Question 1

A radio in a classic car tunes to a particular station by adjusting a circuit element. Which component is primarily responsible for selecting the frequency to which the radio is tuned, and what is the physical principle behind this selection?

Accepted Answer

The capacitor, which, together with the inductor, forms a resonant L-C circuit that selects the frequency by resonance.

Question 2

Which of the following equations correctly gives the instantaneous current in an AC circuit with current amplitude $$I$$ and angular frequency $$\omega$$?

Accepted Answer

$$i = I \cos \omega t$$

Question 3

What is the root-mean-square (rms) value of a sinusoidal current with amplitude $$I$$?

Accepted Answer

$$I_{\mathrm{rms}} = \frac{I}{\sqrt{2}}$$

Question 4

A household wall socket in North America provides an rms voltage of 120 V. What is the amplitude (maximum value) of the voltage supplied?

Accepted Answer

$$V = 170\ \mathrm{V}$$

Question 5

In an AC circuit containing only a resistor, which statement about the phase relationship between voltage and current is correct?

Accepted Answer

The voltage and current are in phase.

Question 6

The amplitude of the voltage across an inductor in an AC circuit is given by which equation?

Accepted Answer

$$V_L = IX_L$$

Question 7

If the frequency of the AC source is increased, what happens to the inductive reactance $$X_L$$ and the capacitive reactance $$X_C$$?

Accepted Answer

$$X_L$$ increases and $$X_C$$ decreases.

Question 8

A loudspeaker system uses a capacitor in the tweeter branch and an inductor in the woofer branch. What is the purpose of this arrangement?

Accepted Answer

To allow high frequencies to the tweeter and low frequencies to the woofer.

Question 9

The impedance $$Z of a $$series L-R-C circuit is given by which formula?

Accepted Answer

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

Question 10

At resonance in a series L-R-C circuit, which of the following is true?

Accepted Answer

$$X_L = X_C$$

Question 11

A transformer has 100 turns on the primary coil and 400 turns on the secondary coil. If the primary voltage is 120 V, what is the secondary voltage (assuming an ideal transformer)?

Accepted Answer

$$V_2 = 480$$\ \mathrm{V}$$

Question 12

Which equation gives the resonance angular frequency $$\$$omega_0$$ for a series L-R-C circuit?

Accepted Answer

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

Question 13

In a pure inductor connected to an AC source, what is the average power consumed over a full cycle?

Accepted Answer

It is zero.

Question 14

A bioelectric impedance analysis device applies a small AC voltage to a patient’s body and measures the resulting current. What property of the body does this technique primarily assess?

Accepted Answer

The electrical conductivity, which is related to body composition (water and fat content).

Question 15

Which of the following best describes the power factor in an AC circuit?

Accepted Answer

It is the ratio of the average power to the apparent power, given by $$\cos \phi.$$

Question 16

A series L-R-C circuit has $$R = 100\ \Omega$$, $$L = 0.5\ \mathrm{H}$$, and $$C = 20\ \mu\mathrm{F}. $$What is the resonance frequency $$f_0 in Hz$$? (Use $$\$$omega_0$$ = \frac{1}{\sqrt{LC}}$$ and $$f_0$$ = \$$omega_0 / 2$$\pi$$)

Accepted Answer

$$f_0$$ \approx 159\ \mathrm{Hz}$$

Question 17

Which of the following statements about transformers is correct?

Accepted Answer

The ratio of secondary to primary voltage equals the ratio of the number of turns in the secondary to the primary coil.

Question 18

In a series L-R-C circuit, if $$X_L \u003e X_C$$, what is the phase relationship between the source voltage and the current?

Accepted Answer

The source voltage leads the current.

Question 19

Which of the following real-world applications best illustrates the use of resonance in an L-R-C circuit?

Accepted Answer

A radio tuning to a specific station frequency.

Alternating Current (AC) Circuits: Concepts, Analysis, and Applications

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