A 120-V rms voltage at 2000 Hz is applied to a 6.0-mH inductor,a 2.0-μF capacitor,and a 200-Ω resistor.What is the rms value of the current in this circuit?
A)1.5 A
B)0.48 A
C)2.5 A
D)3.5 A
E)0.59 A

Question

Quizplus · Accepted Answer

First, we calculate the impedance of the circuit using the formula:

Z = sqrt(R^2 + (Xl - Xc)^2)

where R is the resistance, Xl is the inductive reactance (2πfL), and Xc is the capacitive reactance (1/2πfC). Substituting the given values, we get:

Xl = 2πfL = 2π(2000 Hz)(6.0 mH) = 0.075 Ω
Xc = 1/2πfC = 1/(2π(2000 Hz)(2.0 μF)) = 39.79 Ω
Z = sqrt((200 Ω)^2 + (0.075 Ω - 39.79 Ω)^2) = 200 Ω

Now, we can use Ohm's Law to find the current:

I = V/Z = (120 V rms)/(200 Ω) = 0.6 A rms

Therefore, the answer is E) 0.59 A (rounded to two significant figures).

A 120-V Rms Voltage at 2000 Hz Is Applied to a 6.0-MH