Question 5: Electromagnetic Induction

Question

Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation $$i = {i_0}\sin \omega t$$, where i0 = 10A and $$\omega$$ = 10$$\pi$$ rads$$-$$1. The maximum value of emf in the second coil is

Accepted Answer

Induced emf, $$\varepsilon  =  - M{{di} \over {dt}}$$
where, i is given as, $$i = {i_0}\sin \omega t$$
$$ \Rightarrow \varepsilon  =  - M{d \over {dt}}[{i_0}\sin \omega t]$$
$$ = M\,{i_0}\omega \cos \omega t$$
For maximum value of emf in second coil, cos $$\omega$$t is maximum, i.e., 1.
$${E_{\max }} = M\,{i_0}\omega $$ [$$\because$$ $$\cos \omega t = 1$$]
$$ \Rightarrow 0.001 	imes 10 	imes 10\pi $$
$$ \Rightarrow {E_{\max }} = 0.1$$ $$\pi$$V
Hence, maximum emf value induced in second coil is 0.1 $$\pi$$V.

Answer

0.01 $$\pi$$ V

Answer

1 $$\pi$$ V

Answer

0.1 $$\pi$$ V

Answer

0.05 $$\pi$$ V

Electromagnetic Induction

Two coils A and B have a mutual inductance 0.001 H. The current changes in the first coil according to the equation $i = {i_0}\sin \omega t, where i0 = 10A and \omega = 10\pi rads-$1. The maximum value of emf in the second coil is

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