Question

In a coil of resistance \(8Ω\), the magnetic flux due to an external magnetic field varies with time as \(Φ=\frac{2}{3}(9−t^2)\).The value of total heat produced in the coil, till the flux becomes zero, will be _ \(J\).

Answer 1

Correct Answer: 2

\(R = 8Ω\)

\(Φ=\frac{2}{3}(9−t^2)\)

At\( t = 3, φ = 0\)

\(∈ =|−\frac{dΦ}{dt}|=\frac{4}{3t}\)

\(H=∫_0^3\frac{V^2}{R}dt=∫_0^3\frac{1}{8}×16/9t^2dt\)

= \(\frac{2}{9} \times \bigg(\frac{t^3}{3}\bigg)^3_0 \)

= \(\frac{2}{9} \times 3 \times 27\)

= \(2\) \(J\)