Question

At t = 0, an inductor of zero resistance is joined to a cell of emf ℰ through a resistance. The current increases with a time constant τ. The emf across the coil after time t is

(a) ℰ t/τ.

(b) ℰ (1 - e ^-t/τ)

(c) ℰ e ^-t/τ

(d) ℰ e 2^-t/τ

Answer 1

Correct Answer is: (c) ℰ e ^-t/τ

i = i₀(1 - e ^-t/τ)

di/dt = -i₀ (-1/τ) e ^-t/τ =  ℰ /R. R/L. e^-t/τ

or L di/dt = ℰ e ^{-t/τ =} emf across the coil.