Deck 29: Inductance

Question 1

For the circuit shown in the figure, the inductors have no appreciable resistance and the switch has been open for a very long time.
(a) The instant after closing the switch, what is the current through the 60.0-Ω resistor?
(b) The instant after closing the switch, what is the potential difference across the 15.0-mH inductor?
(c) After the switch has been closed and left closed for a very long time, what is the potential drop across the 60.0-Ω resistor?

Answer 1

(a) 1.43 A
(b) 85.7 V
(c) 0.00 V

Question 2

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 7.3 × 10^-5 J/m³
B) 3.7 × 10^-5 J/m³
C) 3.6 × 10^-4 J/m³
D) 1.2 × 10^-4 J/m³
E) The density cannot be determined without knowing the volume.

Answer 2

3.7 × 10^-5 J/m³

Question 3

How much energy is stored in a room 3.0 m by 4.0 m by 2.4 m due to the earth's magnetic field with a strength of 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 570 mJ.
B) 29 mJ.
C) 10 mJ.
D) 100 mJ.
E) 570 mJ.

Answer 3

29 mJ.

Question 4

At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing?

A) 0.20 A/s
B) 0.40 A/s
C) 0.10 A/s
D) 0.80 A/s

Question 5

At what rate would the current in a 100-mH inductor have to change to induce an emf of 1000 V in the inductor?

A) 100 A/s
B) 1 A/s
C) 1000 A/s
D) 10,000 A/s
E) 10 A/s

Question 6

An insulated wire of diameter 1.0 mm and negligible resistance is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows through it? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 1.2 × 10^-4 J
B) 9.6 × 10^-4 J
C) 4.8 × 10^-4 J
D) 2.4 × 10^-4 J
E) 5.9 × 10^-5 J

Question 7

A series LR circuit contains an emf source of 14 V having no internal resistance, a resistor, a 34 H inductor having no appreciable resistance, and a switch. If the emf across the inductor is 80% of its maximum value 4.0 s after the switch is closed, what is the resistance of the resistor?

A) 14 Ω
B) 1.9 Ω
C) 1.5 Ω
D) 5.0 Ω

Question 8

A series circuit consists of a 0.55-H inductor with internal resistance of 8.0 Ω connected in series with a 4.0-Ω resistor, an open switch, and an ideal 12-V battery.
(a) When the switch is closed, what is the initial current through the 4.0-Ω resistor?
(b) What is the current through the 4.0-Ω resistor a very long time after the switch is closed?

Question 9

For the circuit shown in the figure, the switch has been open for a very long time.
(a) What is the potential drop across the 15.0-mH inductor just after closing the switch?
(b) What is the potential drop across the 70.0-µF capacitor after the switch has been closed for a very long time?

Question 10

What is the self-inductance of a solenoid 30.0 cm long having 100 turns of wire and a cross-sectional area of 1.00 × 10^-4 m2? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 4.19 nH
B) 4.19 pH
C) 4.19 µH
D) 4.19 mH
E) 4.19 H

Question 11

Which of the following statements about inductors are correct? There may be more than one correct choice.

A) When it is connected in a circuit, an inductor always resists having current flow through it.
B) Inductors store energy by building up charge.
C) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is reduced to zero in one time constant.
D) An inductor always resists any change in the current through it.
E) When an inductor and a resistor are connected in series with a DC battery, the current in the circuit is zero after a very long time.

Question 12

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, an open switch, and a 9.0-V ideal power source. After the switch is closed, what is the maximum power delivered by the power supply?

A) 0.40 W
B) 81 W
C) 0.090 W
D) 8.1 W
E) 0.81 W

Question 13

In the figure, the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of 9.6 A/s. The self-induced emf in the solenoid is found to be 8.4 V.
(a) What is the self-inductance of the solenoid?
(b) Which point, a or b is at higher potential?

Question 14

A 45-mH ideal inductor is connected in series with a 60-Ω resistor through an ideal 15-V DC power supply and an open switch. If the switch is closed at time t = 0 s, what is the current 7.0 ms later?

