Question Detail
Question
A given RLC circuit has R=100Ω, L=1H and C=10μF all connected in series with a source of 200sin ωt with ω = 400 rad/s. Calculate the rms current.
Correct Answer
Option B is the correct answer.
Detailed Explanation
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, calculate the impedance (Z) of the series RLC circuit:Z = √(R2 + (X_L - X_C)2) = √(1002 + (400 - 250)2) = √(1002 + 1502) = √(10000 + 22500) = √(32500) ≈ 180.278 ΩThe peak voltage (V_peak) is 200 V. The rms voltage (V_rms) 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 / 180.278 Ω ≈ 0.784 A
Hint
Remember to calculate inductive and capacitive reactances first, then the total impedance, and use the rms voltage to find the rms current.