Alternating Current — Practice

Question 1

The peak voltage of an ac supply is 400 V. Find the rms voltage, and find the peak current if the rms current is 5.0 A.

Accepted Answer

Divide the peak by root two for rms, and multiply rms by root two for peak. Answer: V_rms = 283 V; peak current = 7.07 A.

Question 2

An inductor of 0.20 H is connected to a 50 Hz supply. Find its reactance.

Accepted Answer

Use X_L = omega L with omega = 2 pi f, so the frequency must be converted first. Answer: X_L = 62.8 ohm.

Question 3

A 50 ohm resistor is connected to a 220 V, 50 Hz supply. Find the rms current and the power dissipated.

Accepted Answer

Ohm's law applies directly to rms values in a pure resistor, where the power factor is one. Answer: I_rms = 4.4 A; P = 968 W.

Question 4

A 100 microfarad capacitor is connected to a 110 V, 60 Hz supply. Find its reactance and the rms current.

Accepted Answer

Compute X_C = 1/(omega C), then divide the rms voltage by it. Answer: X_C = 26.5 ohm; I_rms = 4.15 A.

Question 5

A series circuit has R = 30 ohm, X_L = 60 ohm and X_C = 20 ohm. Find the impedance and the phase angle, and say whether the current leads or lags.

Accepted Answer

Combine the reactances first, then use Pythagoras and the tangent relation. Answer: Z = 50 ohm; phi = 53 degrees; the current lags, since the circuit is inductive.

Question 6

A series LCR circuit has L = 2.0 H and C = 50 microfarad. Find the resonant angular frequency and the impedance at resonance if R = 25 ohm.

Accepted Answer

Apply omega_0 = 1 over the square root of LC, then recall what Z reduces to at resonance. Answer: omega_0 = 100 rad/s; Z = 25 ohm.

Question 7

A circuit draws 4.0 A rms from a 200 V rms supply with a phase angle of 60 degrees. Find the average power, the apparent power, and the wattless current.

Accepted Answer

Use P = V I cos(phi) for the true power and I sin(phi) for the wattless component. Answer: P = 400 W; apparent power 800 VA; wattless current 3.46 A.

Question 8

A transformer has 200 primary turns and 3000 secondary turns, with 220 V applied to the primary. If the secondary supplies 0.50 A, find the secondary voltage and the primary current for an ideal transformer.

Accepted Answer

Use the turns ratio for voltage and its inverse for current, since ideal input and output powers are equal. Answer: V_s = 3300 V; I_p = 7.5 A.

Question 9

A series LCR circuit with R = 20 ohm, L = 1.5 H and C = 35 microfarad is driven at its resonant frequency by a 200 V supply. Find the power absorbed.

Accepted Answer

At resonance the impedance collapses to R alone, so the power takes its maximum value. Answer: P = 2000 W.

Practice — Alternating Current

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