The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :
Solution
Magnetic energy, U = ${1 \over 2}$LI$_0^2$<br><br>Given : U = 25% of U<sub>0</sub>.<br><br>$\Rightarrow$ ${1 \over 2}L{I^2} = {1 \over 4} \times {1 \over 2}LI_0^2$<br><br>$\Rightarrow {I^2} = {{I_0^2} \over 4} \Rightarrow I = {{{I_0}} \over 2}$<br><br>$\therefore$ $I = {I_0}(1 - {e^{ - t/\tau }})$<br><br>$\Rightarrow {{{I_0}} \over 2} = {I_0}(1 - {e^{ - t/\tau }})$<br><br>$\Rightarrow {1 \over 2} = {e^{ - t/\tau }}$<br><br>$\Rightarrow {e^{t/\tau }} = 2$<br><br>$\Rightarrow t = \tau \ln 2$<br><br>$\Rightarrow t = {L \over R}\ln 2$
About this question
Subject: Physics · Chapter: Electromagnetic Induction · Topic: Faraday's Laws
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