An ac generator supplies a peak (not rms) voltage of 120.0 V at 60.0 Hz. It is connected in series with a 50.0-$\varOmega$ resistor and a 0.500-H inductor.
-What is the rms voltage of the generator?
A)84.9 V
B)138 V
C)151 V
D)169 V
E)240 V

Question

Quizplus · Accepted Answer

To find the rms voltage, we first need to find the peak current:
I_peak = V_peak / R = 120 V / 50 Ω = 2.4 A

Next, we can use the equation for the rms voltage of an AC circuit with both resistance and inductance:
V_rms = sqrt(V_peak^2 / 2 + I_peak^2 * R^2 + I_peak^2 * XL^2)

where XL is the inductive reactance, given by XL = 2πfL = 6.28 * 60 Hz * 0.500 H = 188.4 Ω.

Substituting the values, we get:
V_rms = sqrt(120^2 / 2 + 2.4^2 * 50^2 + 2.4^2 * 188.4^2) = 84.9 V

Therefore, the best choice is A.

An Ac Generator Supplies a Peak (Not Rms) Voltage of 120.0