Core Practical 7: Investigating Resistivity (Edexcel International A Level Physics)

Revision Note

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Core Practical 7: Investigating Resistivity

Aims of the Experiment

  • The aim of the experiment is to determine the resistivity of a length of wire


  • Independent variable = Length, L, of the wire (m)
  • Dependent variable = The current, I, through the wire (A)
  • Control variables:
    • Voltage across the wire
    • The material the wire is made from

Equipment List

Equipment list table, downloadable AS & A Level Physics revision notes

  • Resolution of measuring equipment:
    • Metre ruler = 1 mm
    • Micrometer screw gauge = 0.01 mm
    • Voltmeter = 0.1 V
    • Ammeter = 0.01 A


Apparatus diagram, downloadable AS & A Level Physics revision notes

  1. Measure the diameter of the wire using a micrometer.
    • The measurement should be taken between 5-10 times randomly along the wire.
    • Calculate the mean diameter from these values
  2. Set up the equipment so the wire is taped or clamped to the ruler with one end of the circuit attached to the wire where the ruler reads 0.
    • The ammeter is connected in series and the voltmeter in parallel with the wire
  3. Attach the flying lead to the test wire at 0.25 m and set the power supply at a voltage of 6.0 V.
    • Check that this is the voltage across the wire on the voltmeter
  4. Read and record the current from the ammeter, then switch off the current immediately after the reading
    • This is to prevent the wire from heating up and changing the resistivity
  5. Vary the distance between the fixed end of the wire and the flying lead in 0.25 m intervals (0.25 m, 0.50 m, 0.75 etc.) until the full length
    • In this example, a 2.0 m wire is used.
    • The original length and the intervals can be changed (e.g. start at 0.1 m and increase in 0.1 m intervals), as long as there are 8-10 readings
  6. Record the current for each length at least 3 times and calculate an average current, I
  7. For each length, calculate the average resistance of the length of the wire using the equation

Resistance Equation

  • Where:
    • R = average resistance of the length of the wire (Ω)
    • V = potential difference across the circuit (V)
    • I = the average current through the wire for the chosen length (A)

  • An example of a table of results might look like this:

Example table of Results, downloadable AS & A Level Physics revision notes

Analysis of Results

  • The resistivity, ρ, of the wire is equal to

Resistivity Equation

  • Where:
    • ρ = resistivity (Ω m)
    • R = resistance (Ω)
    • A = cross-sectional area of the wire (m2)
    • L = length of wire (m)

  • Rearranging for the resistance, R, gives:

Resistance and Resistivity Equation

  • Comparing this to the equation of a straight line: y = mx
    • y = R
    • x = L
    • Gradient, m = ρ / A
  • Therefore, to find resistivity:
    • Plot a graph of the length of the wire, L, against the average resistance of the wire
    • Draw a line of best fit 
    • Calculate the gradient
    • Multiply the gradient by cross-sectional area, A 

ρ = gradient × A

Example Graph sketch, downloadable AS & A Level Physics revision notes

  • To calculate the cross-sectional area, A, of the wire Cross-sectional Area Equation

Evaluating the Experiment

Systematic Errors:

  • The end of the wire that is attached to the circuit (not the flying lead) must start at 0 on the ruler
    • Otherwise, this could cause a zero error in your measurements of the length

Random Errors:

  • Only allow small currents to flow through the wire
    • The resistivity of a material depends on its temperature
    • The current flowing through the wire will cause its temperature to increase 
    • Therefore the temperature is kept constant by small currents
  • The current should be switched off between readings
    • So that there isn't a temperature rise
  • Calculate an average diameter
    • This will reduce random errors in the reading
    • Make at least 5-10 measurements of the diameter of the wire with the micrometer 

Safety Considerations

  • When there is a high current, and a thin wire, the wire will become very hot.
    • Make sure never to touch the wire directly when the circuit is switched on
  • Switch off the power supply right away if you smell burning
  • Make sure there are no liquids close to the equipment,
    • This could damage the electrical equipment
    • Or cause a short circuit which will affect the results

Worked example

A student conducts an experiment to find the resistivity of a constantan wire.

They attach one end of the wire to a circuit that contains a 6.0 V battery. The other end of the wire is attached by a flying lead to the wire at different lengths.

They obtain the following table of results:Worked example table 1, downloadable AS & A Level Physics revision notesThe following additional data for the wire is:Worked example table 2, downloadable AS & A Level Physics revision notesCalculate the resistivity of the wire.

Step 1: Complete the average current and resistance columns in the table

    •     The resistance is calculated using the equation

Resistance EquationWorked example solution table, downloadable AS & A Level Physics revision notes

Step 2: Calculate the cross-sectional area of the wire from the diameter

    • The average diameter is 0.191 mm = 0.191 × 10–3 m
    • The cross-sectional area is equal to

Area Calculation Worked Example

Step 3: Plot a graph of the length L against the resistance R

Worked example gradient from graph 1, downloadable AS & A Level Physics revision notes

Step 4: Calculate the gradient of the graph 

Worked example gradient from graph, downloadable AS & A Level Physics revision notes

fraction numerator capital delta R over denominator capital delta L end fraction space equals space rho over A space equals space fraction numerator 27.00 minus 5.00 over denominator 1.7 minus 0.3 end fraction space equals space 15.71

Step 5: Calculate the resistivity of the wire

rho space equals space g r a d i e n t cross times A space equals space 15.71 cross times open parentheses 2.87 cross times 10 to the power of negative 8 end exponent close parentheses space equals space 4.51 cross times 10 to the power of negative 7 end exponent space straight capital omega straight m

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Author: Joanna

Joanna obtained her undergraduate degree in Natural Sciences from Cambridge University and completed her MSc in Education at Loughborough University. After a decade of teaching and leading the physics department in a high-performing academic school, Joanna now mentors new teachers and is currently studying part-time for her PhD at Leicester University. Her passions are helping students and learning about cool physics, so creating brilliant resources to help with exam preparation is her dream job!