Question 1

A current of 5 A is flowing in a 20 mH inductor. The energy stored in the magnetic field of this inductor is
A)1 J.
B)0.25 J.
C)0.50 J.
D)0.
E)dependent upon the resistance of the inductor.

Accepted Answer

The energy stored in an inductor is given by the formula $ \frac{1}{2} L I^2 $. Substituting the given values, $ L = 20 \, \text{mH} = 0.02 \, \text{H} $ and $ I = 5 \, \text{A} $, the energy is $ \frac{1}{2} \times 0.02 \times 5^2 = 0.25 \, \text{J} $.

Question 2

The energy stored in the earth's magnetic field with a strength of 0.5 × 10^-4 T in a room 3.0 m by 4.0 m by 2.4 m is A)570 mJ. B)29 mJ C)10 mJ. D)100 mJ. E)zero.

Accepted Answer

The energy stored in a magnetic field is given by the formula: U = (B²/2μ₀) × Volume. Substituting B = 0.5 × 10⁻⁴ T, μ₀ = 4π × 10⁻⁷ T·m/A, and the volume of the room (3.0 m × 4.0 m × 2.4 m), we find the energy to be approximately 29 mJ.

Question 3

A charged capacitor is connected to an inductor. At time t = 0 the charge on the capacitor is Q = 6μC. At time t = 2 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)0.78 mA
D)1.53 mA
E)1.19 mA

Accepted Answer

The system is an LC circuit undergoing simple harmonic oscillations. The charge on the capacitor and the current in the inductor are related by conservation of energy. At the first instance when the charge is zero, the energy is entirely in the inductor as magnetic energy, which means the current is at its maximum. The maximum current (I_max) can be found using the formula I_max = Q_max * ω, where ω = 2π/T and T = 4 ms (since the charge is zero at t = 2 ms, which is a quarter of the period). Therefore, I_max = 6μC * (2π/4ms) = 4.71 mA.

Question 4

A charged capacitor is connected to an 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 Q = 3 μC and the current in the circuit is equal to 75 μA. What is the maximum charge of the capacitor?
A)6 μC
B)10 μC
C)8 μC
D)2 μC
E)4 μC

Accepted Answer

The answer of A charged capacitor is connected to an...

Question 5

A solenoid of inductance L = 50 mH has a magnetic energy U = 3 x 10^-4 J with a density u = 0.0042 J/ m³. What is the winding density n of the solenoid? A)58 turns/m B)1584 turns/m C)1200 turns/m D)234 turns/m E)746 turns/m

Accepted Answer

The answer of A solenoid of inductance L = 50...

Question 6

In an LR series circuit connected to a dc source and a switch, the inductor gets 40% of its maximum current 1.8 s after the switch is closed at t = 0 s. What is the time constant of this circuit?
A)0.80 s
B)1.5 s
C)2.5 s
D)3.5 s
E)5.5 s

Accepted Answer

The answer of In an LR series circuit connected to...

Question 7

A 25-mH inductor is connected in series with a 20-Ω resistor through a 15-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the current when t = 2.0 ms?
A)0.40 A
B)0.50 A
C)0.60 A
D)0.70 A
E)0.80 A

Accepted Answer

The current in the circuit follows the equation:

$$ I(t) = \frac{V}{R}(1-e^{-\frac{R}{L}t}) $$

where V is the voltage of the power supply, R is the resistance, L is the inductance, and t is the time since the switch is closed. Plugging in the given values, we get:

$$ I(t) = \frac{15}{20}(1-e^{-\frac{20}{0.025}t}) $$

When t = 2.0 ms, we have:

$$ I(2.0 	ext{ ms}) = \frac{15}{20}(1-e^{-\frac{20}{0.025}(2 	imes 10^{-3})}) \approx 0.60 	ext{ A} $$

Therefore, the answer is choice C, 0.60 A.

Question 8

A 45-mH inductor is connected in series with a 60-Ω resistor through a 15-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the current after 7.0 ms?
A)250 mA
B)650 mA
C)550 mA
D)280 mA
E)850 mA

Accepted Answer

The answer of A 45-mH inductor is connected in series...

Question 9

An LC circuit with an inductance of 36 mH and a capacitance of 25 mF will oscillate with what frequency?
A)1.44 Hz
B)33 Hz
C)0.03 Hz
D)5.3 Hz
E)210 Hz

Accepted Answer

The answer of An LC circuit with an inductance of...

Question 10

A 25.0-mH inductor is connected in series to a 20.0-Ω resistor through a 15.0-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the time constant of this circuit? A)0.800 × 10^-3 s B)0.800 × 10^-2 s C)0.500 s D)1.25 × 10^-3 s E)12.5 × 10^-2 s

Accepted Answer

The answer of A 25.0-mH inductor is connected in series...

Question 11

An LR circuit includes a resistor of resistance R, an inductor of inductance L and a battery of emf E = 10 V. At time t = 0 the current in the circuit is I = 0. At time t = 6.1 ms the current is I = 0.66 A. What are the values of L and R?
A)not enough information given
B)L = 15 mH, R = 20 Ω
C)L = 10 mH, R = 100 Ω
D)L = 50 mH, R = 150 Ω
E)L = 2 mH, R = 10 Ω

Accepted Answer

The answer of An LR circuit includes a resistor of...

Question 12

A solenoid of length l = 0.7 m and radius R = 5 cm stores an amount of energy U = 6 × 10^-6 J when a current I = 0.4 A passes through it. What is the winding density of the solenoid? A)865 turns /m B)472 turns/m C)1078 turns/m D)104 turns/m E)327 turns /m

Accepted Answer

The answer of A solenoid of length l = 0.7...

