A series L − R circuit is connected to a battery of emf V . If the circuit is switched on at t = 0 , then the time at which the energy stored in the inductor reaches ( n 1 ) times of its maximum val

Question

A series L − R circuit is connected to a battery of emf V . If the circuit is switched on at t = 0 , then the time at which the energy stored in the inductor reaches ( n 1 ​ ) times of its maximum value, is :

TestHub · Accepted Answer

Potential energy stored in inductor is given by $U = \frac{1}{2} L^{2}$

$\cup \propto l^{2}$

$\frac{U}{U _{0}} = (\frac{1}{I _{0}})^{2}$

$\frac{1}{n} = (\frac{1}{I _{0}})^{2}$

$\frac{1}{I _{0}} = 1 - e^{- RT / L} = \frac{1}{n}$

$t = \frac{L}{R} ln \frac{n}{n - 1}$

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