An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20 μF i $s ______$ V.

Question

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20 μF i s ______ V.

G1 Physics · Accepted Answer

Image From the source circuit: L = 1 H R = 300 Ω C = 20 μF ω = 100 rad/s V(rms) = 50 V Inductive reactance: X(L) = ωL = 100 Ω Capacitive reactance: X(C) = 1/(ωC) = 1/[100 × 20 × 10⁻⁶] = 500 Ω Impedance: Z = √{[X(L) - X(C)]² + R²} = √[(100 - 500)² + 300²] = 500 Ω Circuit current: I(rms) = V(rms)/Z = 50/500 = 0.1 A RMS voltage across capacitor: V(C,rms) = X(C)I(rms) = 500 × 0.1 = 50 V