Question 16: Electromagnetic Induction

Question

In an inductor of self-inductance $$2 \mathrm{~mH}$$, current changes with time (in sec) according to the relation, $$I=(3 t^2-3 t+8) A$$. The emf becomes zero at

Accepted Answer

To determine when the emf is zero, follow these steps:
Recall that the induced emf in an inductor is given by:
$$\varepsilon = -L \frac{dI}{dt}.$$
Since the self-inductance $$L$$ is a nonzero constant, the emf will be zero when the derivative $$\frac{dI}{dt}$$ is zero.
Differentiate the given current equation with respect to time:
$$I(t) = 3t^2 - 3t + 8.$$
Calculating the derivative:
$$\frac{dI}{dt} = 6t - 3.$$
Set the derivative equal to zero and solve for $$t$$:
$$6t - 3 = 0 \quad \Longrightarrow \quad 6t = 3 \quad \Longrightarrow \quad t = \frac{3}{6} = 0.5 \, 	ext{sec}.$$
Thus, the emf becomes zero at 0.5 sec, which corresponds to Option C.

Answer

2 sec

Answer

6 sec

Answer

0.5 sec

Answer

5 sec

Electromagnetic Induction

In an inductor of self-inductance $2 \mathrm{~mH}, current changes with time (in sec) according to the relation, I=(3 t^2-3 t+8) A$. The emf becomes zero at

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