Required Practical: Resistance of a Wire

This lesson covers the AQA Required Practical for investigating how the length of a wire affects its resistance (AQA 8464, Required Practical Activity 15). This is one of the most frequently examined practicals in the electricity topic.

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Aim

To investigate the relationship between the length of a wire and its resistance.

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Hypothesis

As the length of the wire increases, the resistance increases proportionally. A wire that is twice as long should have twice the resistance, because there are twice as many metal ions for the electrons to collide with.

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Equipment

Item	Purpose
Constantan (or nichrome) wire	The wire being tested — these alloys have a resistance that changes very little with temperature
Metre ruler	To measure the length of wire accurately
Crocodile clips (×2)	To make contact with the wire at measured points
Ammeter	To measure the current through the wire (connected in series)
Voltmeter	To measure the potential difference across the wire (connected in parallel)
Battery / power pack	To provide a potential difference across the circuit
Switch	To turn the circuit on and off — reduces heating of the wire
Variable resistor (optional)	To keep the current low and reduce heating

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Circuit Diagram

flowchart LR
    A["Battery / Power Pack"] --> B["Switch"]
    B --> C["Ammeter (A)"]
    C --> D["Crocodile Clip 1"]
    D --> E["Constantan Wire (length L)"]
    E --> F["Crocodile Clip 2"]
    F --> A
    G["Voltmeter (V)"] -.->|"in parallel across wire"| D
    G -.-> F

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Method

1. Set up the circuit as shown in the diagram above.
2. Attach one crocodile clip at the 0 cm mark on the wire and the other at the 10 cm mark.
3. Close the switch, record the ammeter reading (I) and the voltmeter reading (V). Open the switch immediately to prevent the wire from heating up.
4. Calculate the resistance using $R = \dfrac{V}{I}$R=IV​.
5. Move the second crocodile clip to the 20 cm mark and repeat.
6. Continue increasing the length in 10 cm intervals up to at least 100 cm.
7. Repeat each length measurement at least three times and calculate a mean resistance for each length.

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Recording Results

Length (cm)	V₁ (V)	I₁ (A)	R₁ (Ω)	V₂ (V)	I₂ (A)	R₂ (Ω)	V₃ (V)	I₃ (A)	R₃ (Ω)	Mean R (Ω)
10
20
...
100

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Expected Results

• A graph of resistance (y-axis) vs length (x-axis) should give a straight line through the origin.
• This confirms that resistance is directly proportional to length (for a wire of constant cross-sectional area and material at constant temperature).

graph LR
    subgraph "Expected Graph Shape"
        direction LR
        A["Origin (0,0)"] --> B["Straight line with positive gradient"]
    end

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Variables

Variable Type	Variable	Detail
Independent	Length of wire	Changed in 10 cm intervals
Dependent	Resistance	Calculated from V and I
Control	Material of wire	Use the same wire throughout
Control	Cross-sectional area	Use the same wire (same diameter)
Control	Temperature	Switch off between readings; keep current low

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Key Points for the Exam

Why Use Constantan Wire?

Constantan (or nichrome) has a very low temperature coefficient of resistance — its resistance changes very little with temperature. This means the resistance is affected mainly by length, not by heating.

Why Switch Off Between Readings?

When current flows through the wire, it heats up (due to the transfer of energy by the moving electrons). If the wire gets hot, the resistance increases, which introduces an error into the results. Switching off between readings keeps the temperature approximately constant.

Why Repeat and Calculate a Mean?

Repeating reduces the impact of random errors and makes the results more reliable. Anomalous results (outliers) can be identified and excluded.

How to Improve Accuracy

• Use a micrometer to measure the diameter of the wire at several points and check it is uniform.
• Use a low current or a variable resistor to minimise heating.
• Ensure the wire is straight and not kinked, so the length measurement is accurate.
• Zero the ammeter and voltmeter before use.

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Worked Example

A student measures the following values for a 60 cm length of wire: V = 1.8 V, I = 0.3 A. Calculate the resistance.

$R = \frac{V}{I} = \frac{1.8}{0.3} = 6.0 \text{ Ω}$R=IV​=0.31.8​=6.0 Ω

If the resistance of 30 cm of the same wire is 3.0 Ω, does this support the hypothesis?

Yes — doubling the length (30 cm → 60 cm) doubled the resistance (3.0 Ω → 6.0 Ω), confirming that resistance is directly proportional to length.

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Common Mistakes

Mistake	Correction
Leaving the circuit on between readings	Switch off to prevent the wire heating up and changing resistance
Not repeating measurements	Always take at least 3 readings and calculate a mean
Not controlling the wire material or thickness	Use the same wire for all measurements
Measuring length from the wrong point	Measure from crocodile clip to crocodile clip, not from the end of the ruler
Plotting V or I on the graph instead of R	The graph should show R vs length

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Summary

• This required practical investigates how the length of a wire affects its resistance.
• The independent variable is length; the dependent variable is resistance (calculated from $R = V/I$R=V/I).
• Control variables include the material, cross-sectional area and temperature of the wire.
• Use constantan/nichrome wire because its resistance changes very little with temperature.
• The expected result is a straight line through the origin on a graph of R vs length, showing direct proportionality.
• Switch off between readings and use a low current to reduce heating errors.
• Repeat measurements and calculate a mean to improve reliability.

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Extended Worked Examples

Worked Example 1 — Calculating R at Each Length