Deck 18: Electric Current and Circuits

Question 1

An ohm is equivalent to which of the following?

A) volt/meter
B) coulomb/volt
C) ampere/coulomb
D) volt/ampere
E) ampere·coulomb

Answer 1

volt/ampere

Question 2

One hundred meters of 2.00 mm diameter wire has a resistance of 0.532 Ω. What is the resistivity of the material from which the wire is made?

A) 1.59 × 10^-8 Ω·m
B) 1.67 × 10^-8 Ω·m
C) 2.35 × 10^-8 Ω·m
D) 2.65 × 10^-8 Ω·m
E) 5.40 × 10^-8 Ω·m

Answer 2

1.67 × 10^-8 Ω·m

Question 3

When current flows through a wire

A) electrons are moving in the direction of the current.
B) electrons are moving opposite the direction of the current.
C) protons are moving in the direction of the current.
D) protons are moving opposite the direction of the current.
E) both protons and electrons are moving in the direction of the current.

Answer 3

electrons are moving opposite the direction of the current.

Question 4

The resistance of a wire increases by 3.9% when the temperature of the wire is raised 100°C. What is the temperature coefficient of resistivity of the wire material?

A) 3.9°C⁻¹
B) 0.39°C⁻¹
C) 0.039°C⁻¹
D) 0.0039°C⁻¹
E) 0.00039°C⁻¹

Question 5

A length L₀ of wire has a resistance of 32.0 Ω. The wire is uniformly stretched (i.e., the total volume of the wire is unchanged during the stretching) to four times its original length, or 4 L₀. If a length L₀ is now cut from the stretched wire, what is its resistance?

A) 512 Ω
B) 128 Ω
C) 32.0 Ω
D) 8.00 Ω
E) 2.00 Ω

Question 6

Aluminum has a resistivity of 2.65 × 10⁻⁸ Ω × m. What is the resistance of 15 m of aluminum wire with cross-sectional area 1.0 mm²?

A) 1.6 Ω
B) 0.40 Ω
C) 0.13 Ω
D) 1.3 × 10² Ω
E) 56 Ω

Question 7

One hundred meters of a certain type of wire has a resistance of 7.2 Ω. What is the resistance of 2.5 m of this wire?

A) 18 Ω
B) 1.8 Ω
C) 0.18 Ω
D) 3.0 Ω
E) 0.30 Ω

Question 8

In a liquid, a current is set up between points A and B. Positive ions flow from A to B and carry 6.0 coulombs of positive charge per second, while negative ions move from B to A with 2.0 coulombs of negative charge per second. What is the net current from A to B?

A) 8.0 A
B) −8.0 A
C) 4.0 A
D) −4.0 A
E) 12 A

Question 9

A 1.56-V battery has an internal resistance of 0.120 Ω. What is the maximum current that can be drawn from this battery?

A) infinite (or at least 1000s of amps)
B) 1.56 A
C) 0.190 A
D) 13.0 A
E) 7.50 A

Question 10

A 2.50 A current is carried by a copper wire of radius 1.0 mm. If the density of conduction electrons is 8.0 × 10²⁸ m⁻³, what is the drift velocity of the conduction electrons?

A) 3.0 × 10⁸ m/s
B) 3.2 × 10⁻⁴ m/s
C) 1.6 × 10⁻⁵ m/s
D) 6.2 × 10⁻⁴ m/s
E) 6.2 × 10⁻⁵ m/s

Question 11

A length of wire has a resistance of 18.0 Ω. When the wire is uniformly stretched (i.e., the total volume of the wire is unchanged during the stretching) to triple it original length, what resistance results?

A) 162 Ω
B) 54.0 Ω
C) 18.0 Ω
D) 6.00 Ω
E) 2.00 Ω

Question 12

A variable resistor has a voltage of 12.0 V placed across it. If the resistance is increased 20%, what happens to the current flowing through it?

A) It increases 20%.
B) It increases 25%.
C) It decreases 20%.
D) It decreases 25%.
E) It decreases 17%.

Question 13

Two copper wires, one with twice the diameter of the other, have the same current flowing through them. If the thinner wire has a drift velocity v₁, and the thicker wire has a drift velocity v₂, how do the drift velocities compare?

