Question 1

A transformer is a practical application of which physical principle?

Accepted Answer

Mutual inductance between two coils

Question 2

The mutual inductance $$M$$ between two coils is given by which of the following formulas for a solenoid of length $$l$$, cross-sectional area $$A$$, $$N_1$$ turns (solenoid), and $$N_2$$ turns (coil wrapped around it)?

Accepted Answer

$$M = \mu_0$ N_1$ N_2$ A / l$$

Question 3

Which of the following best describes the energy stored in an inductor with inductance $$L$$ carrying current $$I$$?

Accepted Answer

$$U = \frac{1}{2} L I^2$

Question 4

A coaxial cable has inner radius $$r_1$$ and outer radius $$r_2. $$What is the inductance per unit length?

Accepted Answer

$$L/l = \frac{\mu_0$}{2\pi} \ln \frac{r_2$}{r_1$}$$

Question 5

In an LR circuit with a DC voltage source $$V_0$$, resistor $$R$$, and inductor $$L$$, what is the time constant $$	au$$ for the current to reach approximately 63% of its final value?

Accepted Answer

$$	au = L/R$$

Question 6

For an LC circuit, the angular frequency of oscillation is:

Accepted Answer

$$\omega = \frac{1}{\sqrt{LC}}$$

Question 7

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

Accepted Answer

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

Question 8

In an RLC series circuit driven by an AC source, the total impedance $$Z is $$given by:

Accepted Answer

$$Z = R + j(\omega L - 1/\omega C)$$

Question 9

What is the resonance frequency $$\$$omega_0$$ for a series RLC circuit?

Accepted Answer

$$\$$omega_0$$ = \frac{1}{\sqrt{LC}}$$

Question 10

Which of the following best describes the phase relationship between current and voltage in a pure inductor connected to an AC source?

Accepted Answer

Voltage leads current by $$\frac{\pi}{2}$$

Question 11

A low-pass RC filter has a transfer function $$H(j\omega) = \frac{1}{1 + j\omega RC}. $$What is the magnitude of the transfer function at the cutoff frequency $$\omega_c$$?

Accepted Answer

$$|H(j\omega_c)| = \frac{1}{\sqrt{2}}$$

Question 12

In a high-pass RC filter, what happens to the output voltage as the input frequency approaches zero?

Accepted Answer

The output voltage approaches zero.

Question 13

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

Accepted Answer

$$Z_C = \frac{1}{j\omega C}$$

Question 14

A band-pass filter is designed to:

Accepted Answer

Allow a specific range of frequencies to pass while attenuating frequencies outside this range.

Question 15

In a damped RLC circuit, which case corresponds to the underdamped regime?

Accepted Answer

$$R^2$$ \u003c 4L/C$$

Question 16

The energy density stored in a magnetic field is given by:

Accepted Answer

$$u = \frac{1}{2} \frac{B^2$}{\mu_0$}$$

Question 17

Which of the following best describes the physical meaning of the imaginary part of impedance in an AC circuit?

Accepted Answer

It represents the energy storage part of the circuit element.

Question 18

In a series RLC circuit at resonance, what is the relationship between the inductive reactance $$X_L$$ and the capacitive reactance $$X_C$$?

Accepted Answer

$$X_L = X_C$$

Question 19

Which of the following is the correct expression for the transfer function $$H(j\omega) of a $$low-pass RC filter?

Accepted Answer

$$H(j\omega) = \frac{1}{1 + j\omega RC}$$

Question 20

A real-world application of a resonance circuit is found in FM radios. What component is typically adjusted to tune the radio to different frequencies?

Accepted Answer

The capacitance of a variable capacitor

Inductance, Electromagnetic Oscillations, and AC Circuits: Study Notes

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