Explanation:
D Given,
Voltage of D.C circuit $=100 \mathrm{~V}$
Voltage of A.C circuit $=100 \mathrm{~V}$
Frequency of $\mathrm{AC}, \mathrm{f}=50 \mathrm{~Hz}$
Resistance for D.C supplied, $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}=\frac{100}{1}=100 \Omega$
Where A.C of $50 \mathrm{~Hz}$ is applied and current, is $0.5 \mathrm{~A}$
Hence the impedance, $Z=\frac{V}{I}=\frac{100}{0.5}=200 \Omega$
Impedance, $\mathrm{Z}=\sqrt{\mathrm{R}^{2}+\left(\mathrm{X}_{\mathrm{L}}\right)^{2}}$
$=\sqrt{(\mathrm{R})^{2}+(\omega \mathrm{L})^{2}}$
Squaring both side,
$Z^{2}=R^{2}+\omega^{2} L^{2}$
$\omega^{2} L^{2}=Z^{2}-R^{2}$
$(2 \pi f L)^{2}=(200)^{2}-(100)^{2}=30000$
$2 \pi f L=173.2$
$L=\frac{173.2}{2 \pi f}=\frac{173.2}{2 \times 3.14 \times 50}=0.55 \mathrm{H}$