6.1 The RL Circuit cont.
To see how to use the generic solution, reconsider the RL circuit and let R = 2 W and L = 5 H so that the circuit’s KVL becomes : 5di(t)/dt + 2i(t) = vS(t)
Which in generic form is: di(t)/dt + 0.4i(t) = 0.2vS(t)
By inspection, the time constant is T = 1/0.4 = 2.5 Sec.
Note also that from di(t)/dt + (R/L)i(t) = (1/L)vS(t) that, more generically, the time constant is T = L/R