First slide

Time -Varying current in L-R circuit

Question

In the circuit shown, sliding contact is moving with uniform velocity towards right. Its value at some instance is $12 Ω$ . The current in the circuit at this instant of time will be

Moderate

A

0.5 A
B

More than 0.5 A
C

Less than 0.5 A
D

May be less or more than 0.5 A depending on the value of L

Solution

Since resistance of the circuit is increasing and hence current in the circuit is decreasing, so $\frac{di}{dt}$ is negative.
Current in the circuit is given by $i = \frac{6 - L \frac{di}{dt}}{12}$ .
Since $\frac{di}{dt}$ is negative so the value of numerator will be more than 6 V and hence current in the circuit at that instant will be more than 0.5 A.

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