The Resistance of a Wire Essay
The Resistance of a Wire
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 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 Calculations Resistance (R) Resistance was calculated using each pair of values of V and Iaverage using the relationship R = V/Iaverage Cross-Sectional Area (A) The cross-sectional area was calculated using the relationship A = ? d2/4 d1 d2 daverage A = ? (daverage)2/4 mm mm mm x 10-2 mm2 0. 26 0. 26 0. 26 5. 31 The total area is given by A = Cross-sectional area of one wire x the Number of Wires Resistance and Length Potential Difference (V) Current (I1) Current (I2) Current (Iaverage) Length (L)
Resistance (R) Volts Amps Amps Amps cm Ohms 3Resistance and Area Potential Difference Number of Wires Current Current Current Area 1/Area Resistance (V) (I1) (I2) (Iavge) (A) (1/A) (R) Volts Amps Amps Amps x10-2mm2 mm-2 Ohms Graphs of Results A Graph of Resistance against Length A Graph of Resistance against Area This graph is obviously not a straight line through the origin. A Graph of Resistance against 1/Area Conclusion Resistance and Length The 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 ? Length R ? L Doubling 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 Area The 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/A Doubling 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. Evaluation
Justification of the Conclusions Resistance and Length All of the experimental measurements of resistance and length lie on or close to a straight line through the origin on the graph. Resistance and Area All 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. Uncertainties Measurement of Voltage The Voltage was measured using a 0-5 Volt d. c. Analogue Voltmeter. The smallest scale division on this scale was 0. 2 Volts This gives an uncertainty of + or – 0. 2 Volts allowing for an uncertainty in the setting of the zero on the Voltmeter.
Measurement of Current The 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 Length The 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 Diammeter The diammeter was measured using a Micrometer Screw Gauge The 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 Gauge Resistance The 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. Temperature The 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 Results All 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. Improvements Contact 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 Area Because the final graph used was Resistance against 1/(Cross-Sectional Area) the points plotted were not evenly spaced. Keeping the Temperature of the Wire Constant There 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 Investigation.
Different Materials Different metals have different values for their resistivity ? . A series of experiments could be carried out to measure the resistivities of different metals and alloys. Change of Resistance with Temperature A 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.
University/College: University of Arkansas System
Type of paper: Thesis/Dissertation Chapter
Date: 4 October 2017