Two coils have a mutual inductance $5 imes 10^{-3} \mathrm{H}$. The current changes in the first coil according to the equation $\mathrm{I}_1=\mathrm{I}_0 \sin \omega \mathrm{t}$ where $\mathrm{I}_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} / \mathrm{s}$. What is the value of the maximum…

Question

Two coils have a mutual inductance $5 	imes 10^{-3} \mathrm{H}$. The current changes in the first coil according to the equation $\mathrm{I}_1=\mathrm{I}_0 \sin \omega \mathrm{t}$ where $\mathrm{I}_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} / \mathrm{s}$. What is the value of the maximum e.m.f. in the coil?

Aicharya · Accepted Answer

$\mathrm{e}=\frac{\mathrm{MdI}}{\mathrm{dt}}...(i)$ $\mathrm{e}=\mathrm{M} \frac{\mathrm{~d}}{\mathrm{dt}}\left(\mathrm{I}_0 \sin \omega \mathrm{t}\right)$
Now, $\frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{I}_0 \sin \omega \mathrm{t}\right)=\mathrm{I}_0 \omega \cos \omega \mathrm{t}$ For maximum value of emf, $\frac{\mathrm{dl}}{\mathrm{dt}}$ is maximum $\begin{array}{ll} & \Rightarrow \cos \omega \mathrm{t}=1 \\ \therefore \quad & \frac{\mathrm{dI}}{\mathrm{dt}}=\mathrm{I}_0 \omega ...(ii)\\ \therefore \quad & \mathrm{e}=0.005 \times 10 \times 100 \pi=5 \pi \mathrm{~V} \end{array}$ ...(from (i) and (ii))

Two coils have a mutual inductance $5 \times 10^{-3} \mathrm{H}$. The current changes in the first coil…

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