When voltage is applied to a piece of metal wire, as shown in figure 1.2 (a), the current I flowing through the wire is proportional to the voltage V across two points in the wire. This property is known as Ohm's law, which reads
where R is called resistance, and G is called conductance. The resistance R and the conductance G of the same piece of wire is related by R = 1/G. Resistance is measured in ohms () and conductance in siemens (S or ).
Figure 1.2: Ohm's law. (a) Metal wire; (b) circuit symbol
Any apparatus/device that has this property is called a resistor. Study of the physics of resistance shows that it is proportional to the length of the metal wire, l, and inversely proportional to the cross-sectional area, A, i.e., where the proportionality constant is known as the resistivity of the metal.
We may calculate the power required to
pass current I through a resistor of resistance R using the
previously derived formula, i.e.,
Using the Ohm's law equation, we get The last inequality defines a property called passivity.