Interpret the given data

The coil is not purely inductive, because the applied voltage leads the current by $45^\circ$ instead of $90^\circ$.

So the coil has:

• resistance $R$
• inductive reactance $X_L = 100\ \Omega$
• phase angle $\phi = 45^\circ$

Use the phase angle relation for an $R$-$L$ circuit

For a series $R$-$L$ circuit, $\tan \phi = \frac{X_L}{R}$

Given $\phi = 45^\circ$, $\tan 45^\circ = 1 = \frac{X_L}{R}$

Since $X_L = 100\ \Omega$, $R = 100\ \Omega$

This confirms the resistive part, but for inductance we only need $X_L$ and frequency.

Use the inductive reactance formula

$X_L = \omega L = 2\pi f L$

Given:

• $X_L = 100\ \Omega$
• $f = 1000\ \text{Hz}$

Therefore, $L = \frac{X_L}{2\pi f}$

Substitute values: $L = \frac{100}{2\pi \times 1000}$

$L = \frac{100}{2000\pi} = \frac{1}{20\pi}$

$L \approx \frac{1}{62.83} \approx 0.0159\ \text{H}$

$L \approx 1.59 \times 10^{-2}\ \text{H}$

Match with the given options

The calculated value is approximately $1.6 \times 10^{-2}\ \text{H}$

Among the options, the nearest is:

• D: $1.1 \times 10^{-2}\ \text{H}$

Conclusion

The intended answer is Option D.