Two coils have mutual inductance 0 . 002 H . The current changes in the first coil according to the relation i = i 0 s i n ω t , where i 0 = 5 A and ω = 50 π rad s - 1 . The maximum value of emf in th

Question

Two coils have mutual inductance 0 . 002 H . The current changes in the first coil according to the relation i = i 0 s i n ω t , where i 0 = 5 A and ω = 50 π rad s - 1 . The maximum value of emf in the second coil is π α V . The value of α is

TestHub · Accepted Answer

The amount of flux induced in the second coil due to the first one is given by

$\begin{array}{rcl} ϕ_{2} & = & M i \\ = & M i_{0} s i n ω t . . . (1) \end{array}$

where, $M$ is the mutual inductance of the coils.

The formula to calculate the emf induced can be written as

$ε = - \frac{d ϕ_{2}}{d t} . . . (2)$

From equation (2), it follows that,

$\begin{array}{rcl} ε_{\max} & = & M i_{0} ω \\ = & 0.002 \times 5 \times 50 π V \\ = & \frac{π}{2} V \end{array}$

Hence, $α = 2$ .

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