A 120-V rms signal at 60.0 Hz is applied across a 30.0-mH inductor and a 100-Ω resistor. What is the rms value of the voltage across the resistor?
A) 119 V
B) 60.0 V
C) 100 V
D) 110 V
E) 0.700 V

Question

Quizplus · Accepted Answer

The rms voltage across the resistor is equal to the rms voltage across the inductor, which is given by:$$V_{rms} = I_{rms} * X_L$$where:* $I_{rms}$ is the rms current through the inductor* $X_L$ is the inductive reactance of the inductorThe rms current through the inductor is given by:$$I_{rms} = \frac{V_{rms}}{Z}$$where:* $V_{rms}$ is the rms voltage across the inductor* $Z$ is the impedance of the circuitThe impedance of the circuit is given by:$$Z = \sqrt{R^2 + X_L^2}$$where:* $R$ is the resistance of the resistor* $X_L$ is the inductive reactance of the inductorSubstituting the given values into the equations above, we get:$$I_{rms} = \frac{120 V}{\sqrt{100 \Omega^2 + (2\pi * 60.0 Hz * 30.0 mH)^2}} = 1.19 A$$$$V_{rms} = 1.19 A * 2\pi * 60.0 Hz * 30.0 mH = 119 V$$Therefore, the rms voltage across the resistor is 119 V.

A 120-V Rms Signal at 60