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  • 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 

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 \left (\frac{1}{n} \right ) times of its maximum value, is:
Option: 1 \frac{L}{R}\ln \left (\frac{\sqrt{n}}{\sqrt{n}-1} \right )
Option: 2 \frac{L}{R}\ln \left (\frac{\sqrt{n}+1}{\sqrt{n}-1} \right )
Option: 3 \frac{L}{R}\ln \left (\frac{\sqrt{n}}{\sqrt{n}+1} \right )
Option: 4 \frac{L}{R}\ln \left (\frac{\sqrt{n}-1}{\sqrt{n}} \right )

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\begin{aligned} &\frac{1}{2} \mathrm{Li}^{2}=\frac{1}{\mathrm{n}} \frac{1}{2} \mathrm{Li}_{0}^{2}\\ &\Rightarrow \quad \mathbf{i}=\frac{\mathbf{i}_{0}}{\sqrt{\mathbf{n}}}\\ &\text { During growth of current, }\\ &\mathbf{i}=\mathbf{i}_{0}\left(1-\mathbf{e}^{-t / \tau}\right) \quad\left(\tau=\frac{\mathbf{L}}{\mathbf{R}}\right)\\ &e^{t / \tau}=\frac{\sqrt{n}}{\sqrt{n}-1}\\ &t=\frac{L}{R} \ln \left(\frac{\sqrt{n}}{\sqrt{n}-1}\right) \end{aligned}

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Deependra Verma

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