Question

The magnetic flux linked with a coil at any instant $t$ is given by $\varphi =5t^3-100t+300$, the emf induced in coil at $t=2s$ is

• A. $-40V$
• B. $40V$
• C. $140V$
• D. $300V$

Answer 1

Answer: (B)

$40V$

Given , $\varphi =5t^3-100t+300,t=2s$

Now , $\frac{d\varphi }{dt}=15t^2-100$

The induced emf in a coil is given by ,

$e=-\frac{d\varphi }{dt}$

Hence , $e=-(15t^2-100)=-15t^2+100$

at $t=2s$

$e=-15\times 2^2+100=-60+100=40V$