The Effect of Length on the Resistance of a Constantan Wire

The Effect of Length on the Resistance of a Constantan Wire
Introduction: Resistance is a property dependant on three main factors: ? Resistivity: This is a constant for fixed temperature and other physical conditions. Resistivity is shown by the symbol Ro, and is measured in ohmmeters. ? Length: Directly proportional to resistance, and is measured in meters. This variable is represented by the symbol L. ? Cross sectional area: This factor is indirectly proportional to the resistance, and is measured in m2.It is represented by the symbol A. The formula for resistance is: Resistance=Resistivity*length/cross sectional area Ohms Ohm meters Meters meter squared And Resistance=voltage/current Ohms volts Amperes Apparatus:
1*d.c. supply
6*connecting wires(copper)
1*Rheostat(to act as fixed resistor)
1*meter of Constantan wire(30SWG)
2*crocodile clips
Reasons for selecting the apparatus:
A voltmeter of the range 0-5 will be used in this experiment,
because the potential difference of the whole circuit won?t exceed
this amount.
The same principle will used in selecting the range of the ammeter.
A D.C. supply of 4-5 volts will be used, to prevent overheating and
an increase in resistance. This is because an increase in temperature
will increase the random motion of the delocalised electrons in the
metal lattice, and also the positive metal ions. This will lead to
more frequent collisions between the drifting electrons and the ions,
so that current is reduced.
A wire of 30 swg was selected to control the temperature of the
apparatus, thinner wire would have higher resistance and this variable
would be difficult to calculate.
N.B. For reliability all apparatus must be checked to see if it?s functioning properly. D.C. supply [image]Flowchart: Connector: V Ruler andwire Rheostat Ammeter [image] Crocodile clips [image] Voltmeter Diagram 1-the circuit
The ammeter is placed in series with the circuit.
The voltmeter is placed in parallel to the circuit.
Ruler [image][image][image] Blu tak Diagram-2 the ruler and wire The wire is placed onto the ruler with Blu -tak. It must be pulled tight against the ruler and held tight in place, to ensure the length is accurately measured. Safety rules: The safety aspect of an experiment is always an important issue in carrying out an investigation, thus care should be taken in handling the apparatus. In this experiment, the safety issues are concerned with the temperature of the wires and the use of electricity. A low voltage should be used, because less current will prevent the wires from heating up. Contact with the wire throughout the experiment should be avoided, to prevent electrocution and burning. The surface, on which the circuit is placed, must be kept dry throughout the experiment, to prevent short circuiting. Hypothesis and predictions: Resistance is caused by the current of electrons colliding with the positive ions present in the structure of the wire material. Therefore, an increase in the length of the wire will increase the frequency of these collisions in the same proportion. For example, when the length is doubled, the resistance will also double. The graph of R against L will be a straight line with a positive gradient. A positive correlation will be observed in the scatter graph, demonstrating the direct proportion between length and resistance. Variables: Controlled variables:
Temperature: Using a lower voltage will keep the temperature
more stable. (According to the preliminary experiment a high voltage caused the circuit to overheat.) It would be more accurate to do the experiment on the same day, so the room temperature is the same. (There won?t be a dramatic temperature change in one day. This variable influences the resistance of the wire.) This experiment was carried out in a stable room temperature of 20C. The D.C. supply was switched off when not in use.
Wire material: (Resistivity, density) the wire used is
Constantan. The resistivity is calculated using the results obtained from the experiment, and comparing with a data book.
Cross sectional area:the cross sectional area of the wire
was kept constant. (30SWG=0.315mm) A thinner wire would have higher resistance, and calculating this variable (resistance) would be difficult. Dependant variable:Resistance Independent variable: Length (This variable is changed throughout the experiment.
Any inaccuracy in the experiment would be due to the
change in temperature, or the malfunctioning of the apparatus.
