An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a sinusoidal source with an rms voltage of 12 V. At what frequency will the rms voltage across the resistor be equal to that across the inductor?
A) 114 kHz
B) 5.5 kHz
C) 54 kHz
D) 18 kHz

Question

Quizplus · Accepted Answer

The rms voltage across an inductor is given by V_L = jωL*I, where ω is the angular frequency and I is the rms current through the inductor. The rms voltage across a resistor is given by V_R = IR, where R is the resistance and I is the rms current through the resistor.

We want V_R to be equal to V_L, so we set them equal to each other and solve for ω:

jωL*I = IR

ωL = R

ω = R/L

Plugging in the given values, we get:

ω = 75,000 Ω / 220 mH = 340.91 kHz

However, this is the angular frequency. To find the frequency in hertz, we divide by 2π:

f = ω/2π = 54.27 kHz

Therefore, the answer is C: 54 kHz.

An Ac Circuit Consists of a 220 MH Inductor in Series