First slide

Inductance

Question

The diagram shows a solenoid carrying time varying current l = l₀t. On the axis of the solenoid, a ring has been placed. The mutual inductance of the ring and the solenoid is M and the self-inductance of the ring is L. If the resistance of the ring is R then maximum current which can flow through the ring is

Moderate

A

$\frac{(2 M + L) l_{0}}{R}$
B

$\frac{M I_{0}}{R}$
C

$\frac{(2 M - L) I_{0}}{R}$
D

$\frac{(M + L) I_{0}}{R}$

Solution

$\begin{array}{l} ϕ = M I = M I_{0} t \\ Hence, induced emf ε = \frac{d ϕ}{d t} = M I_{0} \\ Current through ring = \frac{ε}{R} = \frac{M I_{0}}{R} \end{array}$

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