Question 1

Which of the following best describes the energy storage mechanism of an inductor in a circuit?

Accepted Answer

An inductor stores energy in its magnetic field, which is proportional to the square of the current.

Question 2

Given a solenoid with $$n$$ turns per unit length, cross-sectional area $$A$$, and length $$\ell$$, what is the correct formula for its inductance $$L$$?

Accepted Answer

$$L = \mu_0$ n^2$ \ell A$$

Question 3

In an RL circuit, the time constant $$	au is $$defined as:

Accepted Answer

$$	au = \frac{L}{R}$$

Question 4

A resistor ($$R) $$and inductor ($$L) $$are connected in series to a battery of emf $$\mathcal{E}. $$What is the expression for the current $$i(t) as a $$function of time after the switch is closed?

Accepted Answer

$$i(t) = \frac{\mathcal{E}}{R} \left(1 - e$$^{-tR/L}$$\right)$$

Question 5

Which of the following statements about the phase relationship in a purely inductive AC circuit is correct?

Accepted Answer

The voltage leads the current by $$90^\circ.$$

Question 6

A $$8.00\,\mu	ext{F}$$ capacitor is connected to an AC generator with an rms voltage of $$150\,	ext{V}$$ and a frequency of $$60\,	ext{Hz}. $$What is the capacitive reactance $$X_C$$?

Accepted Answer

$$X_C = 332\,\Omega$$

Question 7

In a series RLC circuit, the impedance $$Z is $$given by:

Accepted Answer

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

Question 8

A transformer has $$N_p = 100$$ turns on the primary and $$N_s = 1000$$ turns on the secondary. If the input voltage is $$120\,	ext{V}$$, what is the output voltage?

Accepted Answer

$$1200\,	ext{V}$$

Question 9

Which of the following best explains why high voltage and low current are used for long-distance power transmission?

Accepted Answer

To minimize $$I^2R$ power losses in the transmission lines.

Question 10

At resonance in a series RLC circuit, which of the following is true?

Accepted Answer

$$X_L = X_C$$

Question 11

The average power dissipated in a resistor in an AC circuit is given by:

Accepted Answer

$$P_{av} = I_{rms}^2 R$$

Question 12

A series RLC AC circuit has $$R=250\,\Omega$$, $$L=0.600\,	ext{H}$$, $$C=3.50\,\mu	ext{F}$$, $$f=60.0\,	ext{Hz}$$, and $$\Delta V_{max}=150\,	ext{V}. $$What is the maximum current in the circuit?

Accepted Answer

$$I_{max} = 0.255\,	ext{A}$$

Question 13

In a purely capacitive AC circuit, what is the phase relationship between the current and the voltage across the capacitor?

Accepted Answer

The current leads the voltage by $$90^\circ.$$

Question 14

Which equation correctly gives the resonance frequency $$f_0$$ for a series RLC circuit?

Accepted Answer

$$f_0$$ = \frac{1}{2\pi\sqrt{LC}}$$

Question 15

A generator produces $$100\,	ext{A} at$$ $$4000\,	ext{V}. $$The voltage is stepped up to $$240,000\,	ext{V}$$ for transmission. If the resistance of the line is $$30\,\Omega$$, what is the percentage of power lost in the transmission line?

Accepted Answer

$$0.021\%$$

Question 16

Which of the following is true about energy in a pure inductor in an AC circuit?

Accepted Answer

Energy is alternately stored in and returned from the magnetic field, with no net energy loss.

Question 17

If the frequency of an AC source connected to a capacitor is doubled, what happens to the capacitive reactance $$X_C$$?

Accepted Answer

$$X_C is $$halved.

Question 18

In a phasor diagram for a series RLC circuit, which axis does the voltage across the inductor align with?

Accepted Answer

The positive $$y-$$axis, since it leads the current by $$90^\circ.$$

Question 19

Which of the following is the correct expression for the energy stored in the magnetic field of an inductor?

Accepted Answer

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

AC Circuits: Inductors, Capacitors, and RLC Circuits

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