Question Detail

First, calculate the inductive reactance (X_L) and capacitive reactance (X_C):X_L = ωL = (400 rad/s)(1 H) = 400 ΩX_C = 1/(ωC) = 1/((400 rad/s)(10 × 10⁻⁶ F)) = 1/(4 × 10⁻³) = 250 ΩNext, find the impedance (Z) of the circuit:Z = √(R² + (X_L - X_C)²) = √((100 Ω)² + (400 Ω - 250 Ω)²) = √(100² + 150²) = √(10000 + 22500) = √32500 ≈ 180.28 ΩThe peak voltage from the source is V_peak = 200 V. The RMS voltage is:V_rms = V_peak / √2 = 200 V / √2 ≈ 141.42 VFinally, calculate the RMS current (I_rms):I_rms = V_rms / Z = 141.42 V / 180.28 Ω ≈ 0.784 A.Rounding to two decimal places, I_rms ≈ 0.78 A.