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  4. An inductor (L =100mH ), a resistor (R = 100Ω) and a battery (E = 100 V) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is:

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Q. An inductor (L =100mH ), a resistor (R = 100$\Omega$) and a battery (E = 100 V) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is:Physics Question Image

AIEEEAIEEE 2008

Solution:

This is a combined example of growth and decay of current in an LR circuit.
The current through circuit just before shorting the battery,
$I_{0}===E/R =1A $
[as inductor would be shorted in steady state] After this decay of current starts in the circuit according to the equation $I=I_{0}e^{-t /\tau}$ where $t=L / R.$
$I=1\times e^{-\left(1\times10^{-3}\right) /\left(100\times10^{-3} 100\right)}$
$=\left(1 / e\right)A$

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