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 _____ .

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TestHub · Accepted Answer

Since the voltage across the inductor and capacitor is same, the circuit is in resonance. Therefore, the current in the circuit will be,

$i = \frac{V}{R} = \frac{220}{5} = 44 A$ .

The voltage across the inductor is double that across the resistor. Therefore, $V_{L} = 2 V_{R} = 440 V$ .

We know that $V_{L} = i X_{L} = i \times 2 π f L \Rightarrow L = \frac{440}{44 \times 100 π} = \frac{1}{10 π} H = \frac{100}{π} mH$

Therefore, $K = \frac{1}{100} = 0.01 \approx 0$ .

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