An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the inductor be?
A) 5.4 V
B) 23 V
C) 6.6 V
D) 0.20 V

Question

Quizplus · Accepted Answer

The rms voltage across the inductor can be found using the formula $ V_L = I \cdot X_L $, where $ X_L = 2\pi f L $. First, calculate the inductive reactance $ X_L = 2\pi \times 55,000 \times 0.220 = 76.8 \, \Omega $. The impedance $ Z $ of the circuit is dominated by the inductor since the capacitive reactance $ X_C $ is much larger at this frequency. Therefore, the current $ I = \frac{V_{rms}}{Z} \approx \frac{12}{76.8} \approx 0.156 \, A $. Thus, $ V_L = I \cdot X_L = 0.156 \times 76.8 \approx 12 \, V $, but considering the phase difference, the voltage across the inductor is higher, approximately 23 V.

An Ac Circuit Consists of a 220 MH Inductor in Series