A 120-V rms voltage at 60 Hz is applied across a series combination of a 20-μF capacitor and an unknown resistor.If the rms value of the current in the circuit is 0.60 A,what is the resistance of the resistor?
A)60 Ω
B)120 Ω
C)180 Ω
D)150 Ω
E)200 Ω

Question

Quizplus · Accepted Answer

The reactance of the capacitor is given by Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

Substituting the given values, Xc = 1/(2π x 60 x 20 x 10^-6) = 132.7 Ω (approximately).

The impedance of the series combination of the capacitor and resistor is given by Z = √(R^2 + Xc^2).

Substituting the given values and solving for R, we get R = (Z^2 - Xc^2)/Z, where Z = V/I is the total impedance of the circuit.

Substituting the given values, Z = 120/0.6 = 200 Ω.

Therefore, R = (200^2 - 132.7^2)/200 = 150 Ω (approximately).

Hence, the answer is D) 150 Ω.

A 120-V Rms Voltage at 60 Hz Is Applied Across