resistivity if a nichrome wire
Aim: Throughout this experiment I aim to find out the resistivity of a nichrome wire. To do this I will measure the resistance of the nichrome wire at different lengths and from this I will be able to work out the resistance using the equation:
Apparatus
Apparatus
Range
Accuracy
Purpose
Quantity
Nichrome wire
N/A
N/A
This is the wire that I will be calculating the resistivity for. It's the subject of the investigation.
Power pack
2V-12V
± 1 V
The power pack is used, as it's a supply of the initial voltage. It also creates a potential difference in order for the flow of electrons to occur (current to flow).
Crocodile clips
n/a
N/A
I will be using these to hold them to the nichrome wire and to the voltmeter. I will use two to connect the wire to the voltmeter and the other end attached to 0m on the wire. The other two will be used to move along the different length on the wire, from 0.100m to 1.00m.
4
Micro screw Gauge
0-25mm
± 0.01mm
This will help me measure the diameter of the nichrome wire. For this I can then be able to work out the cross sectional area of the wire by using the following equation: ?r2
Ruler stick
0m-1m
± 0.001m
This is to measure the different length of the nichrome wire.
Wires
N/A
N/A
They are connectors in the circuit. They connect the wire to the power supply, the ammeter and to the voltmeter.
4
Ammeter
0-10 A
± 0.01 A
This is used to measure the flow of electric current in a circuit.
Voltmeter
0-20 V
± 0.01 V
This instrument is used to measure the potential difference between two points in the circuit. Hence, the voltage across the wire.
Nails
N/A
N/A
I will use these to hold the nichrome wire to the meter stick.
2
Dependant and independent variables
Independent variable- The independent variable throughout this investigation will be the length of the nichrome wire. I will change the lengths to determine the voltage for each length. These results will therefore aid me in resolving what the resistance in the wire is.
Controlled variables
All there variables must stay constant in order to prevent them from affecting the dependant variables, and therefore creating anomalous results.
What to be kept constant
Why is it kept constant
How it's going to be kept constant.
Current supplied by the power pack.
Current is one of the factors which affect the resistance of the wire. It can affect the resistance of the wire. So if the current increases the resistance will also increase. This is because resistance is directly proportional to the current.
The power pack voltage will be kept constant, this will then therefore keep the current through the circuit constant.
Nichrome wire
Using different wires will affect my investigation; this is because different wires have different densities which determine its current flow.
I will ensure that I use the same wire throughout my experiment. By doing this I have abolished any chances of having wires of different resistively, cross sectional area or densities.
Equipment
Faults in the equipment due to them being old or broken might affect my results.
I will use the same equipments through my experiment to reduce any anomalous results.
Cross sectional area
The smaller the cross sectional area of the wire the less space that is available for the electrons to pass through, hence, smaller flow of current. However, with a thick wire the resistance is less as there is more space for the electrons to flow through.
I will control this as I will use the same wire throughout my experiment. This will ensure I have the same cross sectional area throughout
Method
. Measure the diameter of the wire using a micrometer screw gauge. It is taken in three places along the wire, and an average reading is taken. [D1 +D2 + D3 / 3].
2. Find the area of the nichrome wire using the formula of, ensuring that the radius is converted into meters.
3. The apparatus is then set. This is done by attaching the nichrome wire to the meter stick using a 2 iron nails. This will ensure that the wire is straight and has no kinks.
4. Attach the power pack to the voltmeter and the ammeter, this is done with the help of 4 pieces of wire and crocodile clips,
5. Set the volt meter to 10 cm.
6. Set the power pack to 2 volts, this will be kept constant.
7. Measure the voltage across the wire, by reading the voltmeter.
8. Repeat the experiment and this time change the voltmeter to 20cm.
9. Repeat this process up till 100cm.
0. Record the readings on the voltmeter and the ammeter (this will be constant) on a table.
A partial diagram of the practical set up.
(Fig 1)
Circuit diagram
(Fig 2)
Background knowledge
Resistance is a measure of a component's ability to an electric current through it. It is the resistance of a material of cubic shape of length of one meter
Good conductors of electricity have low resistance as current is able to pass through the component and poor conductors have high resistance, as there is no current flow.
