What Causes Electrical Resistance?

Electrical resistance is caused by interactions between mobile charge carriers and the material through which they move. In a metal, conduction electrons are scattered by vibrating lattice ions, impurities, and structural defects, transferring electrical energy to the material's internal energy.

This topic is part of B.5 Current and circuits and is studied at both SL and HL.

When a potential difference is applied across a conductor, an electric field causes the conduction electrons to acquire a net drift velocity. Their repeated collisions oppose this ordered motion, so a potential difference is required to maintain the current. Resistance is defined by

$$R=\frac{V}{I}$$

where resistance is measured in ohms, $\Omega$. For a uniform conductor,

$$R=\rho\frac{L}{A}$$

where $\rho$ is the material's resistivity, $L$ is its length, and $A$ is its cross-sectional area.

At the microscopic level, electrons accelerate between collisions, but each collision disrupts their directed motion. The average drift speed therefore remains small even though the electric field acts continuously. A larger scattering rate means a smaller current for the same potential difference, so the resistance is greater. The dissipated energy appears mainly as heating in an ordinary resistor.

For example, if $\rho=1.7\times10^{-8}\,\Omega\,\text{m}$, $L=2.0\,\text{m}$, and , then

$$R=\frac{(1.7\times10^{-8})(2.0)}{1.0\times10^{-6}}=0.034\,\Omega.$$

A common misconception is that current is "used up" by resistance. Current is charge flow; resistance instead causes electrical energy to be transferred, often as thermal energy.

In an IB Explain question, link microscopic collisions to energy transfer and reduced current, then use $R=\rho L/A$ for macroscopic factors. Remember that an ohmic conductor has constant resistance only when physical conditions, especially temperature, remain constant.