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Switch S of the circuit shows in Fig is ...

Switch `S` of the circuit shows in Fig is closed at `t = 0`. If `e` denotes the induced emf in `L` and `I` is the current flowing through the circuit the circuit at time `t`, which of the following graphs is//are correct?

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C, D
When switch is just closed in the circuit shown, at that moment current through the circuit is zero. Hence, e.m.f.induced across inductance `L` will be equal to e.m.f.`E` if the battery.
But as the current through the circuit increases, the induced e.m.f. in the solenoid decreases. But induced e.m.f. in the solenoid is
equal to `|e| = L (di)/(dt)*`
Since `di//dt` decreases as time passes, therefore the graph for induced e.m.f.`e` and time `t` will be as shows in option (c ).
Hence (a) is wrong and (c ) is correct.
The graph for current should be such that at initial moment current of increases of current gradully decreases. Hence, slope of the current-time curve should decrease with time. Therefore, the graph between current and time will be as shows in option (c).
Hnece(b) is wrong and (d) is correct.
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