Describe an experiment to find the resistivity of a wire.

Get a piece of wire, about 1 metre long. Measure the resistance (Ohmmeter or measure V and I and R=V/I) for 8 different lengths of wire (use ruler). Use micrometer to find diameter of wire in several places and orientations, find the mean. Then find Cross-section area=pi(d/2) squared. Plot graph of R against length. gradient =resisitvity/area so multiply gradient by area to find resistivity.

To find the resistivity of the wire, you will need to make measurements of the voltage and current flowing through it together with the physical dimensions of the wire, from which you will calculate the resistivity of the metal.

A bit of theory

The resistance R of a component in a circuit can be given by the equation:

R = V/I,

where V is the potential difference across the component (in our case, across the wire), and I is the current that flows through this component.

The resistance of a wire is given by the equation:

R = ρL/A,

where L is the length of the wire, ρ is the resistivity of the metal from which the wire is made, and A is its cross-sectional area.

To determine the resistivity of the wire, you should build a circuit that contains a battery, an ammeter, and a tested wire connected in series with a flying lead, along with a voltmeter connected in parallel. After that, you need to make measurements of voltage and current for different lengths of wire. Having that data, you can plot a graph of resistance against length, which allows you to calculate the resistivity.

Making measurements and observations

1. Measure the diameter d of the resistance wire using the micrometre. Repeat measurements in several places along the length, rotating the wire slightly.
2. Connect the circuit described above. The flying lead should have a bare conducting end and should be long enough to touch any part of the resistance wire. 
3. Using the flying lead, make a contact with the resistance wire so that the length L of the resistance wire is about 1.00m. Record the readings from the ammeter and the voltmeter. Disconnect the flying lead.
4. Repeat 3 until you have nine sets of readings where L is from 0.10 m to 1.00 m.

Presenting and analysing your data

1. Calculate the resistance R for each length of a wire using the equation R = V/I.
2. Plot a graph of R (y-axis) against L (x-axis). Draw a line of best fit.
3. Calculate an average value for the diameter d of the wire.
4. Calculate the cross-sectional area A of the wire using the following equation: A = ¼πd^2.
5. Determine the gradient of your graph. Gradient = R/L

Now take a closer look at the equation R = ρL/A. When you divide it by L, you will get R/L = ρ/A. The fraction R/L is the gradient of the graph you have found a few steps before. It means that to find the resistivity ρ you need to multiply the gradient of the graph by the cross-sectional area of the wire => ρ = Grad x A

And that's it!

Set up a test wire in series with a power pack and an ammeter. Connect the test wire to the circuit with crocodile clips so the length of the wire can be altered. A variable resistor should be included in the circuit to vary the amount of current flowing. I would include a digram of the circuit but I don't appear to be able to on this platform.

Practical details I have used to perform this practical in class.

Wire: Constantan Wire 28 swg (standard wire gauge)

The diameter of this wire should be 0.376mm.

The resistivity of Constantan wire = 4.9 x 10-7Ωm.

Length of wire: 1m is an ideal length attached to a meter ruler.

Measure current and potential difference every 5cm.

I would collected 10 readings. 

I would set the power pack to 6.0v but I would measured the potential difference of the wire for each length.

Method

1. A typical test wire would be around 30cm long (L=30cm).

2. Move the crocodile clip so the test wire is 5cm long.

3. Open the variable resistor so it is at its maximum resistance. 

4. Record the ammeter reading in the circuit and the voltmeter reading across

    the 5cm test wire.

5. Switch off the apparatus.

6. Move the crocodile clip so the test wire is 10cm long.

7. Switch on the apparatus. 

8. Lower the resistance of the variable resistor until the ammeter reads the

    same value as before.

9. Record the ammeter reading again and the voltmeter reading across the

   10cm test wire.

10. Switch off the apparatus.

11. Repeat steps 6 to 10 for additional values of wire length: 15cm, 20cm, 25cm

     and 30cm or more.

12. Measure the diameter of the wire in several positions along its length and

     calculate the average diameter. Divide this answer in half to obtain the radius.

Calculate the cross-sectional area of the wire using A = π r2

Calculate the resistance of the wire as the length is increased using V = IR. Divide the potential difference readings by the current to obtain the resistance.

Plot a graph of resistance vs length of wire and draw a straight line of best fit.

Calculate the gradient of the line by drawing a triangle and dividing the height by the length.

Resistance = (resistivity x length of wire)/cross-sectional area of the wire

By plotting a graph of resistance vs length of wire, the gradient = resistivity/x-s area

Therefore, resistivity is calculated by multiplying the gradient by the x-s area calculated above.

Risk assessment

Switch the apparatus off between each measurement to prevent the wire heating up and melting. Don't touch the wire as it could burn you.

I would ask students to comment on how accurate (close to the true value) their answer is.

Questions I would ask relating to this experiment.

1. Why is it important to switch the apparatus off between each measurement?

The flow of charge through a wire causes the wire to heat up. This will lead to an increase in resistance. The experiment measures the change in resistance due to the length of the wire. Allowing the wire to heat up too much will introduce another dependent variable (change in temperature) which will affect resistance too. Switching the apparatus off between each measurement will limit how much the wire heats up, thus minimizing the effect of heat on resistance. 

2. Why is it important to keep the current constant?

Current is rate of flow of charge. Keeping the current in the wire constant means the flow of charge carriers past a given point each second remains constant. So the number of collisions between charge carriers (electrons) and positive metal ions will remain relatively constant. The kinetic energy of the positive metal ions and therefore its temperature will tend to remain constant, eliminating an increase in resistance due to an increase in temperature of the wire. 

The resistivity of a wire depends on a number of factors - resistance, length and cross sectional area. Firstly a circuit would need to be constructed using a power supply, variable resistor, wires, crocodile clips, ammeter and the wire you are testing. Measure the diameter of the wire using a micrometer screw guage and repeat measurements two more times and find the average. This measurement can be halved to determine the radius of the wire and then use A = pi x radius squared to calculate the cross sectional area of the wire. Using a meter ruler, measure the length of the wire. For different lengths of wire measure current and potential difference measurements. These can then be used to determine the resistance as resistance = pd divided by current. A graph of resistance on y against length on x can be plotted to find the gradient of the diagonal line. This can be used alongside information about the cross sectional area to determine the resistivity of the wire.

Resistivity is the resistance R of a wire, multiplied by its cross-sectional area A, and divided by its length l;

ρ = RA/l.

So in order to measure the resistivity you would need to find out the resistance in the wire, the area and length. To do this you need a power supply and voltmeter and ohmeter to find the voltage and current (V=IR), a micrometer to measure the width of wire (area = pi*r^2) and a ruler to measure the length of wire. Take at least 5 measurements of each value to obtain an average that way you get a more accurate result.

Hi Xavier with resistance we know that it is directly proportional to the length of a wire and inversely proportional to it cross sectional area. It is also dependent on the type of material (its resistivity)

The most accurate way to determine a materials resistivity

Is to measure the current through and voltage across a range of lengths of wire (usually constantin) and calculate its resistance at those differing lengths. Plot a graph of R against L and determine its gradient. Multiply this value by its cross-sectional area I'm square metres and this will give you that materials resistivity.

Attach the wire to a battery with known voltage and measure the current with multimeter. The multimeter is mounted as it is shown on the picture. The resistance R is given as a ratio between voltage U and current I. R = U/R

Connect the wire to a battery, a switch, an ammeter and a variable resistor. They should all connected in series (i.e., side by side). Then, connect the two terminals of a voltmeter across the wire (to measure Potential difference across it). Take readings of voltage drop (V) at different current (I) values. Plot a graph of V (p.d) on X-axis vs. I(current) on Y-axis and the gradient of the graph (straight line) will give the resistance of this wire.

Grab two electrical outputs (negative and positive) and put them on each end of l length of wire. The longer the wire the more resistivity it has as it takes longer for it to heat up fully. The shorter the wire the shorter amount of t time it takes for it to heat up and turn bright orange.