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

$$V_{\text{rms}} = 120\ \text{V}$$

$$P_{\text{av}} = \frac{1}{2} VI$$

$$P_{\text{av}} = V_{\text{rms}} I_{\text{rms}} \cos \phi$$

Question 1

A radio in a classic car tunes to a particular station by adjusting a circuit element. Which element is most likely being adjusted, and why?

Accepted Answer

The capacitor, because changing capacitance alters the resonant frequency of the circuit.

Question 2

Which equation correctly describes the instantaneous current in a sinusoidal AC circuit?

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

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

Question 4

A wall socket in the United States has a voltage amplitude of $$V = 170\ 	ext{V}. $$What is the rms voltage?

Accepted Answer

$$V_{	ext{rms}} = 120\ 	ext{V}$$

Question 5

In an AC circuit with only a resistor, how are the voltage and current related?

Accepted Answer

Voltage and current are in phase.

Question 6

What is the amplitude of voltage across a resistor in an AC circuit?

Accepted Answer

$$V_R = IR$$

Question 7

For an inductor in an AC circuit, what is the expression for inductive reactance?

Accepted Answer

$$X_L = \omega L$$

Question 8

How does the voltage across an inductor relate to the current in an AC circuit?

Accepted Answer

Voltage leads current by 90°.

Question 9

What is the capacitive reactance for a capacitor in an AC circuit?

Accepted Answer

$$X_C = \frac{1}{\omega C}$$

Question 10

In a loudspeaker crossover network, what is the function of the capacitor in the tweeter branch?

Accepted Answer

It blocks low-frequency signals and passes high-frequency signals.

Question 11

What is the impedance $$Z of an L-R-C $$series circuit?

Accepted Answer

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

Question 12

A patient is measured for body fat using bioelectric impedance analysis. Why is an AC voltage used instead of DC?

Accepted Answer

AC voltage can penetrate fat and water differently, allowing measurement of body composition.

Question 13

What is the average power delivered to a resistor in an AC circuit?

Accepted Answer

$$P_{	ext{av}} = \frac{1}{2} VI$$

Question 14

For a pure inductor or capacitor in an AC circuit, what is the average power delivered?

Accepted Answer

The average power is zero.

Question 15

In a general AC circuit, what is the formula for average power in terms of rms values and the power factor?

Accepted Answer

$$P_{	ext{av}} = V_{	ext{rms}} I_{	ext{rms}} \cos \phi$$

Question 16

At resonance in an L-R-C series circuit, what is the relationship between inductive and capacitive reactance?

Accepted Answer

$$X_L = X_C$$

Question 17

What is the resonance angular frequency $$\$$omega_0$$ for an L-R-C series circuit?

Accepted Answer

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

Question 18

A transformer has 100 turns in the primary coil and 200 turns in the secondary coil. If the primary voltage is 120 V, what is the secondary voltage?

Accepted Answer

240 V

Question 19

Which statement about the power factor in AC circuits is correct?

Accepted Answer

The power factor is 1 for a pure resistor.

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

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