Question 13

Starting from zero, the electric current takes 2 seconds to reach half its maximum possible value in an RL circuit with a resistance R, an inductance L and a battery of emf E. How long will the current take to reach 75% its maximum value (measured from the moment when I = 0)?
A)8 s
B)4 s
C)10 s
D)1 s
E)2 s

Accepted Answer

The time constant τ for an RL circuit is L/R. The current I(t) in an RL circuit is given by I(t) = I_max(1 - e^(-t/τ)). Given that it takes 2 seconds to reach half its maximum value, we can use this to find τ. Solving 0.5 = 1 - e^(-2/τ) gives τ = 2/ln(2). To find the time to reach 75% of the maximum value, solve 0.75 = 1 - e^(-t/τ), which gives t = 4 seconds.

Question 14

A series LR circuit consists of a 2.0-H inductor with negligible internal resistance, a 100-ohm resistor, a switch, and a 9.0-V 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

Accepted Answer

The answer of A series LR circuit consists of a...

Question 15

A capacitor of capacitance C = 5 μF and initial charge Q = 30 μC is connected to an inductor of inductance L = 20 mH. What is the electric current in the circuit when the energy stored in the capacitor is 25% of its maximum value?
A)0.001 A
B)0.08 A
C)0.04 A
D)0.02 A
E)0.01 A

Accepted Answer

The answer of A capacitor of capacitance C = 5...

Question 16

A wire of diameter d = 1 mm is wrapped around a cylindrical core of radius R = 5 cm and length l = 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.2 A passes through it? 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)0.6 × 10^-4 J

Accepted Answer

The answer of A wire of diameter d = 1...

Question 17

Calculate the radius that a loop should have so that the magnetic energy density at its center is equal to 6 mJ/ m³ when a current I = 20A passes through the loop? A)26 cm B)10 cm C)7 cm D)18 cm E)15 cm

Accepted Answer

The answer of Calculate the radius that a loop should...

Question 18

In an LC circuit with an inductance of 40 mH and capacitance of 1.2 mF, the maximum charge on the capacitor is 45 mC during the oscillations which occur. 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

Accepted Answer

The answer of In an LC circuit with an inductance...

Question 19

An LR circuit consists of a 35-mH inductor, a resistance of 12 ohms, an 18-V battery, and a switch. What is the current 5.0 ms after the switch is closed?
A)5.0 A
B)0.27 A
C)0.053 A
D)0.75 A
E)1.2 A

Accepted Answer

The answer of An LR circuit consists of a 35-mH...

Question 20

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 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)cannot be determined with the information given

Accepted Answer

The energy density (u) in a magnetic field is given by u = B²/(2μ₀), where B is the magnetic field and μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A). For a long straight wire, B = μ₀I/(2πr). Substituting I = 12 A and r = 0.25 m, we find B and then calculate u.

Quiz 30: Inductance, Electromagnetic Oscillations, and Ac Circuits

A current of 5 A is flowing in a 20 mH inductor. The energy stored in the magnetic field of this inductor is

The energy stored in the earth's magnetic field with a strength of 0.5 × 10^-4 T in a room 3.0 m by 4.0 m by 2.4 m is

A charged capacitor is connected to an inductor. At time t = 0 the charge on the capacitor is Q = 6μC. At time t = 2 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?

A solenoid of inductance L = 50 mH has a magnetic energy U = 3 x 10^-4 J with a density u = 0.0042 J/ m³. What is the winding density n of the solenoid?

In an LR series circuit connected to a dc source and a switch, the inductor gets 40% of its maximum current 1.8 s after the switch is closed at t = 0 s. What is the time constant of this circuit?

A 25-mH inductor is connected in series with a 20-Ω resistor through a 15-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the current when t = 2.0 ms?

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

An LC circuit with an inductance of 36 mH and a capacitance of 25 mF will oscillate with what frequency?

A 25.0-mH inductor is connected in series to a 20.0-Ω resistor through a 15.0-V dc power supply and a switch. If the switch is closed at t = 0 s, what is the time constant of this circuit?

An LR circuit includes a resistor of resistance R, an inductor of inductance L and a battery of emf E = 10 V. At time t = 0 the current in the circuit is I = 0. At time t = 6.1 ms the current is I = 0.66 A. What are the values of L and R?

A solenoid of length l = 0.7 m and radius R = 5 cm stores an amount of energy U = 6 × 10^-6 J when a current I = 0.4 A passes through it. What is the winding density of the solenoid?

Starting from zero, the electric current takes 2 seconds to reach half its maximum possible value in an RL circuit with a resistance R, an inductance L and a battery of emf E. How long will the current take to reach 75% its maximum value (measured from the moment when I = 0) ?

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

A capacitor of capacitance C = 5 μF and initial charge Q = 30 μC is connected to an inductor of inductance L = 20 mH. What is the electric current in the circuit when the energy stored in the capacitor is 25% of its maximum value?

A wire of diameter d = 1 mm is wrapped around a cylindrical core of radius R = 5 cm and length l = 30 cm to build a solenoid. What is the energy stored in this solenoid when a current I = 0.2 A passes through it?

Calculate the radius that a loop should have so that the magnetic energy density at its center is equal to 6 mJ/ m³ when a current I = 20A passes through the loop?

In an LC circuit with an inductance of 40 mH and capacitance of 1.2 mF, the maximum charge on the capacitor is 45 mC during the oscillations which occur. What is the maximum current through the inductor during the oscillations?

An LR circuit consists of a 35-mH inductor, a resistance of 12 ohms, an 18-V battery, and a switch. What is the current 5.0 ms after the switch is closed?

What is the energy density in the magnetic field 25 cm from a long straight wire carrying a current of 12 A?