School Physics GCSE level Notes: Electricity 3.3 Resistance and dimensions of a wire

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Electricity Section 3:

3.2 Investigating the electrical resistance of a thin wire - variation of length or varying diameter (varying cross-section area)

[Author © Dr WP Brown PhD: Doc Brown's physics exam revision notes suitable for students of UK IGCSE & GCSE level physics courses, ~ US grades 9-10 physics, electricity page updated Feb 8th 2026]

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INDEX for electricity section 3 notes on current, voltage, resistance, energy & charge transfer in circuits

3.2 Investigating the electrical resistance of a wire - variation of length or diameter

Question to be answered.  What factors affect the resistance of a circuit? e.g. how does the length or thickness of a conducting device influence the current flowing i.e. what affects the resistivity of a wire.

circuit diagram to investigate the resistance of a wire varying its length and thickness acting as a resistor

Circuit 30 shows how to investigate the resistance of a wire

A relatively thin wire is fastened at each end onto a meter ruler marked in mm using crocodile clips.

You need an ammeter to measure the current in amps and a voltmeter to measure the p.d. across the wire in volts.

The wire is connected in series with a battery power supply, switch and ammeter to measure the current flowing through the wire in amps.

 

The voltmeter, to measure the p.d, is wired in parallel across the resistance wire.

Note the ammeter is always wired in series with a component, but a voltmeter is always wired in parallel across any component under investigation.

One end of the wire connected through the voltmeter is fixed (on the left), but the other end has a crocodile clip that acts as a moveable contact point to place a various distance along the resistance wire from left to right.

Close the switch to complete the circuit and begin taking readings.

Its best to open the switch between readings to minimise the risk of heating up the wire.

 

You vary the distance d (mm) from the left (0 mm) to a point further along to the right and take a series of pairs of p.d and current readings e.g. every 50 mm (you can work in cm, it makes no difference!).

Using Ohm's Law, you calculate the resistance in ohms from the equation R = V / I

graph of resistance versus length of wireYou can then plot a graph of resistance (Ω) versus the length of the wire d (mm) - shown on the right.

You should find the graph is linear with its x,y origin at 0,0.

This means the resistance is proportional to the length of the wire.

If you don't fix the wire exactly at 0 mm, the graph should still be linear, but, the origin of the line will not be 0,0.

If you repeat the experiment with different diameter wires, you should find the gradient becomes lower, the thicker the wire.

 

The longer the wire, the electrons collide with more metal ions in the metallic lattice, inhibiting their flow.

For the same length of wire, the resistance is less the larger the diameter of the wire.

A thinner wire is more constricted creating a greater resistance against the current flow.

A good analogy is the ease with which water flows through a thin or wider diameter pipe.

If the wire doesn't heat up, the wire should behave as an ohmic conductor i.e. V = IR is consistent over a wide range of current-voltage readings.

The thicker the wire (increase in diameter), there is a greater cross-section area for electrons to flow through, so the number of collisions with the ions of the metal lattice is reduced.

 

INDEX of electricity section 3 notes on current, voltage, resistance, energy & charge transfer in circuits including Ohm's Law investigations

Key points about electric circuits in physics courses - effect of wire length and diameter on its electrical resistance

Information sources for Doc Brown's key points: IGCSE-GCSE physics are based on textbooks & syllabus-specifications for students taking the UK AQA, Edexcel, OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE physics 9-1 level science examinations.

Here's a comprehensive, exam-board-aligned summary on how resistance varies with wire length and diameter, tailored for GCSE/IGCSE Physics students:

Resistance of a Wire – Length & Diameter

Core Principle

The resistance R of a wire depends on:

  • Length ( L )
  • Cross-sectional area ( A ) (related to diameter)
  • Temperature (assumed constant in most GCSE contexts)

Where:

  • R = resistance (Ω)
  • rho = resistivity (Ω·m)
  • L = length of wire (m)
  • A = cross-sectional area (m²)

Not needed for GCSE physics, but ...

The resistance (R) of a wire can be calculated using the formula R = (ρL) / A, where ρ (rho) is the material's resistivity, L is the wire's length, and A is its cross-sectional area.

For a wire with a circular cross-section, the area A can be expressed in terms of its diameter (D) as A = π(D/2)² = πD²/4. Substituting this into the resistance formula gives R = (4ρL) / (πD²).

Effect of Length

  • Longer wire = more resistance
  • Electrons travel further → more collisions with metal ions → greater opposition to current
  • Directly proportional: doubling the length doubles the resistance

Effect of Diameter (or Thickness)

  • Thicker wire = less resistance
  • Larger cross-sectional area → more space for electrons to flow → fewer collisions
  • Inversely proportional to area:
    If diameter doubles, area increases by a factor of 4 (since ( A =     πr2 ) so resistance drops

Required Practical (All GCSE Boards)

Aim: Investigate how resistance changes with wire length

Method Overview:

  • Set up circuit with ammeter, voltmeter, and a wire taped to a ruler
  • Measure current and voltage for different lengths
  • Calculate resistance using ( R = V/I )
  • Plot graph of length versus resistance → should be a straight line through origin

Safety Tip: Use low voltages to prevent wire overheating

Typical Exam Board Syllabus Content

Key Focus
Maybe a required practical on resistance versus length; graph interpretation
Emphasis on practical skills and understanding proportionality
Includes resistance in series/parallel and practical investigation
Focus on circuit diagrams and resistance calculations
Investigates resistance with changing length and cross-sectional area
Strong emphasis on definitions, calculations, and experimental design

Student Tips for Success

  • Practise graphing: length versus resistance should be linear
  • Understand area: Know how diameter affects cross-sectional area
  • Use correct units: Length in metres, area in m², resistance in ohms
  • Revise practicals: Be able to describe method, apparatus, and expected results
  • Think real-world: Longer extension cords have more resistance; thick cables reduce energy loss

Keywords, phrases and learning objectives for the electrical resistance of a wire

Be able to describe the circuit and method to investigating electrical resistance of a wire by varying the wire's length or diameter of the wire.

Be able to analyse and explain the current-voltage graph for the wire including the calculations of results for ohmic conductor.

For a given diameter, know that the longer the wire, the greater its resistance and the resistance is proportional to the length of the wire - assuming it does not increase in temperature.

For a given length of wire, know that the resistance decreases with increase in diameter.

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