Question Detail

To calculate the RMS current (I_rms) in an RLC series circuit, we need the RMS voltage (V_rms) and the impedance (Z) of the circuit (I_rms = V_rms / Z).1. Calculate Inductive Reactance (XL):XL = ωL = 400 rad/s * 1 H = 400 Ω.2. Calculate Capacitive Reactance (XC):C = 10 µF = 10 x 10-6 F.XC = 1 / (ωC) = 1 / (400 rad/s * 10 x 10-6 F) = 1 / (0.004) = 250 Ω.3. Calculate Impedance (Z):Z = √(R2 + (XL - XC)2)Z = √(1002 + (400 - 250)2) = √(10000 + 1502) = √(10000 + 22500) = √(32500) ≈ 180.28 Ω.4. Calculate RMS Voltage (Vrms):From the source v = 200sin ωt, the peak voltage (V_peak) is 200 V.V_rms = V_peak / √2 = 200 V / √2 ≈ 141.42 V.5. Calculate RMS Current (Irms):I_rms = V_rms / Z = 141.42 V / 180.28 Ω ≈ 0.7845 A.Rounding to two decimal places, I_rms ≈ 0.78 A.