Electrical Resistance

Resistance tells us how much a component or wire opposes the flow of electric charge. Think of electric current like water through a pipe: a long, thin, rough pipe makes the flow harder. In circuits, higher resistance means less current for the same battery voltage.

Key equation and units

Voltage (p.d.), current, and resistance are linked by Ohm’s law:

$$V = I R$$

So $R = \frac{V}{I}$. The unit of resistance is the ohm ($\Omega$). A device has 1 $\Omega$ if a p.d. of 1 V makes a current of 1 A flow.

For a constant current, the p.d. increases when resistance increases, because $V = I R$.

What affects resistance?

• Length: longer wire, larger resistance. $$R \propto L$$
• Thickness (cross-sectional area $A$): thicker wire, smaller resistance. $$R \propto \tfrac{1}{A}$$
• Material: some materials let charges move more easily. This is described by resistivity $\rho$: $$R = \rho\, \frac{L}{A}$$
• Temperature (metals): heating a metal usually increases its resistance.

Current–voltage (I–V) behavior

• Resistor of constant resistance (ohmic): V and I are directly proportional. Graph is a straight line through the origin. The ratio $\tfrac{V}{I}$ is constant and equals $R$.
• Filament lamp: the curve gets flatter at higher currents. The filament gets hot, its resistance rises, so each extra bit of voltage produces a smaller increase in current.