Resistance and Special Components

This lesson covers the factors affecting resistance of a wire, the core practical on investigating resistance, and the applications of LDRs and thermistors — as required by the Edexcel GCSE Physics specification (1PH0).

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Factors Affecting the Resistance of a Wire

The resistance of a wire depends on four factors:

Factor	Effect on Resistance	Explanation
Length	Longer wire = more resistance	Electrons must travel further, encountering more collisions with metal ions
Cross-sectional area	Thinner wire = more resistance	Fewer paths for electrons to flow through — like a narrower pipe carrying less water
Material	Different materials have different resistivities	Some materials (e.g. copper) have many free electrons; others (e.g. nichrome) have fewer
Temperature	Higher temperature = more resistance (for metals)	Metal ions vibrate more at higher temperatures, causing more collisions with electrons

Key Relationships

• Resistance is directly proportional to length: if you double the length, you double the resistance.
• Resistance is inversely proportional to cross-sectional area: if you double the area, you halve the resistance.

Exam Tip: At GCSE level, you mainly need to know the effects of length and cross-sectional area on resistance. For Higher tier, you should also be aware of the concept of resistivity (ρ), which is a property of the material itself.

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Core Practical: Investigating How the Length of a Wire Affects Its Resistance

Aim

To investigate how the length of a wire affects its resistance.

Equipment

• Metre ruler
• Constantan (or nichrome) wire attached along the ruler
• Ammeter (in series)
• Voltmeter (in parallel across the wire)
• Power supply (low voltage, e.g. 1–2 V)
• Crocodile clips
• Switch
• Connecting wires

Variables

Variable	Type	Detail
Length of wire	Independent variable (you change this)	Measure from 10 cm to 100 cm in 10 cm intervals
Resistance	Dependent variable (you measure this)	Calculate from R = V/I using ammeter and voltmeter readings
Wire material	Control variable	Use the same wire throughout
Wire diameter	Control variable	Use the same wire (same cross-sectional area)
Temperature	Control variable	Keep current low to avoid heating; switch off between readings

Method

1. Set up the circuit: power supply → switch → ammeter → wire → back to power supply. Connect a voltmeter in parallel across the section of wire being tested.
2. Attach a crocodile clip at the 0 cm mark and another at the 10 cm mark.
3. Close the switch and record the voltmeter (V) and ammeter (I) readings.
4. Open the switch immediately after taking readings to prevent the wire from heating up.
5. Calculate resistance: R = V / I.
6. Move the second crocodile clip to 20 cm and repeat.
7. Continue for lengths of 30, 40, 50, 60, 70, 80, 90, and 100 cm.
8. Repeat the whole experiment at least three times and calculate a mean resistance for each length.
9. Plot a graph of resistance (y-axis) against length (x-axis).

Circuit Diagram

graph TD
    A["Power Supply<br/>(1–2 V)"] --> B["Switch"]
    B --> C["Ammeter (A)"]
    C --> D["Wire under test<br/>(crocodile clips<br/>at set length)"]
    D --> E["Back to<br/>Power Supply"]
    D -.- F["Voltmeter (V)<br/>(in parallel)"]

    style A fill:#2c3e50,color:#fff
    style B fill:#7f8c8d,color:#fff
    style C fill:#e74c3c,color:#fff
    style D fill:#e67e22,color:#fff
    style E fill:#2c3e50,color:#fff
    style F fill:#27ae60,color:#fff

Expected Results

• The graph should be a straight line through the origin.
• This confirms that resistance is directly proportional to length.
• A wire of 50 cm has approximately half the resistance of a wire of 100 cm.

Sources of Error and Improvements

Source of Error	Effect	Improvement
Wire heating up	Resistance increases with temperature, giving inaccurate readings	Use a low voltage; switch off between readings
Poor connections at crocodile clips	Additional resistance at the contacts	Clean the wire; ensure firm clip contact
Measuring length inaccurately	Wrong length recorded	Use a metre ruler; measure from clip to clip
Not waiting for readings to stabilise	Ammeter/voltmeter readings may fluctuate	Wait a few seconds for steady readings

Exam Tip: This is a core practical and is very frequently examined. You may be asked to describe the method, identify variables, draw the circuit, sketch the expected graph, or suggest improvements. Make sure you explain that you keep the current low to avoid heating the wire, as heating would change the resistance and make results unreliable.

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Resistivity (Higher Tier)

Resistivity (ρ, the Greek letter rho) is a property of the material itself. It tells you how much the material resists the flow of current, regardless of the wire's dimensions.

$R = \frac{\rho L}{A}$R=AρL​

Where:

• R = resistance (Ω)
• ρ = resistivity (Ωm)
• L = length (m)
• A = cross-sectional area (m²)

Material	Resistivity (Ωm) at 20°C	Use
Copper	1.7 × 10⁻⁸	Wiring (very low resistivity)
Nichrome	1.1 × 10⁻⁶	Heating elements (higher resistivity)
Constantan	4.9 × 10⁻⁷	Resistance wire experiments

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LDR Applications in Detail

The light-dependent resistor (LDR) has many practical applications that rely on its property of decreasing resistance in brighter conditions.

Automatic Street Lighting

graph TD
    A["Daylight"] --> B["LDR resistance LOW"]
    B --> C["Low voltage across LDR"]
    C --> D["Circuit does NOT switch on lamp"]
    E["Darkness"] --> F["LDR resistance HIGH"]
    F --> G["High voltage across LDR"]
    G --> H["Circuit switches ON lamp"]

    style A fill:#f1c40f,color:#000
    style B fill:#27ae60,color:#fff
    style D fill:#7f8c8d,color:#fff
    style E fill:#2c3e50,color:#fff
    style F fill:#e74c3c,color:#fff
    style H fill:#f1c40f,color:#000

• In bright conditions, the LDR has low resistance, so the voltage across it is small — the lamp stays off.
• In dark conditions, the LDR has high resistance, so the voltage across it increases — triggering the circuit to switch on the lamp.

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Thermistor Applications in Detail

The thermistor (NTC type at GCSE level) has many practical applications that rely on its property of decreasing resistance at higher temperatures.

Thermostat (Temperature Control)