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Question

Consider the circuit shown in figure, (a) Find the current through the battery a long time after the switch S is closed (b) suppose the switch is opened at t=0. What is the time constant of the decay circuit? (c) Find the current through the inductor after one time constant.
1024030_6fd54eaea5e44880bf647c2bb362e2e9.png

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Solution


Current through the battery after a long time,

I=EReq=E(R1+R2)R1R2 as then inductor will not hinder.

When the circuit comes in steady state, that is after a long times, the current through the inductor is

Io=ER1

And, the time constant is τ=LR1 since only R1 affects the current in the inductor, otherwise potential difference is always E across that branch.

Hence,

I=Io1etτ

I=ER11eR1tL

At t=τ

I=ER1(11e)

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