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 $$\frac{1}{K\pi}$$ mH. The value of $$K$$ is ______.

Given that $$|V_L| = |V_C| = 2|V_R|$$, it implies:

$$I \cdot X_L = I \cdot X_C = 2(I \cdot R)$$

$$X_L = X_C = 2R$$

$$X_L = 2 \times 5 = 10\ \Omega$$

$$X_L = 2\pi f L$$

$$10 = 2 \times \pi \times 50 \times L$$

$$L = \frac{1}{10\pi} \times 1000\ \text{mH} = \frac{100}{\pi}\ \text{mH}$$

$$\frac{100}{\pi} = \frac{1}{K\pi}$$

$$100 = \frac{1}{K} \implies \mathbf{K = 0.01}$$