Physics - EMI/AC Question with Solution | TestHub

For dc, $V=IR$ ( $R$ is resistance of inductor) $100=1\times R\Rightarrow R=100\Omega$. For ac, $Z=\sqrt{R^2+X_L^2}$ $\begin{array}{rl}& \because V=IZ\\ & \Rightarrow 100=0.5\sqrt{R^2+X_L^2}\\ & \Rightarrow 100=0.5\sqrt{(100{)}^2+X_L^2}\end{array}$ $\begin{array}{rl}& \Rightarrow 100=\frac{5}{10}\sqrt{(100{)}^2+X_L^2}\\ & X_L^2=(200{)}^2-(100{)}^2=300\times 100\\ & \Rightarrow X_L=\sqrt{3\times (100{)}^2}=100\sqrt{3}\\ & \Rightarrow \omega L=100\sqrt{3}\Rightarrow 2\pi vL=100\sqrt{3}\\ & \Rightarrow 2\times \pi \times 50\times L=100\sqrt{3}\\ & \Rightarrow 100\times \pi L=100\sqrt{3}\\ & \therefore L=\frac{\sqrt{3}}{\pi }=\frac{\sqrt{3}}{3.14}\Rightarrow L=0.55\mathrm{H}.\end{array}$