Current in Electric Circuit/L, R in Series/Condition for Ohm's Law

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]]

Ohm's Law is satisfied by $K$ whenever the current $I$ is at a maximum or a minimum.

Proof
From Electric Current in Electric Circuit: L, R in Series:
 * $L \dfrac {\mathrm d I} {\mathrm d t} + R I = E$

defines the behaviour of $I$.

Let $I$ be at a maximum or a minimum.

Then from Derivative at Maximum or Minimum:
 * $\dfrac {\mathrm d I} {\mathrm d t} = 0$

and so:

which is Ohm's Law.