References to the specification –
Aim Of My Investigation –
The aim of my investigation is to investigate the relationship between resistance and cross sectional area of a wire.
Variables –
Prediction –
Since the theory suggests that
R = 4 . ρ . l
Π . d2
R = 4 . ρ . l . 1
Π d2
So resistance should be proportional to 1 over d squared.
A straight line graph of R versus 1/d2 would give a straight line with a gradient of -
4 . ρ . l
Π
Passing though the origin. All these values will be known.
Method:
Preliminary Experiments:
Determining the length of wire:
By keeping the wire at the longest length that can be effectively measured by the apparatus we have, we will give the largest possible resistance while minimising the uncertainties in the wires length. As the measuring apparatus we have is a one metre rule the wire that will be used will be one meter long wires. This way the uncertainty in measurement is only one percent.
Copper wire 24swg – 30cm wire (0.3m) – 29.9cm
1.5Volts (dc)
Ammeter – 0.2A Testwire – 30.cm
Voltmeter – 0.2V
1.5Volts (dc)
Ammeter – 0-200 mA
Voltmeter – 0.200 mV
A = 0.043A
V = 11.3mV Resistance = 0.255 Ω
V = 11.3mV = 0.0113V V = R = 0.262890689 Ω - 0.26Ω
A = 0.043A I
Determining how to measure resistance:
By using a digital ammeter and voltmeter the uncertainties in the measurement will be kept as low as possible. In these cases both uncertainties are about one percent. If the resistance alone was measured the uncertainty would be a lot higher and therefore the results would be of decreased effectiveness.
Determining the additional resistance:
An additional resistance of three ohms will be added to the circuit. This will lower the current to around one amp which will be enough to protect the ammeter and prevent any major heating in the wire that could, potentially, change the resistance. Since it was found that a thin nicrome wire with two amps passing through it was hot enough to glow red, which would affect the resistance significantly, the current needs to be kept to around one amp. This should still provide a good reading on both the ammeter and the voltmeter while removing the problems faced by temperature on all the test wires.
‘The resistance of a metal increases with an increase of temperature’
(Pg. 87 ‘Essential AS Physics for OCR’ By Jim Breithaupt, Nelson Thornes, ISBN 0 7487 8507 8)
Ohm meter (Ω) – o-200Ω
Constantan Wire – 30 swg.
Resistance – 3.2 Ωhms.
Some after heat change – Temperature changes of less than 10 oc (i.e. changes in room temperature) have little or no effect on resistance.
Determining the wires material:
The wire that has been chosen for use in the experiment is tin coated copper. This has been chosen because there are 9 different gauges of wire we could use as opposed to the 5 we could use for nicrome. This will allow us to take many results from different gauges of the wire.
Nichrome 32swg.
Ammeter – 0-20A
0.1V 800 oc / 1000 oc – Glowing red hot
0.1A
Passing a current through a wire increases the temperature of the wire. After 4.3A Nichrome wire will melt.
Determining Range of values:
The range of diameters that will be tested is fixed by the number of wires that are available for testing.
Max 14swg and min 35swg
Wire Gauges –
14swg 16swg 8swg 20swg 22swg 24swg 25swg
.203mm .163mm .
29swg 35swg
The power supply I will use is a variable power supply. This will enable us to set the current to just below 1 amp, which allows higher voltage and thus a smaller uncertainty in our measurements. I will b using a fixed power supply of 1.5V for my experiment. This will allow me to take results without it overheating.
The circuit will be set up in the following manner.
Instruction –
- Set up the circuit above without turning on the power supply.
- Measure out 1 metre of Copper coated tin wire.
- Connecting the wire into the circuit.
- Turn on the power supply and record the measurement on the ammeter and voltmeter.
- Turn off the power supply.
- Repeat using the different gauges of wire.
Equipment –
Variable power supple,
Digital Ammeter
Digital Voltmeter
Wires
Tin coated copper test wire
Rheostat Resistor
Meter rule
Results –
Percentage uncertainties –
Diameter / m –
Voltage / V –
Current / A –
Resistance / Ω -
Maximum diameter uncertainty – 23%
Maximum voltage uncertainty – 21%
Maximum current uncertainty – 29%
Maximum Resistance uncertainty – 52%
All graphs require units on the axes.
The trend shown here confirms a non-linear relationship between resistance and width of wire. It is consistent with a inverse relationship of some kind. This graph tells us that as the diameter increases, the resistance decreases. When the width is 5.00 E-4 the resistance is about 10 Ω, but when the width is 1.00 E-4 the resistance is nearer 5 Ω.
The graph suggests to us that as 1/d2 increases, as does the resistance. This in turn suggests that as the wire gets thinner the resistance increases.
The reason the 1/d2 is large us because if you square a small number it gets very big. It shows us that resistance is proportional to wire diameter. This is because with a thinner diameter the current has to pass through a small area, whereas with a wider wire the current has a larger area to travel through.
Gradient of the line –
R = 4 . ρ . l . 1 + 0
Π d2
Y = m x +c
The worst case difference between the best data point and the best fit line is 98%.
This can be accounted for by reference to the % uncertainty in my voltage, current, resistance and diameter.
Sources of error –
In my experiment there where several sources of error. Firstly, the diameter of a thinner wire would be more accurate than that of a thicker wire. This is because when they are made they have to be made to a certain percentage accuracy of there thickness, thus a thicker wire will have a bigger margin if error in production. I could improve the accuracy of the diameter of the wire by checking it myself with a micrometer.
Secondly, when measuring out the metre length of wire, the thinner wire will be a more accurate length. This is because the thicker wire is full of kinks and thus is almost impossible to get perfectly straight. One way I could improve the accuracy of measuring the wire is by using sellotape to hold the wire to the meter rule while I measured the wire.
Thirdly, the voltage and current I recorded in my results is particularly accurate. This is because the ammeter and voltmeter is not very accurate. The only way to improve these readings is to use a more accurate ammeter and voltmeter.
Fourthly, I only did one set of results for my experiment. This means I could not take mean results. If I was doing this experiment again I would take multiply results and take a mean of these results.
