Current in Electric Circuit/L, R in Series/Constant EMF at t = 0/Corollary 2

Theorem
Consider the electrical circuit $K$ consisting of:
 * a resistance $R$
 * an inductance $L$

in series with a source of electromotive force $E$ which is a function of time $t$.


 * [[File:CircuitRLseries.png]]

Let the electric current flowing in $K$ at time $t = 0$ be $0$.

Let a constant EMF $E_0$ be imposed upon $K$ at time $t = 0$.

The electric current $I$ in $K$ is given by the equation:
 * $I = \dfrac {E_0} R \left({1 - e^{-R t / L} }\right)$

Proof
From Electric Current in Electric Circuit: L, R in Series: Constant EMF at $t = 0$:
 * $I = \dfrac {E_0} R + \left({I_0 - \dfrac {E_0} R}\right) e^{-R t / L}$

Setting $I_0 = 0$:

Hence the result.