Q: In a series LR circuit with $$L = 0.220\ \mathrm{H}$$ and $$R = 30\ \Omega$$, connected to a $$12.0\ \mathrm{V}$$ battery, what is the time constant $$\tau$$?

$$\tau = \frac{L}{R} = \frac{0.220}{30} = 0.0073\ \mathrm{s}$$

Question 1

Which of the following best describes the physical meaning of the mutual inductance $$M_{21} in $$the equation $$\$$\mathcal{E}_2 = -M_{21} \frac{$$dI_1$$}{dt}\$?

Accepted Answer

It is the proportionality constant relating the induced emf in coil 2 to the rate of change of current in coil 1.

Question 2

Given the formula $$\$$	au = \frac{L}{R}\$ for the time constant of an LR circuit, what does the time constant physically represent?

Accepted Answer

The time it takes for the current to reach approximately 63% of its final value after the switch is closed.

Question 3

In the context of electromagnetic oscillations in an LC circuit, which of the following statements is correct?

Accepted Answer

The total energy oscillates between the electric field of the capacitor and the magnetic field of the inductor.

Question 4

A 1200-pF capacitor is fully charged to 500 V and then connected to a 75-mH inductor. What is the frequency of oscillation in the resulting LC circuit?

Accepted Answer

$$f = \frac{1}{2\pi\sqrt{LC}}$$

Question 5

In an LRC circuit, resonance occurs when:

Accepted Answer

$$X_L = X_C$$

Question 6

Which of the following is true about the current and voltage in an inductor in an AC circuit?

Accepted Answer

The current lags the voltage by $$\$$\frac{\pi}{2}\$ radians.

Question 7

A high-pass filter is constructed using a capacitor. What is its main function in an AC circuit?

Accepted Answer

It allows high-frequency signals to pass while blocking low-frequency (including DC) signals.

Question 8

The impedance $$Z of a $$series LRC circuit is given by which of the following expressions?

Accepted Answer

$$Z = \sqrt{R^2$ + (X_L - X_C)^2$}$$

Question 9

In a transformer, which principle allows the transfer of energy from the primary coil to the secondary coil?

Accepted Answer

Mutual inductance

Question 10

Which of the following best describes the effect of increasing the resistance in an LRC circuit at resonance?

Accepted Answer

The peak current at resonance decreases.

Question 11

A solenoid has $$N$$ turns, cross-sectional area $$A$$, and length $$l. $$Which formula gives its self-inductance $$L$$?

Accepted Answer

$$L = \mu_0$ \frac{N^2$ A}{l}$$

Question 12

In a series LR circuit with $$L = 0.220\ \mathrm{H}$$ and $$R = 30\ \Omega$$, connected to a $$12.0\ \mathrm{V}$$ battery, what is the time constant $$	au$$?

Accepted Answer

$$	au = \frac{L}{R} = \frac{0.220}{30} = 0.0073\ \mathrm{s}$$

Question 13

Which of the following is a correct statement about the energy in an ideal LC circuit?

Accepted Answer

The total energy remains constant and oscillates between the capacitor and the inductor.

Question 14

In a phasor diagram for an LRC circuit, what does the phase angle $$\phi$$ represent?

Accepted Answer

The phase difference between the total voltage and the current.

Question 15

Which of the following is true about the current in a capacitor in an AC circuit?

Accepted Answer

The current leads the voltage by $$\$$\frac{\pi}{2}\$ radians.

Question 16

What is the condition for maximum power transfer between two connected circuits?

Accepted Answer

The output impedance of the first circuit equals the input impedance of the second circuit.

Question 17

Which of the following is a practical application of mutual inductance?

Accepted Answer

Wireless charging of devices

Question 18

In a three-phase AC power system, what is the main advantage over a single-phase system?

Accepted Answer

The power flow is much smoother.

Electromagnetic Induction, AC Circuits, and Wave Optics: Study Notes

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