A) v₁ = v₂
B) v₁ = 2 v₂
C) 2 v₁ = v₂
D) v₁ = 4 v₂
E) 4 v₁ = v₂

Question 14

Silver contains 5.8 × 10²⁸ conduction electrons per m³. How many conduction electrons are in a 1.0 m length of silver wire of diameter 2.6 mm?

A) 1.9 × 10⁵
B) 4.7 × 10⁴
C) 3.1 × 10²³
D) 1.2 × 10²⁴
E) 6.0 × 10²³

Question 15

An ampere, A, is equivalent to a

A) V/m.
B) V·C.
C) C/s.
D) C·s.
E) N/V.

Question 16

A potential difference of 12.4 V is placed across a 4.1 Ω resistor. What is the current in the resistor?

A) 51 A
B) 3.0 A
C) 0.33 A
D) 16 A
E) 8.3 A

Question 17

If a 22 Ω resistor has a current of 2.0 A flowing through it, what is the potential difference across it?

A) 0.091 V
B) 44 V
C) 11 V
D) 24 V
E) 20 V

Question 18

A resistor has a resistance of 30 Ω at 20°C. If the temperature coefficient of resistivity is 4.5 × 10⁻³ °C⁻¹, what is its resistance at 200°C?

A) 24 Ω
B) 27 Ω
C) 48 Ω
D) 54 Ω
E) 57 Ω

Question 19

If 64 coulombs flow along a wire in 4.0 seconds, what is the average current?

A) 64 A
B) 32 A
C) 16 A
D) 4.0 A
E) none of these choices are correct

Question 20

Of the common battery sizes AAA, AA, C, and D, which provides the highest emf?

A) AAA
B) AA
C) C
D) D
E) all have the same emf

Question 21

Capacitors of values 1.0 F, 2.0 F, 3.0 F, and 6.0 F are connected in series across a 12 V power supply. Which capacitor has the greatest potential difference across it?

A) the 1.0 F capacitor
B) the 2.0 F capacitor
C) the 3.0 F capacitor
D) the 6.0 F capacitor
E) they all are equal

Question 22

In the diagram, if the current through R₁ is 5 A up, and the current through R₃ is 3 A up, what is the current in R₂?

A) 8 A up
B) 8 A down
C) 2 A up
D) 2 A down
E) more information is needed

Question 23

If R₁ = 6 Ω, R₂ = 8 Ω, R₃ = 2 Ω, ε₁ = 4 V, and ε₂ = 14 V, what is the current in R₂?

A) 1 A up
B) 1 A down
C) 2.5 A up
D) 2.5 A down
E) 5 A down

Question 24

Four 12 Ω resistors are connected together. What is the least resistance that can be attained with these resistors by connecting them in various ways?

A) 12 Ω
B) 6.0 Ω
C) 3.0 Ω
D) 2.0 Ω
E) 1.0 Ω

Question 25

A 6.0 Ω resistor and a 3.0 Ω resistor are connected in series to a 1.5 V battery of negligible internal resistance. What is the current in the 3.0 Ω resistor?

A) 2.0 A
B) 0.50 A
C) 0.25 A
D) 0.17 A
E) 0.75 A

Question 26

Two capacitors of values 6.0 mF and 9.0 mF are connected in series to a 30.0 V power supply. What is the resulting potential difference across the 6.0 mF capacitor?

A) 30 V
B) 18 V
C) 12 V
D) 6.0 V
E) 3.0 V

Question 27

Two capacitors of values 6.0 mF and 9.0 mF are connected in series. What is the capacitance of the combination?

A) 15 mF
B) 7.5 mF
C) 3.0 mF
D) 3.6 mF
E) 54 mF

Question 28

A 12.0 V battery has an internal resistance of 0.080 Ω. If the battery supplies 100 A when connected to a starter motor, what is the resistance of the motor?

A) 0.080 Ω
B) 0.20 Ω
C) 0.0012 Ω
D) 0.040 Ω
E) 0.012 Ω

Question 29

Four 12 Ω resistors are connected together. Which of the following resistances cannot be formed using all 4 resistors?

A) 48 Ω
B) 9.0 Ω
C) 12 Ω
D) 60 Ω
E) 20 Ω

Question 30

A 6.0 Ω resistor and a 3.0 Ω resistor are connected in parallel to a 1.5 V battery of negligible internal resistance. What is the current in the 3.0 Ω resistor?

