The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first.
[i₁, i₂ and i₃ are respective current in circuit (1), (2) and, (3)]

Question

The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first.

[i₁, i₂ and i₃ are respective current in circuit (1), (2) and, (3)]

Infinity Learn · Accepted Answer

Just after the switch is closed maximum emf is induced in the inductor which opposes the flow of current and the current in the inductor becomes zero . So $$i1=0$$, $$i2=ER$$ and $$i3=E2R$$. Hence $$i2$$>$$i3$$>$$i1$$. A long time after the key is closed, the inductor behaves like a resistanceless wire Therefore ,$$i1=E2R$$,$$i2=ER2=2ERand$$ $$i3=ER$$. So $$i2$$>$$i3$$>$$i1$$.

The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first.
[i₁, i₂ and i₃ are respective current in circuit (1), (2) and, (3)]

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The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first.[i1, i2 and i3 are respective current in circuit (1), (2) and, (3)]

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