Consider a RL circuit as shown below , with the initial current of \(I_0\)
Similar to analysis of RC circuit, but this time applying KVL around the loop.
\(v_L + v_R = 0\)
\(L \dfrac{di}{dt} + Ri =0\)
\(i(t) = I_o e^{-\dfrac{Rt}{L}}\)
Thus, the time constant can be defined as:
\(\tau = \dfrac{L}{R}\)
The unit of the time constant is in seconds.
The current of the inductor can be represented as:
\(i(t) = I_0 e ^{-\dfrac{Rt}{L}}\)