An oscillating circuit consisting of a capacitor with capacitance C=10 F , a coil with inductance L=6.0 H and active resistance R=10 . The mean power that should be fed to the circuit to maintain undamped harmonic oscillations with an external driving power with 50 ~Hz and a V_m of 280 ~V is

Step-by-step solution

R=10 L=6 H , C=10 H impedance of the circuit, Z= R^2+ (X_C-X_L )^2 Capacitive reactance, X_C= 1 C = 1 2 f C X_C= 1 2 314 50 10 10⁻⁶ =318.47 Inductive reactance X_L= L=2 f L aligned X_L & =2 314 50 6 10⁻⁶ & =18.84 10⁻⁴ aligned Resistance, R=10 gathered Z= 10^2+ (318.4-18.84 10⁻⁴ )^2 Z= 100+(318.39)^2 = 101477.36 Z=318.55 rms current, i_ rms = V_ rms Z = V₀ / 2 Z i_ rms = 280 2 318.55 =0.621 ~A gathered As energy is only dissipated in resistance as heat and no power dissipates in capacitor and inductor, so average po