The instantaneous magnetic flux linked with a coil is given by $\phi=(15t^3-100t^2+40) Wb$. The emf induced in the coil at time $t = 1 s$ is:

+155 V

The correct answer is Option (4) → +155 V

Induced electromotive force (emf), $E=-\frac{d\phi}{dt}$ [Faraday law]

where,

$\phi$ = Magnetic flux

$t$ = time

$\phi(t)=(15t^3-100t^2+40)Wb$ [given]

$\left.-\frac{d\phi}{dt}\right|_{t=1}=\left.-\frac{d}{dt}\right|_{t=1}(15t^3-100t^2+40)$

$=\left[45t^2-200t\right]_{t=1}$

$=-(-155)V$

$=155V$