Electricity

Learning objectives

• Relate current to charge and drift velocity.
• Use resistivity with conductor dimensions.
• Interpret current–voltage characteristics.

The big idea

Current is the rate at which charge crosses a section. In a metal, many mobile electrons have a small net drift superimposed on random motion. Conventional current is opposite to electron drift.

Resistance depends on material, geometry and temperature. Resistivity characterises a material under specified conditions. A non-ohmic component does not have a straight current–voltage characteristic through the origin at fixed operating conditions.

1. Current links microscopic motion with measurement

Current is charge crossing a section per second. In a metal, electrons have random motion plus a small net drift. Conventional current points opposite that electron drift. The relationship I = nAvq uses carrier density, cross-sectional area, drift speed and charge magnitude. A larger current does not necessarily mean each electron has a much larger drift speed: carrier density and conducting area also matter.

2. Potential difference is an energy ratio

A potential difference of 3 V means 3 J transferred per coulomb across the specified component. This is not a statement that current is 3 A or that every charge has lost all of its energy. Energy and charge accounting are different. For a resistor in steady operation, P = VI gives the transfer rate; combining it with V = IR produces I²R or V²/R where the same component values apply.

3. Resistivity removes geometry from resistance

For a uniform wire, R = ρL/A. A longer wire has more resistance; a thicker wire has less under the same material and temperature conditions. If diameter doubles, area becomes four times larger, so resistance becomes one quarter, not one half. Use area rather than diameter in the formula. Material resistivity can change with temperature, so changing current enough to heat a wire can also change the relationship being measured.

4. A characteristic records operating behaviour

An ohmic resistor at constant temperature has a straight current–voltage characteristic through the origin. A filament lamp’s increasing temperature changes its resistance, producing a curve. A diode is strongly direction-dependent. State which variable is on which axis before interpreting a slope: on a V-against-I graph, V/I corresponds to resistance, while the axes reversed describe a different gradient. Curved characteristics require care when comparing ratios and tangents.

A method you can reuse

1. Identify carrier type, current direction and component voltage.
2. Convert wire dimensions and calculate area.
3. Check whether temperature and material properties remain fixed.
4. Choose the electrical power expression consistent with known quantities.
5. Interpret slopes only after checking the axes and whether the graph is linear.

Equations and relationships

Investigate and explain

Measure voltage and current for a low-voltage resistor without allowing it to heat significantly; plot the results.

Compare charge transfer, wire geometry and circuit current as distinct models. Static charging is not steady current, and an ideal resistor does not capture every temperature-dependent characteristic.

Open the interactive investigation

Check your understanding