A) 2.0 A
B) 0.50 A
C) 0.25 A
D) 0.17 A
E) 0.75 A

Question 31

Three wires are connected at a junction. One of the wires carries a current of 4 A into the junction, while another carries 5 A into the junction. What is the current in the third wire?

A) 4 A away from the junction
B) 9 A away from the junction
C) 4 A into the junction
D) 9 A into the junction
E) 1 A away from the junction

Question 32

Two capacitors of values 6.00 mF and 9.00 mF are connected in series to a 30.0 V power supply. What is the resulting charge on the 6.00 mF capacitor?

A) 180 mC
B) 270 mC
C) 90.0 mC
D) 108 mC
E) 200 mC

Question 33

A three-cell flashlight has 3 batteries in series, each with an emf of 1.5 V. If the bulb has a resistance of 50 Ω, what current flows when the flashlight is operating? (Assume the internal resistance of the batteries is negligible.)

A) 30 mA
B) 10 mA
C) 27 mA
D) 90 mA
E) 11 A

Question 34

A 12.0 V battery is connected across a 4.00-Ω resistor. If the current through the resistor is 2.80 A, what is the internal resistance of the battery?

A) 0.200 Ω
B) 0.286 Ω
C) 4.29 Ω
D) 3.71 Ω
E) 0.800 Ω

Question 35

The arrangement shown is composed of four 6.0 mF capacitors. What is the capacitance of the combination?

A) 24.0 mF
B) 4.5 mF
C) 8.0 mF
D) 9.0 mF
E) 12.5 mF

Question 36

A 12.0 V battery is connected across a 4.00 Ω resistor. If the current through the resistor is 2.80 A, what is the terminal voltage of the battery?

A) 12.0 V
B) 12.8 V
C) 11.6 V
D) 11.2 V
E) 9.6 V

Question 37

In the diagram, each resistor is 3 ohms, and the battery is 9 volts. What is the current through the middle resistor?

A) 3 A to the right
B) 3 A to the left
C) 9 A to the right
D) 9 A to the left
E) 1 A to the left

Question 38

What is the resistance of this combination of resistors?

A) 4.0 Ω
B) 12 Ω
C) 13 Ω
D) 14 Ω
E) 15 Ω

Question 39

Capacitors of values 1.0 F, 2.0 F, 3.0 F, and 6.0 F are connected in series across a 12 V power supply. Which capacitor has the greatest charge on it?

A) the 1.0 F capacitor
B) the 2.0 F capacitor
C) the 3.0 F capacitor
D) the 6.0 F capacitor
E) they are all equal

Question 40

Four 12 Ω resistors are connected together. What is the maximum resistance that can be attained with these resistors by connecting them in various ways?

A) 12 Ω
B) 24 Ω
C) 36 Ω
D) 48 Ω
E) 44 Ω

Question 41

A capacitor is connected in series with a resistor and a switch. With the switch open, the capacitor is charged to 9.0 V. When the switch is closed, how long will it take for the voltage across the capacitor to drop to 6.0 V if the time constant of the circuit is 4.0 s?

A) 0.3 s
B) 1.2 s
C) 1.6 s
D) 2.7 s
E) 12 s

Question 42

Three resistors, R₁ = 9.0 Ω, R₂ = 3.0 Ω, and R₃ = 1.0 Ω, are connected in parallel to a 9.0 V battery. What is the power dissipated by R₂?

A) 2.0 W
B) 3.0 W
C) 9.0 W
D) 27 W
E) 81 W

Question 43

A 2.0 Ω resistor is connected across a 6.0 V power supply. An ammeter with internal resistance of 1.0 Ω is used to measure the current in this circuit. What is the ammeter reading?

A) 4.0 A
B) 3.0 A
C) 2.0 A
D) 1.0 A
E) an ammeter with less resistance than the rest of the circuit will not produce a reading

Question 44

A flashlight, which uses two 1.5 V batteries in series, is turned on for 2.0 minutes. If the current in the flashlight is 100 mA, what is the energy dissipated?

A) 12 J
B) 9.0 J
C) 72 J
D) 36 J
E) 18 J

Question 45

In a series circuit consisting of a 12.0 V source of emf, a 2.00 mF capacitor, a 1.00 kΩ resistor and a switch, what is the voltage across the capacitor at a time of one time constant t after the switch is closed?

