Question

The flux linked with a circuit is given by $\varphi =t^3+3t-7$. The graph between time (x-axis) and induced emf (y-axis) will be

• A. A straight line through the origin
• B. Straight line with positive intercept
• C. Straight line with negative intercept
• D. Parabola not through origin

Answer 1

Answer: (D)

Parabola not through origin

We given the flux linked with circuit $\varphi =t^3+3t-7$
as, $e=-\frac{d\varphi }{dt}$
$=-\frac{d}{dt}(t^3+3t-7)=-3(t^2+1)$
Clearly the graph between e and t (along x axis) will be a parabola.
At $t=e,e=-3(\ne 0)$
$\therefore$ The parabola would not pass through the origin.