A series LCR circuit having R =44 , ~L =2 H and C =25 ~F is connected to a variable frequency of 220 V . What is the average power transferred to the circuit in one complete cycle if the frequency of supply equals the natural frequency of the circuit?

Step-by-step solution

The natural frequency of a series LCR circuit is given by the resonant frequency f₀ = 1 2 LC . At resonance, the inductive reactance X_L equals the capacitive reactance X_C , which implies the net impedance of the circuit is equal to the resistance R . Given R = 44 , L = 2 H , and C = 25 10⁻⁶ F . The voltage V = 220 V is the RMS voltage. At resonance, the current in the circuit is I = V Z = V R . I = 220 44 = 5 A . The average power P transferred to the circuit in an LCR circuit is given by P = V_ rms I_ rms . At r