Practice question

**Average power in LCR** P_avg = V_rms I_rms cos φ, cos φ = R/Z power factor, φ phase between V and I, tan φ = (X_L - X_C)/R. For R=80 Ω, X_L=100 Ω, X_C=40 Ω, X_L-X_C=60 Ω, Z=√(80²+60²)=100 Ω, cos φ=0.8, V_rms=240 V, I_rms=2.4 A, P=240×2.4×0.8=460.8 W, only R dissipates. Resonant angular frequency: ω₀ = (1/√(L C)) . L = 1.5 H , C = 35 × 10⁻⁶ F . ω₀ = (1/√(1.5 × 35 × 10⁻⁶)) ≈ 138.3 rad/s . f₀ = (ω₀/2π) = (138.3/6.28) ≈ 22 Hz . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms