An Investigation into the Factors Affecting the Resistance of a Wire.

current has twice as many ways to go, the resistance of the combination will be halved.The cross-sectional area has doubled and the resistance will be half that of one wire on its own.With three pieces of wire side by side the electric current has three times as many ways to go, the resistance of the combination will be one third.The cross-sectional area has trebled and the resistance will be one third that of one wire on its own.The Resistance of the wire is inversely proportional to its cross-sectional area.R ∝ 1/AMeasuring ResistanceResistance=Potential DifferenceCurrentIn order to measure the resistance of a wire or a combination of wires we have to measure the potential difference across the resistor in Volts and the Current through the resistor in Amps.The circuit used to do this is shown below.PredictionsResistance is directly proportional to the length of the wire provided that the cross-sectional area is constant.This means that a graph of resistance against length will be a straight line through the origin.Resistance is inversely proportional to the cross-sectional are of the wire provided that the length is constant.This means that a graph of resistance against 1/(cross-sectional area) will be a straight line through the origin.Preliminary ExperimentAim of the Preliminary ExperimentA preliminary experiment will be carried out to find out the following:The most suitable voltage to be used.The range of values for the length of wire that can be investigated.A suitable value for the length of wire used when investigating the effect of cross-sectional area.ApparatusThe apparatus that will be used is as follows:32 s.w.g. Constantan Wire2 Crocodile ClipsMetre Rule6 Connecting LeadsA Low-Voltage d.c. Power Supply ()-12V)An Ammeter (0-1A and 0-5A d.c.)A Voltmeter (0-5V d.c.)A Variable Resistor (0-47Ohms)DiagramMethod1. The apparatus was set up as in the diagram above and the voltage across the wire was set to be 3Volts.This was achieved by setting the power supply to 6 Volts and then adjusting the rheostat.2. The initial length of the Constantan wire was set to be 1.2 metres. The distance between the crocodile clips was adjusted until it was 100 cm as measured with the metre rule.The wire was laid out in a straight line on the desk so that any heat generated would be lost to the surroundings.3. The value of the current through the wire was measured using the ammeter and recorded.4. The length of wire between the crocodile clips was then reduced to 30 cm, the voltage adjusted and the current recorded.5. I tried adjusting the crocodile clips so that the length of wire between them was 20 cm.Results1. The following results were obtained in the preliminary experiment.Voltage VCurrent ILengthResistanceVoltsAmpscmOhms3.01.10302.73.00.341008.62. When the length of the wire was adjusted to 20 cm, it started to get very hot and so the power supply was switched off and no measurements were taken.ConclusionThe minimum length of wire that will be used during the main experiment will be 30 cm.The voltage across the wire will always be adjusted to be 3.0 Volts.There is no maximum limit on the length of the wire but a maximum value of 100 cm was chosen.This will give an adequate number of measurements to allow me to draw a graph as long as the graph is in fact a straight line as predicted.I decided that for the second experiment, studying the variation of resistance with cross-sectional area, I would use 30 cm lengths of wire but that I would reduce the voltage to just 1 Volt to stop the wire from getting too hot.References1. Co-ordinated Science - Physics (Second Edition) by S.Pope and P.Whithead2. SEG (Double Award) Physical Processes - The Revision GuideNumber of MeasurementsResistance and LengthThe length of the wire between the crocodile clips will be varied from 30 cm to 100 cm in 10 cm steps i.e. 30 cm, 40 cm etc.This will give a total of 8 pairs of values for resistance and lengthThis should be sufficient to draw the predicted straight line graph.Resistance and AreaIn order to vary the cross-sectional area of the wire I decided to connect identical lengths of wire side by side.There was a limit on the number of wires that could be connected like this using the crocodile clips. This limit was six wires.This would still give six values for the area and the resistance of the wires.This is just enough to draw the predicted straight line graph.Main ExperimentMeasurement and ObservationApparatusThe same apparatus was used as in the Preliminary Experiment plus the following additional items.Micrometer