The magnetic flux through a coil perpendicular to the plane is varying according to the relation \( \phi = (7t^{3} + 3t^{2} - 2t - 2)\,\mathrm{Wb} \). If the resistance of the coil is 10 \( \Omega \), the induced current through the coil at \( t = 2\,\mathrm{s} \), will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 9.4\,\mathrm{A} \)
By Faraday's law the induced emf is the rate of change of flux, \( \varepsilon = -d\phi/dt \), and the induced current is \( I = |\varepsilon|/R \).
\( \displaystyle \frac{d\phi}{dt} = 21t^{2} + 6t - 2 \)
\( \displaystyle |\varepsilon|_{t=2} = 21(2)^{2} + 6(2) - 2 = 84 + 12 - 2 = 94\,\mathrm{V} \)
\( \displaystyle I = \frac{94}{10} = 9.4\,\mathrm{A} \)