A 20 mH inductor, 100 μF capacitor and 50 Ω resistor are connected in series to an AC source V = 10 sin(314t) V. Find the average power dissipated in the circuit.
Options

Question

A 20 mH inductor, 100 μF capacitor and 50 Ω resistor are connected in series to an AC source V = 10 sin(314t) V. Find the average power dissipated in the circuit.

G1 Physics · Accepted Answer

Step 1: Instantaneous source v=10sin314t has peak V₀=10V and RMS voltage V(RMS)=10/√2V. Step 2: Reactances: X(L)=ωL=314×0.020=6.28Ω, X(C)=1/(ωC)=1/(314×100×10⁻⁶)≈31.85Ω. Step 3: Z=√[50²+(6.28−31.85)²]≈56.16Ω; P=I(RMS)²R=(10²/2)(50/Z²)≈0.79W. Answer C. Final answer: (C) 0.79 W.