RL Circuit

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:

\(i(t) = I_0 e ^{-\dfrac{Rt}{L}}\)