Georg Simon Ohm
Wikimedia Commons

Ohm’s law states that the voltage across a resistor is directly proportional to the current going through the resistor. Denoting the constant of proportionality with $R$ (the resistance), one can express Ohm's law mathematically as $$\begin{equation}V=RI\end{equation}$$ or $$\begin{equation}I=\frac{V}{R}\end{equation}$$ where voltage $V$ and current $I$ are shown in Fig. 1. It is important to note that the value of the current calculated using Ohm’s law depends on how the voltage $V$ is defined. As shown in the figure, the current is assumed to flow from the $+$ node to the $–$ node; depending on the sign of $V$, this current can be either positive or negative.

If we introduce the conductance as the reciprocal of the resistance $G=\frac{1}{R}$, Ohm's law becomes $V=\frac{I}{G}$ or $I=GV$. (Please do not confuse conductance $G$ with gain $G$, which is a quantity that will be defined later in this webbook.)

The SI unit of resistance is ohm (${\class{mjunit}{Ω}}$). The name comes from the German physicist Georg Ohm (1789–1854), who formulated Ohm’s law, establishing the fundamental relationship between voltage, current, and resistance in an electrical circuit. The unit for conductance is siemens (${\class{mjunit}{S}}={\class{mjunit}{Ω^{-1}}}$), also known as mho (${\class{mjunit}{℧}}$).

• Ohm's law
  Circuit with 1 resistor and 1 voltage source (analytical)
  Circuit with 1 resistor and 1 voltage source (numerical)
  Circuit with 1 resistor and 1 voltage source (numerical design)