To work this out we generally use this simple formula:
Resistance (Ohms) = Voltage (Volts)
Current (Amps)
There are many factors that affect the resistance of a wire these include:
The Temperature: When temperatures are increased, more energy is provided through heat. The electrons in the wire gain more kinetic energy causing them to vibrate more.
This means that the collision ...
This is a preview of the whole essay
Good conductors of electricity have low resistance as current is able to pass through the component and poor conductors have high resistance, as there is no current flow.
To work this out we generally use this simple formula:
Resistance (Ohms) = Voltage (Volts)
Current (Amps)
There are many factors that affect the resistance of a wire these include:
The Temperature: When temperatures are increased, more energy is provided through heat. The electrons in the wire gain more kinetic energy causing them to vibrate more.
This means that the collision of the electrons increase between the electrons and the ions in the wire. Therefore there is of a less chance that the electrons are being carried across the component. So, as the temperature increases, resistance increases, therefore the flow of current decreases.
Length: The shorter the wire the less collisions that occur between the electrons, so resistance decreases and vice versa. The longer the wire, the further the electrons have to travel in order for them to create a continues electrical flow, this means that they loose energy in the way as some of the energy is transferred to particles that they collide with randomly in the wire.
Resistance is directly proportional to length. If I double the length of the wire the resistance increases by a factor of 2, hence doubles.
Resistance ? length
Thickness of the wire: The thinner the wire or the smaller the cross sectional are of the wire, the higher the resistance. This is because there is a reduced amount of space available for the current to flow through (the electrons). Therefore this means that the electrons are more likely to collide with particles.
So we can say that resistance is inversely proportional to the cross sectional are of the wire. Decreasing the cross sectional area of a wire by a factor of 2 means that we are decreasing the current flow by a factor of 2, and so on.
Resistance ? 1
A
Combining the to formulas:
R ? l + Resistance ? l = R ? l
A A
(Expression 1) (Expression 2) (Expression 3)
Provided that the temperature is constant, then the only other variable is the type of material it self. Some materials have a higher resistance than others due to size and shape. The number describing this property of the material is called the resistivity. This is given the symbol ?.
So therefore expression 3 becomes:
R = ? ? l
A
(Expression 4)
This equation rearranged will them become
? = R ? l
A
(Expression 5)
Points to note:
My final graph will have a positive correlation. This is because the formula
? = R ? l corresponds to the formula y = mx + c.
A
Therefore:
So therefore this leaves you with: m = p
a
(Expression 6)
(Expression 7) (Expression 8)
Expression 8 is the simplest and easiest way of finding the resistivity of the nichrome wire. All I have to do is multiply the gradient value buy the cross sectional area of the wire.
Hypothesis
Taking all this information into account, I think that as I increase the length of the nichrome wire the resistance will also increase. I also think that on my graph of length against resistance, there will be a positive correlation as length is proportional to length.
Safely: Safely precautions have to be ensured while doing the experiment at all times.
. DRY gloves must be worn at all times as the nichrome wire is not covered with an insulator; therefore I have to ensure that I do not get electrocuted by the flowing current.
2. Power must be switched off, when the crocodile clips are being removed from the nichrome wire. It must also be switched off before handling the wire as it could cause electrocution.
3. I will ensure that any loose material from my clothing is tucked in, so that it doesn't interfere with other operations that I will be undertaking.
4. I will ensure that there are no breakages in the insulation of the circuit wire.
5. When choosing the electrical appliances, for example the ammeter or voltmeter, I will make sure that it has label on it, which approves that it has been constructed in accordance with nationally-accepted electrical standards.
6. I will ensure that all electrical components are kept away from water.
7. I will keep the voltage very low as it could melt the wire.
Data analysis
Length (m)
Voltage 1
(Volts)
Voltage 2
(Volts)
Voltage 3
(Volts)
Average voltage (Volts)
Current
(Amps)
Resistance (ohms)
R=V/I
0.100m
0.200m
0.300m
0.400m
0.500m
0.600m
0.700m
0.800m
0.900m
.000m
I will then plot a scatter graph of the relationship between length and resistance. The length will be on the x-axis and the resistance will be displayed on the y-axis.
Calculating the cross sectional area of the nichrome wire
I will measure the diameter of the wire using a screw gauge. I will take this reading from 3 parts of the wire (at 20cm, 50cm and at 80cm). I will then work out the average.
