The magnetic flux through a coil placed in a magnetic field is given by: \( \phi = (5t^{3} + 4t^{2} + 2t - 5)\,\mathrm{Wb} \). The resistance of the coil is \( 10\,\Omega \). The induced current through the coil at \( t = 2\,\mathrm{s} \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7.8 A
By Faraday's law the induced emf is the rate of change of flux, \( \varepsilon = |d\phi/dt| \), and the current follows from Ohm's law.
\( \displaystyle \varepsilon = \frac{d\phi}{dt} = 15t^{2} + 8t + 2 \)
\( \displaystyle \varepsilon(2) = 15(4) + 8(2) + 2 = 60 + 16 + 2 = 78\,\mathrm{V} \)
\( \displaystyle I = \frac{\varepsilon}{R} = \frac{78}{10} = 7.8\,\mathrm{A} \)