In a series LCR circuit connected to an ac source, the rms voltages across the inductor, capacitor, and resistor are 80 V , 20 V , and 80 V respectively. If the peak current in the circuit is 5 2 A , what are the power factor and the average power dissipated in the circuit?

Step-by-step solution

Given: V_L = 80 V V_C = 20 V V_R = 80 V Peak current, I₀ = 5 2 A The rms voltage of the source is given by phasor addition: V_ rms = V_R^2 + (V_L - V_C)^2 V_ rms = 80^2 + (80 - 20)^2 V_ rms = 6400 + 3600 = 10000 = 100 V The rms current is: I_ rms = I₀ 2 = 5 2 2 = 5 A The power factor ( ) is: = V_R V_ rms = 80 100 = 0.8 The average power dissipated in the circuit is: P = V_ rms I_ rms P = 100 5 0.8 = 400 W (Alternatively, P = V_R I_ rms = 80 5 = 400 W ) Answer: 0.8 , 400 W