In a laboratory experiment to study electromagnetic induction, the current in the primary coil is changed according to the relation Ip(t)=I0(1−e−t/τ), where I0 and τ are constants.
(i) Starting from Faraday’s law, obtain an expression for the instantaneous emf induced in the secondary coil in terms of the mutual inductance M, I0, τ and t.
(ii) If M=0.12H, I0=5.0A and τ=4.0ms, calculate the magnitude of the induced emf at t=0.5τ.
(iii) The secondary of resistance 2.0Ω is closed on itself. Derive an expression for the instantaneous power dissipated in the secondary and state whether this power is supplied by or extracted from the source driving the primary.