An inductor-coil of inductance 20 mH having resistance 10 Ω is joined to an ideal battery of emf 5.0 V. Find the rate of change of the induced emf at t= 0, (b) t = 10 ms and (c) t = 1.0 s.

Sol L = 20 mH; e =5.0 V, R = 10 Ω Τ = L/R = 20x10^-3/10, i base 0 = 5/10 i = i0(1 – e^–t/τ)^2 ⇒ i = i base 0 – i base 0 e^-t/τ^2 ⇒ iR = i0R – i0Re^t / τ^2 (a) 10 x di/dt = d/dt i base 0 R + 10 x 5/10 x 10/ 20x 10^-3 x e^-0x10/2x10^-2 = 5/2 x 10^-3 x 1 = 5000/2 = 2500 = 2.5 x 10^-3 V/s. b) Rdi/dt = R x i base 0 x 1/τ x e-t/τ t = 10 ms = 10 x 10^-3 s dE/dt = 10 x 5/10 x 10/20x 10^-3 x e^-0.01x 10/2x10^-2 = 16.844 = 17 V/’ c) For t = 1 s dE/dt = Rdi/dt = 5/2 10^3 x e^10/2x10^-2 = 0.00 V/s.