An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-$\Omega$ resistor, a 400-mH inductor, and a 200-$\mu$F capacitor. The rms current in amperes is:
A) 0.125
B) 0.135
C) 0.18
D) 0.20
E) 0.40

Question

Quizplus · Accepted Answer

The impedance of the circuit is calculated using the formula Z = sqrt(R^2 + (X_L - X_C)^2), where X_L = ωL and X_C = 1/(ωC). Substituting the given values, Z = sqrt(50^2 + (80 - 25)^2) = sqrt(50^2 + 55^2) = sqrt(2500 + 3025) = sqrt(5525) ≈ 74.3 Ω. The rms current is then I = V/Z = 10/74.3 ≈ 0.135 A.

An Ac Generator Producing 10 V (Rms) at 200 Rad/s Ω\OmegaΩ

An Ac Generator Producing 10 V (Rms) at 200 Rad/s $\Omega$