Factors Affecting the Resistance of a Wire

The resistance of a wire depends on four factors.

Length

Resistance is proportional to length: $R \propto L$.

A longer wire has more resistance because charge carriers (electrons) must travel further and encounter more ions in the lattice.

Doubling the length doubles the resistance.

Cross-sectional area

Resistance is inversely proportional to cross-sectional area: $R \propto \frac{1}{A}$.

A thicker wire has less resistance because there is more space for electrons to flow (like a wider pipe carries more water).

Doubling the area halves the resistance.

Material

Different materials have different resistivities. Metals like copper and silver have low resistance (good conductors). Materials like nichrome have higher resistance (used in heating elements).

Temperature (for metals)

For most metals, resistance increases with temperature. Higher temperature means the metal ions vibrate more vigorously, making it harder for electrons to flow past them.

Investigating resistance vs length

1. Set up a circuit with a power supply, ammeter, and a length of resistance wire connected via crocodile clips.
2. Connect a voltmeter in parallel across the wire.
3. Vary the length of wire in the circuit.
4. For each length, record $V$ and $I$, and calculate $R = V/I$.
5. Plot $R$ vs $L$. A straight line through the origin confirms $R \propto L$.

Common errors and how to correct them

• Saying resistance decreases with length. Longer wire = more resistance.
• Not controlling temperature during the experiment (use low current to minimise heating).

How to apply this in an exam

State the proportionality relationships ($R \propto L$, $R \propto 1/A$). Explain the mechanism in terms of electron flow. Describe how to investigate one factor while controlling the others.