RL Series DC Circuit

Where $\mathcal{E}$ is the EMF of the battery that charges the circuit.

Growth

$i(t)=\frac{\mathcal{E}}{R}(1-e^{-\frac{R}{L}t})$

Decay

$i(t)=\frac{\mathcal{E}}{R}{e}^{-\frac{R}{L}t}$