Length
Diameter (m)
Average (m)
0.200
0.500
0.800
I will then use the average diameter to find out the radius (by halving this value), this will then help me to work out the cross sectional area of the nichrome wire by applying the figures to the formula ?r².
Errors encountered with and Action proposed to minimise errors
Some of the errors that might occur during the investigation are the kinks in the wire, hearing of the wire, rusting of the nails and fluctuations in the readings.
I encountered with a few problems whilst doing my experiment. They were as follows:
- Excess heat: this was the heat that entered the wire unnecessarily. This was due to the voltage providing more kinetic energy to the flowing electrons in the wire. This meant that the electrons would vibrate more, heating up the wire and increasing the resistance. To overcome this problem I allowed the wire to cool down, by allowing 30 second intervals between each reading, as it allowed the wire to return back to room temperature, and minimising the amount of heat in the wire.
- Kinks: The thickness of the wire differed along the wire. The wire may was therefore not uniformly thick. This caused a change in the cross sectional area of the wire. To overcome this problem, I used an plier to even out the thickness of the wire
Implementation
Table of results
I have taken the average by simply adding all the 3 voltage readings together and dividing them by 3.
For example the fist reading (0.100m) was done as follows:
0.39 + 0.36 + 0.37
3
= 0.37 volts
Working out the resistance.
I used the equation V= IR to work out the resistance at each length. I rearranged this equation to R = V/I.
The voltage value I used was the average voltage as it's the most reliable.
For the first length: 0.37 / 0.24 = 1.54
Length (m)
V1
(Volts)
V2
(Volts)
V3
(Volts)
Average voltage (Volts)
Current
(Amps)
Resistance (ohms)
R=V/I
0.100
0.39
0.36
0.37
0.37
0.24
.54
0.200
0.75
0.74
0.76
0.75
0.24
3.13
0.300
.23
.22
.25
.23
0.24
5.13
0.400
.63
.59
.57
.59
0.24
6.63
0.500
2.00
.96
2.04
2.00
0.24
8.33
0.600
2.34
2.32
2.33
2.33
0.24
9.71
0.700
2.68
2.72
2.74
2.71
0.24
1.2
0.800
3.12
3.11
3.11
3.11
0.24
2.9
0.900
3.50
3.51
3.52
3.51
0.24
4.6
.00
3.94
3.93
3.91
3.92
0.24
6.3
(A table to show the voltmeter readings, their average ammeter readings)
Diameter of the wire
Length
Diameter 1 (m)
Average (m)
0.200
0.3 x 10-3
0.3 x 10-3
0.500
0.3 x 10-3
0.800
0.3 x 10-3
I plotted a graph with length against the resistance. This is because it will help me to work out the resistivity. ? = gradient x area
(See graph paper)
The graph shows a steady increase in the resistivity of the wire, hence, positive correlation. This suggests that there were no anomalous results in my readings as all the points in the graph were flowing. This also suggests that my hypothesis was correct and as the length of the nichrome wire increases, the resistivity also increased. My graph also suggests that the length is directly proportional the length.
) The cross sectional area of the wire
Radius: 0.3 x 10-3 ÷ 2 = 1.5 x 10-4 m
? (1.5 x 10 -4) 2 = 7.07 x 10 -8 m. (This is my result for the cross sectional area of the nichrome wire.)
2) Finding the gradient
4.6 / 0.9 = 16.2 ? m-1
3) Working out the resistivity
These two figures will now help me to work out the resistivity of the nichrome wire.
? = gradient x area
? = (16.2 ? m-1 ) X (7.07 x 10 -8 m) = 115 x 10 -8 ? m
The real resistivity of nichrome wire is: 110 × 10-8 ? m
My value for the resistivity of the nichrome wire is 116 x 10 -8 ? m. This is 5 ? m larger than the real value. This suggests that my experiment was not 100% accurate. This can be caused my many sources of errors in my investigation. However, I was close to the real value for the resistivity of the nichrome wire.
