In the given circuit, the magnitude of V L and V C are twice that of V R . Given that f = 50 Hz , the inductance of the coil is 1 K π mH . The value of K is _____ .

Step-by-step solution

Since the voltage across the inductor and capacitor is same, the circuit is in resonance. Therefore, the current in the circuit will be, i = V R = 220 5 = 44   A . The voltage across the inductor is double that across the resistor. Therefore, V L = 2 V R = 440   V . We know that V L = i X L = i × 2 π f L ⇒ L = 440 44 × 100 π = 1 10 π   H = 100 π mH Therefore, K = 1 100 = 0 . 01 ≈ 0 .