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:
Answer & explanation
Correct answer: option 4
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]
$\left.-\frac{d\phi}{dt}\right|_{t=1}=\left.-\frac{d}{dt}\right|_{t=1}(15t^3-100t^2+40)$
$=\left[45t^2-200t\right]_{t=1}$
$=-(-155)V$
$=155V$