A) 0.632 V
B) 6.32 V
C) 7.59 V
D) 8.65 V

Question 46

Three resistors, R₁ = 4.0 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the total power dissipated by the circuit?

A) 2.0 W
B) 4.0 W
C) 5.1 W
D) 9.0 W
E) 20 W

Question 47

A good ammeter has ________ resistance and a good voltmeter has ________ resistance. "Good" means that it affects the system being measured by very little.

A) low, low
B) low, high
C) high, high
D) high, low
E) medium, no

Question 48

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. What is the time constant for this circuit?

A) 10.0 s
B) 2.00 s
C) 0.693 s
D) 0.0825 s
E) 1.00 ms

Question 49

By how much does the current fall after the switch is closed in a series RC circuit when three time constants have elapsed?

A) 5.0%
B) 38%
C) 62%
D) 95%
E) 100% since after 2 time constants the current is 0

Question 50

Raising the current through a resistor from 8.50 A to 11.3 A increases the power by

A) 33%.
B) 77%.
C) 113%.
D) 157%.
E) 0% (no change).

Question 51

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value?

A) 0.693 s
B) 2.30 s
C) 4.61 s
D) 9.00 s
E) 18.0 s

Question 52

Three resistors, R₁ = 9.00 Ω, R₂ = 3.00 Ω, and R₃ = 1.00 Ω, are connected in parallel to a 9.00 V battery. What is the total power dissipated in the circuit?

A) 180 W
B) 117 W
C) 99.0 W
D) 80.1 W
E) 18.0 W

Question 53

A variable resistor is connected to a constant voltage source. When the resistance is increased from 5.5 Ω to 9.3 Ω, what happens to the power dissipated?

A) no change
B) a 35% decrease
C) a 41% decrease
D) a 59% decrease
E) a 69% decrease

Question 54

A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 Ω resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value?

A) 0.693 s
B) 1.39 s
C) 2.00 s
D) 1.69 s
E) 0.0250 s

Question 55

Three resistors, R₁ = 4 Ω, R₂ = 3.0 Ω, and R₃ = 2.0 Ω, are connected in series to a 9.0 V battery. What is the power dissipated by R₁?

A) 2.0 W
B) 4.0 W
C) 5.1 W
D) 9.0 W
E) 2.3 W

Question 56

When the voltage across a resistor is decreased by 50%, what happens to the power dissipated?

A) It increases by 50%.
B) It decreases by 50%.
C) It decreases by 25%.
D) It decreases by 71%.
E) It decreases by 75%.

Question 57

A 1000 Ω resistor is in a circuit with 30.0 mA flowing through it. A voltmeter with internal resistance 1000 Ω is used to measure the voltage across the resistor. What is the reading on the voltmeter if a total current of 30.0 mA still flows in the circuit?

A) 30.0 V
B) 29.9 V
C) 27.0 V
D) 15.0 V
E) 3.00 V

Question 58

Copper has 8.5 × 10²⁸ current-carrying electrons per m³. A copper wire of radius 0.15 mm carries a current of 17 mA. What is the average drift velocity for the electrons?

A) 2.7 × 10⁻⁹ m/s
B) 56 × 10⁻⁶ m/s
C) 18 × 10⁻⁶ m/s
D) more information is needed for this calculation

Question 59

The watt, W, is equivalent to which of the following?

A) A·V
B) C·J
C) C/J
D) A/V
E) V²/A

Question 60

If R₁ = 6.0 Ω, R₂ = 8.0 Ω, R₃ = 2.0 Ω, ε₁ = 4.0 V, and ε₂ = 14 V, what is the power supplied to the circuit by ε₁?

A) 4.0 W
B) 8.0 W
C) 12 W
D) 16 W
E) 20 W

Question 61

Two carbon cylinders have radii r and 2r, and they both have length L. What is the resistance of the first if the resistance of the second is 12Ω?

A) 48 Ω
B) 12 Ω
C) 24 Ω
D) 3 Ω
E) 6 Ω

Question 62

In an RC circuit with an initially uncharged capacitor, the time constant is the time that is required for the current through the resistor to reach what percentage of its initial value?

