Resistance of a metal wire against temperature

Practical method

Aim

Investigate how the resistance of a metal wire varies with temperature and find its temperature coefficient.

Variables

Independent variable: temperature
Dependent variable: resistance
Control variables: the same coil of wire; small measuring current.

Apparatus

• Coil of copper wire in a test tube
• Water bath with kettle and ice
• Thermometer
• Ohmmeter or ammeter–voltmeter circuit
• Stirrer

Method

1. Place the coil in a test tube of oil (or water if insulated) in a water bath with a thermometer.
2. Measure the resistance at 0 °C using ice water.
3. Heat the bath in steps of 20 °C, stirring and waiting for a steady resistance reading at each temperature.
4. Plot R against temperature θ: R = R₀(1 + αθ), so the gradient is R₀α.

Sample results

Copper coil; small current from the ohmmeter.

Analysis

R increases linearly with temperature, with gradient 0.039 Ω °C⁻¹ and R₀ = 10.00 Ω. α = \(\dfrac{0.039}{10.00}\) = 3.9 × 10⁻³ °C⁻¹, the accepted value for copper. Increased lattice vibrations scatter conduction electrons more often.

Uncertainty

Resistance is read to ±0.01 Ω (0.1%) and temperature to ±0.5 °C. The main uncertainty is the coil lagging the bath temperature.

Errors and improvements

Risk assessment

Common mistakes

• Reading temperature before thermal equilibrium.
• Ignoring the lead resistance.
• Treating α as the gradient without dividing by R₀.

Worked analysis

Gradient = \(\dfrac{13.12 - 10.00}{80}\) = 0.039 Ω °C⁻¹. α = \(\dfrac{\text{gradient}}{R_{0}}\) = \(\dfrac{0.039}{10.00}\) = 3.9 × 10⁻³ °C⁻¹.

Common misconception

Metals have higher resistance when hot because electrons collide more often with vibrating ions, not because there are fewer electrons.