An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal emf. If the frequency of the emf is 25 kHz, what is the rms voltage across the resistor?
A) 7.0 V
B) 9.4 V
C) 11 V
D) 5.0 V

Question

Quizplus · Accepted Answer

First, we need to find the impedance of the circuit:

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

where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance (which is 0 for this purely inductive circuit).

$X_L = 2\pi f L = 2\pi (25 	ext{ kHz})(220 	ext{ mH}) = 34.56 	ext{ }\Omega$

$Z = \sqrt{(75 	ext{ k}\Omega)^2 + (34.56 	ext{ }\Omega)^2} = 75.10 	ext{ k}\Omega$

Now, we can find the current:

$I = \frac{V}{Z}$

$I_{rms} = \frac{12 	ext{ V}}{75.10 	ext{ k}\Omega} = 0.16 	ext{ mA}$

Finally, we can find the voltage across the resistor:

$V_R = IR = (0.16 	ext{ mA})(75 	ext{ k}\Omega) = 12 	ext{ V}$

Note that the voltage across the inductor will be equal in magnitude to the voltage across the resistor, but will be out of phase with it by 90 degrees.

An Ac Circuit Consists of a 220 MH Inductor in Series