A) 63%
B) 90%
C) 37%
D) 100%
E) 50%

Question 63

A capacitor in an RC circuit is charged, storing 1.25 mJ of energy. What is the time required to discharge this capacitor (say, to 1% of its initial charge), as compared to the time required to discharge (to 1%) an identical capacitor in an identical RC circuit which has stored 2.5 mJ of energy instead?

A) twice the time
B) half the time
C) the same time
D) the answer depends on the values of R and C.

Question 64

A wire of radius 0.15 mm is made of an unknown metal and carries a current of 8.4 mA. The drift velocity for electrons in the wire is measured to be 36 × 10⁻⁶ m/s. What is the charge carrier density of the metal from which the wire is made?

A) 1.3 × 10²⁹ m⁻³
B) 2.1 × 10²⁸ m⁻³
C) need more information to do this calculation.
D) 4.2 × 10³⁰ m⁻³

Question 65

In order to protect a delicate electronic component in a circuit from large currents, a fuse should be placed

A) internally inside the component.
B) in contact with the ground and the component.
C) in series with the component.
D) in parallel with the component.

Question 66

Two identical circuits have a capacitor in series with a resistor and a switch. In circuit A, the resistor has resistance R, while in circuit B, its resistance is 4R. The capacitors are identical. Each capacitor begins fully charged, and each circuit is open. When each circuit is completed (i.e., the switch in them is closed), the capacitor will begin to discharge. If a time t is required for circuit A's capacitor to fully discharge (say, by 99%), what time will be required for circuit B's capacitor to do the same?

A) 4t
B) 2t
C) t
D) 0.5t
E) 0.25t

Question 67

In a circuit, three pieces of wire labeled A, B and C are joined at a common point D. If wire B carries 1.5 mA in a direction away from D, and wire C carries current 1.3 mA toward D, what does wire A carry?

A) 0.2 mA toward D
B) 0.2 mA away from D
C) 2.8 mA toward D
D) unable to determine
E) 2.8 mA away from D

Question 68

An electron beam contains 1.5 × 10¹⁷ electrons per m³ and is confined to circular cross-sectional region of diameter 0.025 mm. The electrons in the beam are extremely energetic and travel at nearly the speed of light. What is the current in the beam?

A) 1.4 A
B) 3.5 mA
C) 350 mA
D) 14 mA

Question 69

A bird can safely land on a bare, high-voltage power line because

A) if both feet are touching the bare wire, they are at approximately the same potential, and therefore little or no current flows through the bird's body.
B) its internal resistance is very high, so very little current will flow.
C) the line cannot deliver enough current to harm it.
D) its feet are good insulators, and therefore it is protected.

Question 70

A carbon resistor is made of a cylinder of carbon, of diameter 7.4 mm. If the resistivity of carbon is 3.5 × 10⁻⁵ W·m, and a potential difference of 0.15 V causes a current of 12 A to flow through the resistor, what is the length of the cylinder?

A) 6.1 cm
B) 1.5 cm
C) 0.15 cm
D) 0.5 cm

Question 71

A carbon resistor is made of a cylinder of carbon, of length 1.5 cm. If the resistivity of carbon is 3.5 × 10⁻⁵ Ω·m, and a potential difference of 0.15 V causes a current of 12 A to flow through the resistor, what is the radius of the cylinder?

A) 6.5 mm
B) 12 mm
C) 3.7 mm
D) 1.2 mm

Question 72

In a three-pronged plug, the purpose of the third prong is to

A) provide a short circuit to ground.
B) prevent excessive power use by inefficient appliances.
C) create a stronger connection to the outlet when plugged in.
D) provide a path to ground in the event of a short circuit to the case of an appliance.

Question 73

Copper has 8.5 × 10²⁸ current carrying electrons per m³. A copper wire carries a current of 17 mA, and the drift velocity of the electrons is measured to be 18 × 10⁻⁶ m/s. What is the wire's radius?

A) 0.15 mm
B) 0.27 mm
C) 2.7 mm
D) 1.5 mm

Question 74

Two carbon cylinders have radii 2r and r, and the first has length 2L, while the second has length L. What is the resistance of the first if the resistance of the second is 12 Ω?

A) 48 Ω
B) 6 Ω
C) 12 Ω
D) 24 Ω

Question 75

In an RC circuit with an initially uncharged capacitor, the time constant is the time that is required for the charge on the capacitor to reach what percentage of its final value?

A) 50%
B) 37%
C) 100%
D) 63%
E) 90%