3.10 Core Practical 2: Investigating Resistivity

Core Practical 2: Investigating Resistivity

Aims of the Experiment

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

Variables

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

Method

Apparatus diagram, downloadable AS & A Level Physics revision notes

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
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
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
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
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
Record the current for each length at least 3 times and calculate an average current, I
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

$ρ = \frac{R A}{L}$

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:

$R = \frac{ρ L}{A}$

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

$ρ = g r a d i e n t \times A$

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

To calculate the cross-sectional area, A, of the wire

$c r o s s s e c t i o n a l a r e a, A = \frac{π d^{2}}{4}$

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
- Do not touch the wire directly when the circuit is switched on
Switch off the power supply between readings, and immediately if you smell burning
Keep liquids away from electrical equipment

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 notes The following additional data for the wire is: Worked example table 2, downloadable AS & A Level Physics revision notes Calculate the resistivity of the wire.