# Experiments with Resistivity

Experiments with Resistivity and Youngs Modulus.

Detailed Plan

I will do an experiment using Wire A’ all I know about this is that it has a SWG of 32. I will find the material that this wire is made out of by working out its resistivity. When I know value this I can simply look it up in the table of resistivity to find the material.

The Resistivity Equation is:

Resistance = Resistivity x Length the Wire / Cross Section Area of Wire

Symbols and Units:
Resistance – R, measured in Ohms ()
Resistivity – , measured in Ohm Meters (m)
Length – L, measured in Meters (m)
Cross Section Area – A, measured in meters (m)

I will draw a graph of this equation with L/A as the x value and R as the y value to find out resistivity (which is the gradient) as I can measure length and area and I can calculate resistance as it is Voltage/Current.

Prediction

the value of resistance will increase with the length of wire used

the Wires cross sectional area should be constant all the way along

Variables

To Be Kept The Same:
Voltage coming from the power pack – 4V
The Piece of wire used (thickness and area)
Same Ammeter, Voltmeter, cables, etc…

That Will Change:
The Length of the wire
The Temperature of all the components (although not desired as it may alter readings)

Proposed Method

For this experiment you will need to find out the Cross section area of the wire, the length of the wire and the resistance of the wire, which you can work out by finding the current and voltage of the piece of wire at each length and applying the equation:

Resistance = Voltage / Current

So for my experiment I will change the length of my wire and at each interval record to wires thickness, the voltage and the current passing through it. I will then plot the graph of

Resistance = Resistivity x Length of the Wire
Cross Section Area of Wire

So the resistivity of my wire will be the gradient of my graph. Which is calculated by the change in x value / by the change in y value.

Method
1. Collect all equipment as in apparatus list
2. Measure out around 120cm of wire to stretch across the ruler so I have reasonable excess to attach my crocodile clips too.
3. Measure the thickness of the wire using a micrometer at 3 different stages along its length to take an average in case it is uneven. I can then halve this value to find the radius and apply rules of mathematics to find the area of the wires cross section
4. Secure the wire so it is taught along the ruler using sellotape
5. Connect all wires to the power pack, ammeter, voltmeter etc making sure the components are in series or parallel depending on their function
6. Attach crocodile clips to each end of the wires and connect them to the beginning value of 1m of wire
7. Set the power pack to 4v (will not change this)
8. Record readings of both current and voltage
9. Turn power pack off for around 5 second for it too cool down
10. Move the crocodile clip up or down 10cm to the next length required
11. Repeat from step 8 until all lengths are recorded

Range of readings = 0.100m 1.000m and 1.000m 0.100m
I will do repeats of any result which is wildly of the general trend of others to ensure any initial random errors.

Apparatus Required

Ammeter Range: +20 to -20, to the nearest 0.01 of a Volt
Voltmeter Range: +20 to -20, to the nearest 0.01 of an Amp
Micrometer Range: 0.01mm to 2.500 cm, to the nearest 0.01 of a mm
Meter Ruler Range: 1mm to 1m, to the nearest mm
Power Pack Range: 1 to 15 volts, to the nearest Volt (set at 4V)
Crocodile Clips
Sellotape
Cables
Wire SWG: 32, Unknown material

Safety Considerations

Before adjusting the wire to the desired legnth, leave it to cool for a few seconds to avoid being burnt

I will take a reading of both current and voltage when the wire is at lengths of 0.100, 0.200, 0.300, 0.400, 0.500, 0.600, 0.700, 0.800, 0.900 and 1.000 m and then backwards in 10 cm intervals so 1.000, 0.900, 0.800, 0.700, 0.600, 0.500, 0.400, 0.300, 0.200, and 0.100. I will then use an average of the 2 results to get an average current and voltage for each length of wire then find the resistance

Reason For Procedure

I will take these readings because as the experiment goes on the temperature of the wire will increase and this will most likely effect the resistance of the wire so I will take a reading from each measurement when the wire is hot and when the wire is cold so I can take an average and hopefully rule out a systematic error in this area.

Justification For Design

To find resistivity I will draw the graph of R= x L
A
In comparison to Y = MX + C
This gives . Y Axis = Resistance
X Axis = Length / Cross Section Area
So my choice of variables was the length or cross section area of the wire. I have chosen to calculate L/A before plotting my graph instead of plotting L as the y axis as it prevents later calculations using the gradient and I have on simple calculation to find out my resistivity which is simply to find the gradient:

Change in X

Aspects of the plan based on predictions

I cannot really predict the outcome of my experiment but I will take 2 readings of voltage and current as I assume the wire will heat up and affect the readings as the experiment goes on.

