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Step 1An inductor is a passive electrical device which stores energy in a magnetic field when current is passed through it. Also called Choke, coil and reactor.Details Given:\begin{array}{l}V_{\max }=0.500 \mathrm{~V} \\ \mathrm{I}(t)=(0.500 \mathrm{~A}) \cos \left(275 s^{-1} t\right)\end{array}Step 2I(t)=I_{m} \cos (\omega t)Comparing with the given Equation\begin{array}{c}I_{m}=0.500 \mathrm{~A} \\\omega=275 \mathrm{~s}^{-1}\end{array}To find \mathrm{X}_{L}\begin{aligned}I_{m} & =\frac{V_{m}}{X_{L}} \\& \Rightarrow X_{L}=\frac{V_{m}}{I_{m}} \\& \Rightarrow X_{L}=\frac{0.500}{0.500}=1 \\& \because X_{L}=\omega L \\& \Rightarrow \omega L=1 \\& \Rightarrow 275 L=1 \\& \Rightarrow L=\frac{1}{275} \mathrm{H} \\& \Rightarrow L=3.64 m H\end{aligned}Step 3The self-inductance of the inductor is 3.64mH ...