Question

The current $i$ in an induction coil varies with time $t$ according to the graph shown in the figure. Which of the following graphs shows the induced emf in the coil with time ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C



We know that the induced emf in the inductor is given by,

$E=-L\frac{di}{dt}$

Initially the current is constant, i.e. $\frac{di}{dt}=0$

Therefore, the initial value of emf induced is zero.

Now, for $t=t_1$ to $t=t_2$ current is decreasing at a constant rate.

Therefore, $\frac{di}{dt}$ is constant and negative.

Hence, induced emf $E=-L\frac{di}{dt}$ is positive.

For $t=t_2$ to $t=t_3$ current is increasing at a constant rate.

Therefore, $\frac{di}{dt}$ is constant and positive.

Hence, the induced emf $E=-L\frac{di}{dt}$ will be negative.


Therefore, only option $\left(\text{C}\right)$ represents the correct variation of emf with time.