Measuring the Effect of Resistance Wire Length on Resistance

Electrical resistance tells us how difficult it is for current to flow through a material. For GCSE and A Level Physics students, one of the clearest ways to explore resistance is by measuring how it changes with the length of a wire.

This simple experiment reinforces the relationship:

$$R \propto L$$

when the material, thickness, and temperature of the wire are kept constant.

Using a power supply, ammeter, voltmeter, and nichrome wire stretched along a metre ruler, students can collect accurate data and see the relationship first-hand.

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The Science

The resistance of a wire depends on:

• length (L) – doubling the length doubles the resistance

• cross-sectional area (A) – thinner wires have higher resistance

• resistivity (ρ) – each material has its own natural resistance

• temperature – higher temperatures increase resistance in metals

The formula is:

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

When only the length changes, resistance increases in direct proportion to it.

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The Experiment

Equipment:

• Nichrome or constantan resistance wire

• Metre ruler

• Ammeter

• Voltmeter (or multimeter)

• Low-voltage DC power supply

• Crocodile clips

• Connecting leads

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Method

1. Attach the wire securely to a metre ruler.

2. Connect one crocodile clip at the zero mark.

3. Move the second clip to different lengths (e.g. 20 cm, 40 cm, 60 cm, 80 cm, 100 cm).

4. For each length:

   • switch on the power supply

   • record voltage and current

   • calculate resistance using

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

5. Keep the current low to avoid heating, which changes resistance.

6. Plot a graph of R against L.

The graph should be a straight line through the origin, showing direct proportionality.

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Typical Results

Length (cm)	Voltage (V)	Current (A)	Resistance (Ω)
20	0.40	0.40	1.0
40	0.80	0.40	2.0
60	1.20	0.40	3.0
80	1.60	0.40	4.0
100	2.00	0.40	5.0

This pattern is typical: resistance increases linearly with length.

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Why It Works in Teaching

Students see the equation in action.
By plotting their own data, they can identify:

• proportional relationships

• gradient meaning (resistance per metre)

• how resistivity could be calculated with known cross-sectional area

This experiment also supports required practical skills for GCSE Physics.

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Skills Highlight

• Building simple electrical circuits

• Taking accurate voltage and current readings

• Calculating resistance

• Producing linear graphs

• Controlling variables such as temperature and wire thickness