1. The problem statement, all variables and given/known data Initially switch is at 0. At t = 0 seconds switch is put at 1. After 1 time constant switch is put at 2. Find equation for current for t > 2 2. Relevant equations current through inductor tries to remain constant. i(t) through inductor in series RL circuit is i(t) = [ i(initial) - i(final) ] e(-R*t/L + i(final) 3. The attempt at a solution At t < 0 I(t) is 0. For t > 0 switch is in position 1. i(t = 0+ ) = i(t = 0- ) = 0. for t much more than 0, the inductor will be short circuit and i will be 100 volts / 1 ohm = 100 A. so equation for t > 0 = (initial current - final current) e-R*t/L + final current = (0 - 100)e(-1 * t / 1 + 100 = 100 (1 - e(-t)) Now at t = 1 time constant switch is at position 2. time constant = L/R = 1/1 = 1 second. At t = 1 second, i(t) = 100 (1 - e-1) = 63A Now at t = 1 second switch is at position 2. So initial current is same as earlier which is 63A. Final current is 50A. So we get answer as [ initial - final ] e(-t) + final which is (63 - 50 ) e-t + 50 = 50 + 13e(-t) But in answer they've given 50 + 13e-(t-1) Where did the -1 part come from?