An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 5O Hz nows through it. The ratio of inductive reactance to its resistance is_____.$$(\pi=3.14)$$

$$E = \frac{1}{2} L I_{\text{rms}}^2$$ $$\implies$$ $$16 = \frac{1}{2} L (2)^2$$

$$L = 8\text{ H}$$

$$X_L = 2\pi f L$$ $$\implies X_L = 2 \times 3.14 \times 50 \times 8$$ $$\implies X_L = 2512\ \Omega$$

$$P = I_{\text{rms}}^2 R$$

$$32 = (2)^2 R$$ $$\implies R = 8\ \Omega$$

$$\text{Ratio} = \frac{X_L}{R}$$ $$\implies \text{Ratio} = \frac{2512}{8}$$

$$\text{Ratio} = 314$$