Question

The current $i$ in a coil varies with time as shown in the figure. The variation of induced emf with time would be

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Induced emf, $\text{e}=-\text{L}\frac{\text{di}}{\text{dt}}$
For $0\le \text{t}\le \frac{\text{T}}{4}$ ,
i-t graph is a straight line with positive constant slope.
$\therefore \frac{\text{di}}{\text{dt}}=\text{constant}$
$\Rightarrow \text{e}=-\text{ve}$ and constant For $0\le \text{t}\le \frac{\text{T}}{4}$
For $\frac{\text{T}}{4}\le \text{t}\le \frac{\text{T}}{2},$
$\because$ i is constant $\therefore \frac{\text{di}}{\text{dt}}=0$
$\Rightarrow \text{e}=0$ For $\frac{\text{T}}{4}\le \text{t}\le \frac{\text{T}}{2}$
For $\frac{\text{T}}{2}\le \text{t}\le \frac{3\text{T}}{4}$ ,
i-t graph is a straight line with negative constant slope.
$\therefore \frac{\text{di}}{\text{dt}}=\text{constant}$

⇒ e = + ve and constant For $\frac{\text{T}}{2}\le \text{t}\le \frac{3\text{T}}{4}$
For $\frac{3\text{T}}{4}\le \text{t}\le \text{T}$ ,
i is zero $\therefore \frac{\text{di}}{\text{dt}}=0$
$\Rightarrow \text{e}=0$ For $\frac{3\text{T}}{4}\le \text{t}\le \text{T}$
From this analysis, the variation of induced emf with time as shown in the figure below.