Two coils have mutual inductance of 0.004\ H . The current changes in the first coil according to the relation i = i_0 ω t , where i_0 = 6\ A and ω = 100π\ rad/s . The maximum value of emf induced in second coil is

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Quantrex Academy · Accepted Answer

Correct answer: B. 2.4π\ V

The induced emf in the second coil is given by

e = -M \dfrac{di}{dt}

.

Given

i = i_0\cos\omega t

, differentiating with respect to time gives

\dfrac{di}{dt} = -i_0\omega\sin\omega t

.

Substituting this into the emf equation gives

e = M i_0\omega\sin\omega t

.

The maximum value of the induced emf is

e_{\text\max} = M i_0\omega

.

Substituting the given values

M = 0.004\ \text{H}

,

i_0 = 6\ \text{A}

, and

\omega = 100\pi\ \text{rad/s}

:

e_{\text\max} = 0.004 \times 6 \times 100\pi = 2.4\pi\ \text{V}

.

Answer:

2.4\pi\ V

Two coils have mutual inductance of 0.004\ H . The current changes...

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