20 Ω
B) 10 Ω
C) 25 Ω
D) 15 Ω
E) 3.2 Ω

Question 61

The circuit below contains 5 identical light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

A) A: The one closest to the positive terminal of the battery.
B) A and C: The bulbs closest to the positive terminal of the battery.
C) A and B: Because they are closest to the terminals of the battery.
D) C and D: Because they receive current from A and B and from E.
E) E: Because the potential difference across E is that of the battery.

Question 62

The circuit below contains three 100-W light bulbs and a capacitor. The emf is 110 V and the capacitor is fully charged. Which light bulb(s) is(are) brightest?

A) A
B) B
C) C
D) A and B
E) A and C

Question 63

The diagram shown represents a portion of a wire in a circuit. A current is flowing in the wire in the direction shown. Under the convention that it is positive charge that flows the electric field points in the direction of the current. How can the electric field change direction where the wire bends?

A) There is an excess of negative charge in the center of the wire.
B) There is an excess of positive charge at the bottom end of the wire.
C) There is an excess of negative charge at the right end of the upper portion of the wire.
D) There is an accumulation of positive charge on the surface, particularly at the bend, such that the sum of electric fields gives the new electric field.
E) There is an accumulation of electrical potential as the current traverses the wire: The higher potential in the lower half is the source of the field.

Question 64

The circuit below contains 3 100-W light bulbs and a capacitor. The emf is 110 V. Which light bulb(s) is(are) brightest? (Assume the capacitor is fully charged.)

A) A
B) B
C) C
D) A and B
E) All three are equally bright.

Question 65

The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

A) A
B) B
C) C
D) D
E) C and D

Question 66

Which of the identical light bulb(s) is(are) brightest when the capacitor has half its maximum charge?

A) A
B) B
C) C
D) A and B
E) All three are equally bright.

Question 67

A parallel circuit consists of a 100 V DC power source, a 100 Ω resistor, and a variable resistor of resistance R, which varies from 0 to 100 Ω. The current in the circuit is

A) directly proportional to R.
B) inversely proportional to R.
C) directly proportional to (100 Ω + R).
D) inversely proportional to (100 Ω + R).
E) neither directly nor inversely proportional to R or to (100 Ω + R).

Question 68

The capacitors are completely discharged in the circuit shown below. The two resistors have the same resistance R and the two capacitors have the same capacitance C. After the switch is closed, the current

A) is greatest in C₁.
B) is greatest in C₂.
C) is greatest in R₁.
D) is greatest in R₂.
E) is the same in C₁, C₂, R₁ and R₂.

Question 69

A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is

A)
.
B) R.
C)
.
D) NR.
E) 4NR.

Question 70

The circuit below shows three resistors in series. R₃ > R₂ > R₁. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.

A) E₃ < E₂ < E₁.
B) E₂ < E₁ = E₃.
C) E₁ = E₂ = E₃.
D) E₁ = E₃ < E₂.
E) E₁ < E₂ < E₃.

Question 71

The circuit below contains three resistors, A, B, and C, which all have equal resistances. The emf ε = 110V. Which resistor generates the most thermal energy after the switch is closed?

A) A
B) B
C) C
D) A and B
E) All three generate equal amounts of thermal energy.

Question 72

The circuit below shows three resistors in parallel. R₃ > R₂ > R₁. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest.

A) E₃ < E₂ < E₁.
B) E₂ < E₁ = E₃.
C) E₁ = E₂ = E₃.
D) E₁ = E₃ < E₂.
E) E₁ < E₂ < E₃.

Question 73

The circuit below contains three 100-W light bulbs and a capacitor. The emf ε = 110V. At the instant the switch S is closed, which light bulb is brightest?

A) A
B) B
C) C
D) A and B
E) All three are equally bright.

Question 74

A circuit consists of N resistors, all of resistance R, connected as shown below. A potential difference V is applied to the circuit. The equivalent resistance of the circuit is

A)
.
B)
.
C) R.
D) NR.
E) 2NR.

Question 75

The circuit below contains 4 100-W light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

A) A
B) B
C) C
D) D
E) C and D

Question 76

A series circuit consists of a 100 V DC power source, a 100 Ω resistor, and a variable resistor of resistance R, which varies from 0 to 100 Ω. The current in the circuit is

A) directly proportional to R.
B) inversely proportional to R.
C) directly proportional to (100 Ω + R).
D) inversely proportional to (100 Ω + R).
E) neither directly nor inversely proportional to R or to (100 Ω + R).

Question 77

The battery is disconnected from a series RC circuit after the capacitor is fully charged and is replaced by an open switch. When the switch is closed,

A) the current through the resistor is always greater than the current through the capacitor.
B) the current through the resistor is always less than the current through the capacitor.
C) the current through the resistor is always equal to the current through the capacitor.
D) the capacitor does not allow current to pass.
E) the current stops in the resistor.

Question 78

Which two circuits are exactly equivalent?

A) A and B
B) B and C
C) C and D
D) D and E
E) B and E

Question 79

A circuit consists of 2N resistors, all of resistance R, connected as shown below. A potential difference V is applied to one end, and the other end is at ground potential. The equivalent resistance of the circuit is

A)
.
B) R.
C)
.
D) NR.
E) 2NR.

Question 80

The circuit below contains three 100-watt light bulbs and a capacitor. The emf ε = 110V. The capacitor is fully charged. Which light bulb(s) is(are) dimmest?

A) A
B) B
C) C
D) A and B
E) All three are equally bright (or dim).