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 inverse of the resistance $G=1/R$, Ohm's law becomes $V=I/G$ or $I=GV$. (Please do not confuse conductance $G$ with gain $G$, which is a quantity that will be defined later in the webbook.)

The unit for resistance is ohm ($Ω$); the unit for conductance is siemens ($S$), also known as mho.

• 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)