Screw Gauge6 35 cm length of 32 s.w.g. Constantan wireDiagramResistance and LengthResistance and AreaMethodResistance and Length1. The circuit was connected as shown in the first diagram.2. The length of the wire between the two crocodile clips was set to 30 cm using the metre rule.The wire was laid out in a straight line on the desk so that any heat generated would be lost to the surroundings.3. The low voltage power supply was set to 6 Volts d.c..4. The power supply was switched on and the rheostat adjusted until the Potential Difference across the wire was 3.0 Volts.5. The reading on the ammeter was recorded (I1).6. Steps 2 to 5 were repeated and a second value for the current was recorded (I2).The average value of (I1) and (I2) was recorded as (Iaverage) in the results table.7. Steps 2 to 6 were repeated but increasing the length of the wire on each occasion by 10 cm until the length of the wire was 100 cm.Resistance and Area1. The circuit was connected as shown in the second diagram but starting with just one 30 cm length of wire between the crocodile clips.The wires were laid out in a straight line on the desk so that any heat generated would be lost to the surroundings.2. The low voltage power supply was set to 2 Volts d.c..3. The power supply was switched on and the rheostat adjusted until the Potential Difference across the wire was 1.0 Volt.4. The reading on the ammeter was recorded (I1).5. Steps 1 to 4 were repeated and a second value for the current was recorded (I2).The average value of (I1) and (I2) was recorded as (Iaverage) in the results table.6. Steps 1 to 5 were repeated but the number of wires between the crocodile clips was increased by one each time until the total number of wires was 6.7. The diammeter of the Constantan wire was measured using the Micrometer Screw Gauge.The diammeter was measured at two different places along the wire and the average value used in the calculation of the area.Measurements;The length of wire between the crocodile clips was measured (L) using the metre rule.The Potential Difference across the wire (V) was measured using the Voltmeter.The Current through the wire was measured twice and the average taken.This measurement was made using the Ammeter.The diammeter of the wire (d) was measured using the Micrometer Screw Gauge.Results and CalculationsResistance (R)Resistance was calculated using each pair of values of V and Iaverage using the relationshipR = V/IaverageCross-Sectional Area (A)The cross-sectional area was calculated using the relationshipA = πd2/4d1d2daverageA = π(daverage)2/4mmmmmmx 10-2 mm20.260.260.265.31The total area is given byA = Cross-sectional area of one wire x the Number of WiresResistance and LengthPotential Difference (V)Current (I1)Current (I2)Current (Iaverage)Length (L)Resistance (R)VoltsAmpsAmpsAmpscmOhms3.00.340.350.351008.573.00.360.370.37908.113.00.400.410.41807.323.00.480.470.48706.253.00.560.550.56605.363.00.670.660.67504.483.00.820.820.82403.663.01.101.101.10302.73Resistance and AreaPotential DifferenceNumber of WiresCurrentCurrentCurrentArea1/AreaResistance (V)  (I1) (I2) (Iavge) (A) (1/A) (R)Volts AmpsAmpsAmps x10-2mm2mm-2Ohms1.010.240.240.245.318.94.171.020.460.480.4710.69.42.131.030.700.700.7015.96.31.431.040.960.940.9521.24.71.051.051.201.151.2026.63.80.831.061.401.301.3531.93.10.74Graphs of ResultsA Graph of Resistance against LengthA Graph of Resistance against AreaThis graph is obviously not a straight line through the origin.A Graph of Resistance against 1/AreaConclusionResistance and LengthThe graph of Resistance against the length of the wire is a striaght line passing through the origin.This means that the Resistance is directly proportional to the length of the wire as long as the cross-sectional area is constant.Resistance ∝ LengthR ∝ LDoubling the length of the wire causes the Resistance to double.This agrees with the prediction that I made using my scientific background knowledge.Resistance and AreaThe graph of Resistance against cross-sectional area is NOT a straight line through the origin.The graph of 1/(cross-sectional area) is a straight line through the origin.This means that the Resistance is inversely proportional to the cross-sectional area of the wire as long as the length is constant.Resistance ∝ 1/(cross-sectional area)R ∝ 1/ADoubling the cross-sectional area of the wire causes the Resistance to halve.This agrees with the prediction that I made using my scientific background knowledge.EvaluationJustification of the ConclusionsResistance and LengthAll of the experimental measurements of resistance and length lie on or close to a straight line through the origin on the graph.Resistance and AreaAll of the experimental measurements of resistance and 1/(cross-sectional area) lie on or close to a straight line through the origin on the graph.UncertaintiesMeasurement of VoltageThe Voltage was measured using a 0-5 Volt d.c. Analogue Voltmeter.The smallest scale division on this scale was 0.2 VoltsThis gives an uncertainty of + or - 0.2 Volts allowing for an uncertainty in the setting of the zero on the Voltmeter.Measurement of CurrentThe Current was measured using a 0-1 Amp d.c. Analogue Ammeter and a 0-5 Amp d.c. Analogue Ammeter.The smallest scale division on the 0-1A scale was 0.02 Amps.This gives an uncertainty of + or - 0.02 Amps allowing for an uncertainty in the setting of the zero on the Ammeter.The smallest scale division on the 0-5A scale was 0.1 Amps.This gives an uncertainty of + or - 0.1 Amps allowing for an uncertainty in the setting of the zero on the Ammeter.Changing from one scale to another is bad practice as the two scales may not have been similarly calibrated.Measurement of LengthThe length of the wire was measured using a metre rule.The smallest scale division on the rule was 1mm.This gives an uncertainty of + or - 1mm.There is an uncertainty of + or - 0.5mm at each end of the length of wire.It was difficult to ensure that no kinks occurred in the wire. Kinks in the wire would have meant that the wire was actually longer than the measured value.Measurement of DiammeterThe diammeter was measured using a Micrometer Screw GaugeThe smallest scale division on the Micrometer Screw Gauge was 0.01mm.This gives an uncertainty of + or - 0.01 mm allowing for an uncertainty in the setting of the zero on the Micrometer Screw GaugeResistanceThe contacts between the crocodile clips and the wire may have introduced extra resistance into the circuit.The amount of extra resistance cannot be estimated and will have changed during the course of the investigation.TemperatureThe resistance of a metal wire does change with temperature and despite keeping the voltage low, the temperature of the wire will have changed during the investigation.Constantan wire was selected for the investigation because its resistance does not change very much as the temperature changes.The wire was laid out on the desk so that any heating effect would be minimised. The heat generated would have been lost to the surroundings.The resistance of a metal wire increases as the temperature goes up.Anomalous ResultsAll of the values plotted on the graphs of Resistance against Length and Resistance against 1/(cross-sectional area) were close to the straight line (the line of best fit).This was certainly true within the limits of accuracy of the experiments.There were no anomalous results.ImprovementsContact Resistance at the Crocodile Clips.It should be possible to develop a technique for connecting the wires into the circuit which would eliminate any uncertainty due to the contacts.This might involve soldering connections to the wire under test.This would involve quite a lot of extra work which would not be justified by the increase in accuracy obtained.Increased Number of Values of Cross-Sectional AreaBecause the final graph used was Resistance against 1/(Cross-Sectional Area) the points plotted were not evenly spaced.Keeping the Temperature of the Wire ConstantThere are two ways in which the temperature of the wire could have been kept more nearly constant.Using much smaller values for the applied Potential Difference and therefore the current through the wire.This could have been achieved by placing a large value resistor in series with the wire - say 0-5000 Ohms.We would have needed to use a much more sensitive ammeter and voltmeter.Placing the wire in a water bath as shown in the diagram below.The temperature of the wire would have been the same as the water bath.A large amount of heat energy is needed to change the temperature of the water bath because of the high value for the Specific Heat Capacity of water.Extension of the InvestigationDifferent MaterialsDifferent metals have different values for their resistivity ρ .A series of experiments could be carried out to measure the resistivities of different metals and alloys.Change of Resistance with TemperatureA series of experiments could be carried out to measure the change in resistance of a fixed length of Constantan wire as the temperature of the wire is changed.This could be done by placing the wire under test in a water bath and changing the temperature of the water bath by heating it with a Bunsen burner.The length and cross-sectional area of the wire would be kept constant.