Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation , where and rad/s. The maximum value of emf in the second coil is V. The value of is

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Solution

Q.
Two coils have mutual inductance 0.002H. The current changes in the first coil according to the relation $i = i_{0} \sin ω t$ , where $i_{0} = 5 A$ and $ω = 50 π$ rad/s. The maximum value of emf in the second coil is $\frac{π}{α}$ V. The value of $α$ is _____. [2024]

Ans.
(2) $ϕ = M i = M i_{0} \sin ω t$

$EMF = - M \frac{d i}{d t} = - 0.002 (i_{0} ω \cos ω t)$

${EMF}_{\max} = i_{0} ω (0.002) = (5) (50 π) (0.002)$

${EMF}_{\max} = \frac{π}{2} V$

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