A8d Preliminary Results or secondary sources

Length of wire = 0.100 m
Resistance 1 = 2.13
Resistance 2 = 2.09

Resistance = Resistivity x Length the Wire
Cross Section Area of Wire

Average Resistance = 2.11
Wire Thickness = 0.270 mm

So 2.11 = x 0.100 => 2.11= x 1.75 x10
5.73 x10^6

P = 2.11 = 1.06 x10^ -6 m
1.75 x10^6

Identifying Significant Sources of Error

Anything measured is a source of error

– Length of the wire
– Current
– Voltage
– Thickness of the wire

Length Min reading 0.10 m, + or – 1mm, max error = 1%
Current Min reading 0.13 Amps, + or 0.01 amps, max error = 8%
Voltage Min reading 2.24 Volts, + or 0.01 volts max error = 1%
Thickness Min reading 0.27mm, + or 0.01 mm, max error = 4%

Maximum equipment error = 14% (with rounding)

Proposed action to minimize errors

To prevent systematic errors whilst measuring the current and voltage, I will take 2 readings for each when the wire is cool and when it is warm and then take an average.
Whist measuring the thickness of the wire I will take 3 readings from different places on the wire and then take an average.

Information taken from graph gradient intercept

Gradient = 14.5 / 13.25 x10^6 = 1.09 x10^ -6
Intercept = 0.25

RESISTIVITY = 1.09 x10^ -6 m

Conclusion

I found the resistivity of the wire to be 1.09 x 10^6 m by finding my gradient values (Y X, change in Y Change in X) which was 14.5 13.25 x10^6 and according to the table of resistivity (in the appendix) my wire is made out of Nichrome as its resistivity is 1.10 x10 m so I am only 0.01 out.

Supports my prediction?

My predictions were correct as the resistance of my wire did increase and the diameter and therefore cross sectional area of my wire were equal all the way along.

Evaluating Evidence

Possible sources of error

Length of the wire
Current
Voltage
Area of the wire

The readings when the length of wire was 30cm and 90cm appear to be slightly of the trend more than the others but they still follow the line of best fit pretty well.

My repeat readings all varied from the first readings but this was pretty constant with all the readings and was expected due to the rise in temperature of the wire as the experiment went on.

Discrepancies between expected results and experimental evidence

My experimental evidence (Preliminary Results) as shown in A8d suggested a final value of around 1.06 x10 ^6 m (as Below)

Length of wire = 0.100 m
Resistance 1 = 2.13
Resistance 2 = 2.09

Resistance = Resistivity x Length the Wire
Cross Section Area of Wire

Average Resistance = 2.11
Wire Thickness = 0.270 mm

So 2.11 = x 0.100 => 2.11= x 1.75 x10
5.73 x10^6

P = 2.11 = 1.06 x10^ -6 m
1.75 x10^6

And my final value using all of my data and graph gave me an answer of 1.09 x10^ -6 m, so I think both sets of my results were very accurate.

Indication of most significant measurements

Judging by graphs line of best fit I have three values which have slight random errors, the value at 10.47 x10 ^6, 5.24 x10 ^6 and 15.56 x10 ^6 on the x axis. However the line of best fit corrects these errors as my formulae means my gradient gave me the resistivity.

My most significant source of error I think was the length of the wire as I had to use crocodile clips which are 5mm across so therefore I can only get within 5mm to my measurement

0.10m + or 5mm = 5% error

So the new total error is 18%

Estimate the error or uncertainty in all measurements

Also see above section for error calculations
Length Min reading 0.10 m, + or – 5mm, max error = 5%
Current Min reading 0.13 Amps, + or 0.01 amps, max error = 8%
Voltage Min reading 2.24 Volts, + or 0.01 volts max error = 1%
Thickness Min reading 0.27mm, + or 0.01 mm, max error = 4%

Total Error = 18%

So my resistivity has a range of: 0.89 x10^ -6 m to 1.29 x10^ -6 m

My answer of 1.09 x10^ -6 m falls virtually in the middle of these two bounds so I think my answer was reasonably accurate.

Determining Systematic and Random errors

Random errors are quite easy to spot on my graph as they do not fit the line of best fit, and although I had no huge errors, I have three values which have slight random errors, the value at 10.47 x10 ^6, 5.24 x10 ^6 and 15.56 x10 ^6 on the x axis.

Systematic errors are slightly harder to spot but all it will affect is the position of my line and this doesn’t effect my gradient, which is what gives me my value so it doesn’t make much difference.