A) 250 mA
B) 650 mA
C) 550 mA
D) 280 mA
E) 850 mA

Question 15

An LR circuit contains an ideal 60-V battery, a 42-H inductor having no resistance, a 24-Ω resistor, and a switch S, all in series. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. How long after closing the switch will the potential difference across the inductor be 24 V?

A) 1.6 s
B) 1.4 s
C) 1.8 s
D) 1.9 s
E) 2.1 s

Question 16

An LR circuit contains an ideal 60-V battery, a 51-H inductor having no resistance, a 21-Ω resistor, and a switch S, all in series. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. When the voltage across the resistor is equal to the voltage across the inductor, what is the current in the circuit?

A) 1.4 A
B) 0.57 A
C) 1.1 A
D) 0.86 A
E) 1.7 A

Question 17

What resistance should be added in series with a 3.0-H inductor to complete an LR circuit with a time constant of 4.0 ms?

A) 0.75 k Ω
B) 12 Ω
C) 0.75 Ω
D) 2.5 Ω

Question 18

The mutual inductance between two coils is 10.0 mH. The current in the first coil changes uniformly from 2.70 A to 5.00 A in 0.160 s. If the second coil has a resistance of 0.600 Ω, what is the magnitude of the induced current in the second coil?

Question 19

A 96-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoid at its center. The coil's resistance is 9.9 ohms. The mutual inductance of the coil and solenoid is 31 μH. At a given instant, the current in the solenoid is 540 mA, and is decreasing at the rate of 2.5 A/s. At the given instant, what is the magnitude of the induced current in the coil? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 7.8 μA
B) 6.3 μA
C) 9.4 μA
D) 11 μA
E) 13 μA

Question 20

A solenoid of length 0.700 m having a circular cross-section of radius 5.00 cm stores 6.00 µJ of energy when a 0.400-A current runs through it. What is the winding density of the solenoid? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 865 turns/m
B) 472 turns/m
C) 1080 turns/m
D) 104 turns/m
E) 327 turns/m

Question 21

In an LC circuit containing a 40-mH ideal inductor and a 1.2-mF capacitor, the maximum charge on the capacitor is 45 mC during the oscillations. What is the maximum current through the inductor during the oscillations?

A) 3.7 A
B) 42 A
C) 10 A
D) 6.5 A
E) 2.5 A

Question 22

Consider the circuit shown in the figure. The battery has emf ε = 25 volts and negligible internal resistance. The inductance is L = 0.80 H and the resistances are R₁ = 12 Ω and R₂ = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch is closed.
(a) What is the current in the resistor R₁ just after the switch is closed?
(b) After leaving the switch closed for a very long time, it is opened again. Just after it is opened, what is the current in R₁?

Question 23

A charged capacitor is connected to an ideal inductor. At time t = 0, the charge on the capacitor is equal to 6.00 μC. At time t = 2.00 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?

A) 2.38 mA
B) 4.71 mA
C) 0.780 mA
D) 1.53 mA
E) 1.19 mA

Question 24

A charged capacitor is connected to an ideal inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. At time t = 0 the capacitor is fully charged. At a given instant later the charge on the capacitor is measured to be 3.0 μC and the current in the circuit is equal to 75 μA. What is the maximum charge of the capacitor?

A) 6.0 µC
B) 10 µC
C) 8.0 µC
D) 2.0 µC
E) 4.0 µC

Question 25

An ideal solenoid is 18.5 cm long, has a circular cross-section 2.20 cm in diameter, and contains 545 equally spaced thin windings. This solenoid is connected in a series circuit with an open switch, a 15.0-Ω resistor, and a battery of internal resistance 5.00 Ω and open-circuit terminal voltage of 25.0 V. (μ₀ = 4π × 10^-7 T ∙ m/A)
(a) What is the maximum amount of energy that the solenoid will store after closing the switch?
(b) How long after closing the switch will it take for the stored energy in the solenoid to reach one-half of its maximum value?

Question 26

An LC circuit consists of a 3.4-µF capacitor and a coil with a self-inductance 0.080 H and no appreciable resistance. At t = 0 the capacitor has a charge of 5.4 µC and the current in the inductor is zero.
(a) How long after t = 0 will the current in the circuit be maximum?
(b) What will be this maximum current?