Question 299: Electromagnetic Induction

Question

Two coils $$\mathrm{A}$$ and $$\mathrm{B}$$ have mutual inductance 0.008 $$\mathrm{H}$$. The current changes in the coil A, according to the equation $$\mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega \mathrm{t}$$, where $$\mathrm{I}_{\mathrm{m}}=5 \mathrm{~A}$$ and $$\omega=200 \pi ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The maximum value of the e.m.f. induced in the coil $$B$$ in volt is

Accepted Answer

$$e=M \frac{d I}{d t}$$
Given: $$M=0.008, I_m=5 A, \omega=200 ~\mathrm{rad} / \mathrm{s}$$
$$	herefore \quad \mathrm{e}=0.008 	imes \mathrm{I}_{\mathrm{m}} \omega \cos \omega \mathrm{t}$$
For $$\mathrm{e}=\mathrm{e}_{\max }, \cos \omega \mathrm{t}=1$$
$$\begin{aligned}
	herefore \quad \mathrm{e}_{\max } & =0.008 	imes \mathrm{I}_{\mathrm{m}} 	imes \omega \
& =0.008 	imes 5 	imes 200 \pi \
& =8 \pi
\end{aligned}$$

Answer

$$4 \pi$$

Answer

$$8 \pi$$

Answer

$$10 \pi$$

Answer

$$16 \pi$$

Electromagnetic Induction

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