The instantaneous magnetic flux linked with a coil is given by \( \phi = (15t^{3} - 100t^{2} + 40)\,\mathrm{Wb} \). The emf induced in the coil at time \( t = 1\,\mathrm{s} \) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → +155 V
By Faraday’s law the induced emf is \( \varepsilon = -\frac{d\phi}{dt} \). The emf at an instant needs the derivative of the flux, evaluated at that time.
\( \displaystyle \frac{d\phi}{dt} = \frac{d}{dt}\left(15t^{3} - 100t^{2} + 40\right) = 45t^{2} - 200t \)
\( \left.\frac{d\phi}{dt}\right|_{t=1} = 45 - 200 = -155\,\mathrm{V} \)
\( \varepsilon = -\frac{d\phi}{dt} = +155\,\mathrm{V} \)