First slide

Time -Varying current in L-R circuit

Question

Switch S of the circuit shown in fig is closed at t = 0. If e denotes the induced e.m.f. in L and i, the
current flowing through the circuit at time t, then which of the following graphs fig shows the variation of e with i

Difficult

A
B
C
D

Solution

When switch S it closed, at that moment the current in the circuit is zero. So, the induced e.m.f. across the inductance is equal to e.m.f. E of the battery. As current increases, the induced e.m.f. in the inductance decreases. If at any instant t, the current in the circuit is i, then applying Kirchhoff's law, we have
$iR + e = E or e = (E - iR)$
So, the graph between e and i will be a straight line having negative slope.

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