A series circuit with , H and F is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
2000 W (or 2 kW)
Explanation
At resonance, the circuit behaves as a purely resistive circuit. The inductive reactance equals capacitive reactance (XL = XC), making the impedance minimum and equal to resistance R. The phase difference between voltage and current becomes zero, resulting in maximum power transfer with power factor = 1.
Solution Steps
Step 1: At resonance (natural frequency), XL = XC, so impedance Z = R = 20 Ω
Step 2: Current in the circuit, I = V/Z = V/R = 200/20 = 10 A
Step 3: At resonance, phase difference φ = 0°, so power factor cos φ = 1
Step 4: Average power transferred = I²R = (10)² × 20 = = 2000 W