Q.

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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a

(i) i2>i3>i1i1=0  (ii) i2>i3>i1

b

(i) i2i1i1≠0  (ii) i2>i3>i1

c

(i) i2=i3=i1i1=0  (ii) i2>i3>i1

d

(i) i2=i3>i1i1≠0  (ii) i2>i3>i1

answer is A.

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Detailed Solution

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.
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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)]