A 120-V rms voltage at 1.0 kHz is applied to a 2.0-mH inductor,a 4.0-μF capacitor and a resistor.If the rms value of the current in this circuit is 0.40 A,what is the value of the resistor?
A)300 Ω
B)95 Ω
C)420 Ω
D)120 Ω
E)240 Ω

Question

Quizplus · Accepted Answer

The inductive reactance is XL = 2πfL = 2π(1.0 kHz)(2.0 mH) = 12.6 Ω. The capacitive reactance is XC = 1/(2πfC) = 1/(2π(1.0 kHz)(4.0 μF)) = 398 Ω. The impedance of the circuit is Z = √(R^2 + (XL - XC)^2) = √(R^2 + (12.6 Ω - 398 Ω)^2) = R. The rms current is I = V/Z = 0.40 A. Therefore, R = V/I = 120 V/0.40 A = 300 Ω.

A 120-V Rms Voltage at 1