Table of errors (absolute/ percentage errors)
Length (meters)
Average voltage
(volts)
Current
absolute error (amps)
Current percentage error (%)
Voltage absolute error
Voltage percentage error (%)
0.100 0.001
0.37
0.240.01
0.24 4.17 %
0.37 0.015
0.37 4.05
0.200 0.001
0.75
0.240.01
0.24 4.17 %
0.75 0.01
0.75 1.33
0.300 0.001
.23
0.240.01
0.24 4.17 %
.23 0.015
.231.22
0.400 0.001
.59
0.240.01
0.24 4.17 %
.59 0.03
.59 1.89
0.500 0.001
2.00
0.240.01
0.24 4.17 %
2.00 0.04
2.00 2.00
0.600 0.001
2.33
0.240.01
0.24 4.17 %
2.33 0.01
2.33 0.43
0.700 0.001
2.71
0.240.01
0.24 4.17 %
2.71 0.03
2.71 1.11
0.800 0.001
3.11
0.240.01
0.24 4.17 %
3.11 0.005
3.11 0.16
0.900 0.001
3.51
0.240.01
0.24 4.17 %
3.51 0.01
3.51 0.28
.000 0.001
3.92
0.240.01
0.24 4.17 %
3.92 0.015
3.92 0.38
Current percentage error
The current was a constant reading all they way throughout the circuit. So it had an absolute error of 0.01 as this was the ammeters accuracy.
To calculated the percentage error for the current as follows:
0.01 x 100 = 4.17% (3 s.f) Therefore the percentage error for the current is 0.24 4.17 %
0.24
Voltage error
Absolute: I first work out the voltage absolute error. I done this by calculating the range and then halving that value.
Range = Highest value (v) - lowest value (v)
2
So I worked out the fist value as follows:
0.39 - 0.36 = 0.015 (this is the error) 0.37 0.015 V
2
Percentage: I worked this out by simply making the absolute error a percentage from the actual average voltage.
So: 0.37 0.015 V 0.015 x 100 = 4.05 % 0.37 4.05 %
0.37
Combined error table or results
Length (meters)
Voltage (volts) error (%)
Current(amps) error (%)
Resistance (ohm ?)
errors (%)
0.100 0.001
0.37 4.05
0.24 4.17
.548.22
0.200 0.001
0.75 1.33
0.24 4.17
3.135.50
0.300 0.001
.231.22
0.24 4.17
5.135.39
0.400 0.001
.59 1.89
0.24 4.17
6.636.06
0.500 0.001
2.00 2.00
0.24 4.17
8.336.17
0.600 0.001
2.33 0.43
0.24 4.17
9.714.62
0.700 0.001
2.71 1.11
0.24 4.17
1.295.27
0.800 0.001
3.11 0.16
0.24 4.17
2.964.33
0.900 0.001
3.51 0.28
0.24 4.17
4.634.45
.000 0.001
3.92 0.38
0.24 4.17
6.334.55
(A table to show the % errors for the voltages, current and resistance)
The % error for the resistance: to work out the percentage errors for the resistance I simply added the % error of the current to the % error of the voltage. To work out the resistance I used ohms law: V=IR. I however rearranged this equation in order to make the resistance the subject. This therefore becaie R= V/I
For example: (0.100m length)
R= V/I
0.37 / 0.24 = 1.54
4.05% + 4.17% = 8.22 %
Therefore this will become: 1.54 ? 8.22 %
After I done all of there calculations I plotted a graph of resistance errors. This will enable me to work out the gradient errors and therefore the errors of the resistivity of the nichrome wire.
Gradient errors
To find out the gradient errors, I plotted a graph of resistivity against length, however I also plotted the maximum and minimum error for each resistance.
I then calculated my gradient for the maximum gradient and the minimum gradient. I then got the following results:
Maximum gradient: 9.3 ? / 0.575 = 16.2 ? m-1
Minimum gradient: 9 ? / 0.626m = 14.4 ? m-1
I will now work out the percentage error for the gradient of the graph resistance against gradient. I am doing this as it will then help me to work out the percentage errors for the resistivity of the nichrome wire.
Error in the gradient: 1/2 (16.2 - 14.4) x 100 = 5.56%
16.2
So therefore the gradient error is: 1.64 5.56%
Resistivity percentage error.
