Question 212: Electromagnetic Induction

Question

The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses $\mathrm{dI} / \mathrm{dt}$ is shown graphically by figure

Accepted Answer

We know that the current through the inductor is increasing at a constant rate. This means that $\frac{\mathrm{dI}}{\mathrm{dt}}$ is constant.
The formula for the induced emf (e) in an inductor is: $\mathrm{e} = -\mathrm{L} \frac{\mathrm{dI}}{\mathrm{dt}}$.
Since $\frac{\mathrm{dI}}{\mathrm{dt}}$ is constant, the induced emf $\mathrm{e}$ will also be constant (but negative because of the minus sign).
This means that if we plot $\mathrm{e}$ versus $\frac{\mathrm{dI}}{\mathrm{dt}}$, the graph will be a straight line. The line will have a slope of $-\mathrm{L}$ and will pass through the origin.
This is shown in graph A, which matches option (B) in the choices.

Answer

B

Answer

A

Answer

D

Answer

C

Electromagnetic Induction

The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses \mathrm{dI} / \mathrm{dt} is shown graphically by figure

Choose the correct answer: