Measurement of the resistivity of Nichrome

• Wire A ─ 28-gauge Nichrome wire
• Wire B ─ 32-gauge Nichrome wire

The following method was used to gain the data.

How to measure the cross-sectional area of the wire?

The cross-sectional area can be worked out by the formula:

 

So I just need to work out the diameter of the wire.

1. I stuck two wires separately onto two rulers. Make sure both wires started from 0cm then ended at 100cm on the rule.

2. I checked the micrometer screw gauge, whether the zero is coinciding with the datum line. If not, there will be a positive or negative zero error and will affect the accuracy.

3. The micrometer screw gauge was used to measure diameters of wires. As those wires may not be uniform, I measured both of them every 10cm and get 10 measurements for each. The micrometer can be accurate to 0.01mm. In order to minimize the error I add an estimative digit, and the reading now is to 3 decimal places. 

(Reading recorded in Table A)

How to measure the electrical resistance?

The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it.

   

(Ohm’s Law)

1. Check if there is a zero error of the ammeter and the voltmeter.

2. The apparatus shown in the diagram below was set up. Check whether the ammeter and the voltmeter are linked in the correct range.

At first I measured Wire A

Fasten a clip which has connected with the lead to one end of the wire. And use the other clip to nip an iron slice.

The circuit measures the voltage (V) across the part of wire connected in and the current (I) that is drawn from the cell and pass through this part of wire.

3. I placed the iron slice on the wire so as to make sure that there is current flow in the circuit.

4. The iron slice was placed on the wire 5cm away from the end which nipped by the clip.

5. I recorded the reading on the ammeter and the voltmeter after they stop varying. It is the first set of reading.

The voltmeter I used is a digital one. I can easily find the reading which is given by 2 decimal places. However, the ammeter is the one with a needle. For the current, I could only estimate the second decimal place.

6. I moved the iron slice along the wire (the length then altered), measured voltage and current every 5cm until I got 20 sets of reading.

(Reading recorded in Table B)

After that, I used the same method to measure Wire B. (Reading recorded in Table C)

Data Processing

All the data in the table blow is in 3 decimal place.

Then I used those data to plot graphs separately for Wire A and Wire B with Excel.

Add a straight best fit line across those points.

Graph plotting

Error bar

To find the error bar on the y-axis, I need to calculate the percentage uncertainty of resistance.

But how to work out that?

From Table A, I could find that the wire is not uniform. So I calculate the standard deviation of the values I got for the diameter. The standard deviation of a collection of numbers is a measure of the dispersion of the numbers from their mean value. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large.

Use the equation:

ρ = R1L /A1    ①

ρ = R2L /A2    ②

Let ①over②, I would get R1 /A1 = R2 /A2

Rearrange the equation R1 /R2 = A1 /A2

As A = πd²/4

Therefore R1 /R2 = d12 /d22

Rearrange it R1 = d12 × R2 / d22

From the equation above I could get that the Rmax = dmax2×R /d2

Maximum value of percentage uncertainty of resistance (Max) = (Rmax - R) / R

Substitute Rmax = dmax2×R /d2  into the equation above,

Max = (dmax2 /d2) -1

d = the mean of d

dmax = the mean of d + standard deviation

Use the same method; I got the Minimum percentage uncertainty of resistance

Minimum value of percentage uncertainty of resistance (Min) = (Rmin - R) / R

Rmin = dmin2×R /d2

Min = (dmin2 /d2) -1

dmin = the mean of d-standard deviation

The data in the table below is in 3 decimal place

Add a straight line at both sides of the best fit line. Those lines should be inside any three error bars. Work out their gradients.

Gradient calculation

The data in the table below is in 3 decimal place

Calculate the uncertainty of gradient

Maximum value of uncertainty of gradient (Max) = (Red line gradient/Best fit line gradient) -1

Minimum value of uncertainty of gradient (Min) = (Blue line gradient/Best fit line gradient) -1

Uncertainty calculation

The data in the table below is in 3 decimal place

So the gradient for Graph A (Wire A) is 0.104±1.9%

   the gradient for Graph B (Wire B) is 0.196±1.0%

Getting the results

Using the equation ρ = gradient × A

uncertainty of resistivity = uncertainty of gradient + uncertainty of area

The data in the table below is in 3 decimal place

From the table above, I can get the Final Results,

The resistivity for Wire A is 1.13×10-6Ω·m±4.5%

The resistivity for Wire B is 1.14×10-6Ω·m±2.6%

I can see find that the result for Wire A and Wire B is nearly the same, but the result for Wire B is more accurate than that for Wire A.

As the uncertainty is calculated by both uncertainty of cross-sectional areas and uncertainty of gradients which depend on the diameters (gradients depend on Error bar which worked out by diameters). The reason for that might be the diameters I measured for Wire B is more uniform than those for Wire A. Wire A is not as uniform as Wire B

Conclusion

In this coursework, I measured the resistivity of Nichrome which I found is 1.13×10-6Ω·m±4.5% and 1.14×10-6Ω·m±2.6%.

From Wikipedia, I have found the electrical resistivity of Nichrome at room temperature is 1.08 × 10-6Ω·m, which is very near to the value I have got. However, it is still likely to be a bit higher than expected.

Hereunder is the uncertainty and error analysis

As Nichrome is an alloy, the resistivity won’t be affect much by temperature.

There are several possible sources of error and uncertainty in the experiment.

1. The most likely error might be reading the ammeter and voltmeter. As the voltage and current are always changing, it is hard to read precisely. If there is a reading error, the resistances will be changeable and uncertain, that affects the uncertainly of gradients.

I supposed that I could measure the voltage and current several times and record the reading. Then work out the mean which is considered to be more reliable.

2. From the graph, we can find that the gradients didn’t meet y-axis at the origin, which is different from what I expected. It shows that except the resistance of wire, there must be some other resistors in the circuit. In my opinion, the iron slice which was placed on the wire is the one which must have added a resistance to the circuit. This might have an effect on the gradient. As iron is a metal, the resistivity will increase with temperature. When there is a current flow in the circuit, the iron slice will get hot. The resistivity of iron goes up, therefore the resistance increases, and leads to the increase in total resistance in the circuit during the experiment.

What I could do to improve is to work out the resistance of the iron slice and remove it when plotting the graph. In order to keep the iron slice from getting hot, I should not keep the circuit work for too long. So I need to get the reading as fast as possible.

Bibliography

Websites used

Books used

Advancing physics text book

Data

Table B

28-gauge Nichrome wire (Wire A)

Table C

32-gauge Nichrome wire (Wire B)