Question

The magnetic flux linked with a coil at any instant '$t$' is given by $\varphi =5t^3-100t+300,$ the e.m.f. induced in the coil at $t=2\text{sec}$ is

• A. $40\text{V}$
• B. – $40\text{V}$
• C. $300\text{V}$
• D. $140\text{V}$

Answer 1

The correct option is A $40\text{V}$

From Faraday's law of induction,

$E=-\frac{d\varphi }{dt}=-\frac{d}{dt}(5t^3-100t+300)$

$E=-(15t^2-100)$

Put $t=2\text{sec}$

$\therefore E=40\text{V}$

Hence, option $\left(\text{B}\right)$ is the correct answer.