In a coil of resistance 10 Ω, the variation of induced current developed by changing magnetic flux through it is shown in the graph. The magnitude of change in flux through the coil (in Wb) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2
By Faraday’s law the induced emf is \( e = -d\phi/dt \), so the induced current is \( i = e/R \). The charge that flows is the area under the i–t graph, and it is fixed by the total change in flux.
\( \displaystyle q = \int i\,dt = \frac{1}{R}\int\left|\frac{d\phi}{dt}\right|dt = \frac{\Delta\phi}{R} \)
From the graph, the current falls from 4 A to zero in 0.1 s, so the area is a triangle.
\( \displaystyle q = \frac{1}{2} \times 4\,\mathrm{A} \times 0.1\,\mathrm{s} = 0.2\,\mathrm{C} \)
\( \Delta\phi = qR = 0.2\,\mathrm{C} \times 10\,\Omega = 2\,\mathrm{Wb} \)