Diameter error: the average diameter of the nichrome wire was: 0.3 millimetres
0.01 x 100 = 3.3%
0.3
3.3 x 2 = 6.7 % (this is the area error)
So therefore my area error = 7.07 x 10 -8 m 6.7 %
So this concludes my resistivity error to become: 115 x 10 -6 ? m 12.3%
Sources of likely error
Systematic errors and random errors:
Sources of likely error
Effect to the investigation
To minimise errors
Heating of the wire
Heating due to the power can result in the electrons in the wire gaining more kinetic energy and therefore vibrating more. This increases the current flow and therefore increases the resistance of the wire.
I could have over come this problem by letting the wire to cool down. Approximately 30 seconds.
Kinks in the wire
Kinks in the wire causes a change in the cross sectional area of the wire
To overcome this problem, the wire could have been stretched out using an applier.
Rusting of the nails
The rusting of the wire contributes to the errors in the results. This is because the rust in the nail contributes to the amount of current it conducts.
To overcome this problem the rust can be cleaned with sandpaper, or even replaced by new ones.
Thickness of wire
This may differ on the wire, as the wire may not be uniformly thick. This causes a change in the cross sectional area of the wire.
To overcome this problem, the wire could have been stretched out evenly using a plier, to even out the thickness of the wire.
Fluctuations in the readings
The readings on the voltmeter and the ammeter kept flickering (was not stable).
To minimise errors, I tries to use the readings that was most common. I.e. kept coming up all the time.
Random errors:
Voltmeter and ammeter: there equipments assist in providing reasonably accurate results. However due to humanly errors the wrong readings could be read off. They also display results to two decimal places, in future I would use a more accurate digital voltmeter and ammeter which display more than two decimal places to get more accurate readings.
Temperature: although I allowed 30 seconds intervals in between each reading allowing the wire to cool down whilst the power pack was turned off, the temperature of the wire may have not reached the initial temperature (room temperature) and would therefore the electrons would have had more kinetic energy and this will vary the resistance. In future, I was to carry this investigation again I would wait for a longer time period for my wire to cool down, for it to return back to room temperature.
Crocodile clips: The crocodile clip used throughout this experiment were about 3 mm wide, at each of the repeat readings it might have been on different positions due to humanly errors. This means that the length which the voltage had been measured was different, therefore affecting my results. In future, if the experiment were to be repeated a needle or a thinner crocodile clip could be used as a connection, as it would help assure pinpoint accuracy.
Systematic errors.
Calibration: calibration of all the equipment must be correctly carried out and made sure they are correct. For example, if the micrometer or the ruler was not calibrated correctly the readings taken may have been inaccurate; in future I will make certain that all equipment is correctly calibrated.
Impurities: they might have been impurities within the wire that affected my results and reduced the reliability. To reduce this in future, I would use a different wire samples.
The main huge source of error is the calculation of the cross sectional area of the wire. This is because when squaring the radius of the wire the error of the area also doubles. Therefore most of my error comes from this part of the calculation.
Due to all these errors my experiment was not 100% accurate. This can be caused my many sources of errors in my investigation.
However, the results were close together for each repeat, this suggests that they were precise and were accurate enough and the method used was appropriate.
There were no anomalous results in my readings this therefore suggests that the experiment was carried out with precision, and that the method used was appropriate. It allowed me to tabulate the results on an understandable table which could then be analysed.
Improvements
I believe that the technique I used to find out the resistivity of the nichrome wire was not the best as I could have went through another set of procedures and methods that would have aided me to find out the resisitvity more acutely. There were many limitations in the method which caused this investigation not to be 100% accurate.
If I was to do this investigation another time, I would have made many changes to the method and even the technique used to find out the resistivity of the nichrome wire.
- Data loggers/ computer software - I would have used data loggers as they would calculate the cross sectional area of the wire accurately and also would have given me an accurately plotted graph. It would also have worked out the gradient and therefore the resistance.
- Ohm meter - this devise would directly measure the resistivity without any long calculations.
- Different equipment - I would change the equipment used, such as the screw gauge and used electronic ones that would display readings digitally. This would decrease any systematic errors in the calculations.
Throughout my experiment there were no significant errors. All my readings had a positive correlation and there were no significant anomalous results. My graph showed length of the wire being directly proportional to the resistance in the wire, with no discrepancies in the points plotted. This suggests that my investigation was carried out with precision, and that my method was appropriate.
Resistivity of Nichrome Wire
Candidate number:
Centre number:
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Fatima Osman 12.1 Dr Pithia