As many readings were taken as possible, so there was a
Wide range of results obtained and achieving a good conclusion would be possible. Method: The circuit will be set up as shown on the diagram in page iii and IV. Throughout setting up the apparatus, the power pack will be switched off and the pointer will remain at zero, for reasons stated in the safety rules. In this investigation, ten readings will be taken and a voltage of four volts will be utilised as stated in the previous pages. (In the preliminary experiment a high voltage caused the wire to overheat, thus a lower voltage of four was used. Using this voltage reduced the resistance caused by temperature). The readings will be taken, starting from 1 meter and ending at 0.1 meters. (10 different lengths of the same wire will be used).These number of readings will give a wide range of data to draw a conclusion from. For each reading, 0.1 meters will be reduced; the voltmeter and ammeter readings will be recorded in a table. The resistance will then be calculated using the two known values (voltage and current). (R=V/I) Between taking the readings, the D.C. supply will remain switched off, to reduce the temperature, and keep the resistance caused by this variable as small as possible. The experiment will be repeated three times, thus three values will be obtained from the three readings taken. The resistance of each reading will be calculated, and the average of the resistances determined, to obtain a more accurate value for resistance. Once the average resistance values are calculated, to two significant figures, the results will be analysed, by the use of a line graph and a scatter graph. The points will have to be accurately plotted on the graph of R against L and the line of best fit will be sketched. Earlier on in the investigation the formula Resistance=resistivity*length/surface area was introduced. When the graph of R against L is sketched, the gradient will be: Resistivity/surface area A length of slightly more than one meter was used, because The crocodile clips will keep a small length of the wire out of the circuit. The crocodile clips will be moved along the wire, to change the variable, length. When changing the length the D.C. supply should be switched off. For convenience and more accuracy, the readings started from one meter. (The second readings were taken starting from 0.1 m.) The resistance was calculated, using R=V/I as stated in the introduction. The average resistance was calculated by finding the mean of the three resistances. All the procedures described above were carried out in the experiment, and all the readings were recorded in the table. The values were as follows: L (meters) I1 (Amperes) V1 (volts) R1 (ohms) I2 (Amperes) V2 (volts) R2 (ohms) I3 (amperes) V3 (volts) R3 (ohms) average R(ohms) 1 0.20 1.2 6.0 0.20 1.2 6.0 0.2 1.2 6.0 6.0 0.9 0.20 1.1 5.5 0.20 1.1 5.5 0.2 1.1 5.5 5.5 0.8 0.20 1.0 5.0 0.20 1.0 5.0 0.2 1 5.0 5.0 0.7 0.20 0.9 4.5 0.20 0.9 4.5 0.2 0.9 4.5 4.5 0.6 0.20 0.8 4.0 0.20 0.85 4.3 0.2 0.85 4.3 4.2 0.5 0.20 0.75 3.8 0.20 0.7 3.5 0.2 0.7 3.5 3.6 0.4 0.20 0.6 3.0 0.20 0.6 3.0 0.2 0.6 3.0 3.0 0.3 0.20 0.5 2.5 0.20 0.5 2.5 0.2 0.5 2.5 2.5 0.2 0.25 0.35 1.4 0.25 0.4 1.4 0.25 0.35 1.4 1.4 0.1 0.25 0.2 0.8 0.25 0.2 0.8 0.25 0.2 0.8 0.8 1st readings 2nd readings 3rd readings Table of current, voltage, resistance and average resistance of three readings Table of values used for plotting the graph of R against L Length (meters) Average resistance(ohms) 1 6.0 0.9 5.5 0.8 5.0 0.7 4.5 0.6 4.2 0.5 3.6 0.4 3.0 0.3 2.5 0.2 1.4 0.1 0.8 Conclusion: Once the graph of R against L is plotted, and the line of best fit is sketched, a hypothesis can either be established or contradicted. In this case, the hypothesis was irrefutable, as the graph obtained from the readings showed a positive correlation. Therefore, a direct proportion between the two variables, resistance and length was observed. Thus it can be concluded that an increase in length will increase the resistance of a conductor: The longer the length of the material, the more frequent the collisions between the drifting and delocalised electrons. Therefore, the resistance will also increase. The gradient of the graph was used to calculate the resistivity of Constantan. If the value calculated, proves to be equal to the value in the data book, further accuracy of the experimental data will be proven. Further proof of the theory was observed in the correlation of the scatter graph, which followed a positive pattern .A clear proportion was observed, and also the gradient of the graph, which was positive. Calculations: Resistivity/Cross sectional area=gradient of the graph so Resistivity=cross sectional area*gradient of the graph Cross sectional area=Pi*radius squared -3 -4 Diameter=0.315*10 mthus,radius=diameter/2=1.6*10 -8 Cross sectional area=7.8*10 meters squared Gradient=6/0.9=6.7 -8 -7 Resistivity=7.8*10*6.7=5.2*10ohm meters N.B: For the gradient a length difference of 0.9 meters and average resistance value of 6 ohms was used. The resistivity value calculated by using experimental data in this investigation, matched the value obtained from a data book which was 52 micro ohm cm.If the value in the data book is converted into ohm meters it will be exactly identical to the calculated value. Thus the values obtained from the readings were accurate enough to determine the value for the unknown resistivity of the Constantan wire. Evaluation: The possible sources of error can be divided into two groups: 1-Systematic errors 2-Random errors Systematic errors involve the malfunctioning of the apparatus involved in taking readings. In this experiment, both the voltmeter and ammeter were at zero when not in use, and were functioning perfectly. Random errors involve mistakes made when recording a reading. In this experiment, the only random error involved changing the length of the wire by the use of crocodile clips. There were no anomalous results, as all results followed the expected pattern. Ideally, it would be expected for the three readings taken to be equal, but for certain lengths in this experiment the three resistances varied. Two discrepancies in this experiment: 1- At L=0.6m 4.3-4.0=0.3 error=0.3/4.0*100=7.5% 2- At L=0.5m 3.8-3.5=0.3 error=0.3/3.8*100*=7.9 The discrepancies mentioned above did not have a significant effect on the outcome of the results, and possibly could have been due to a random error in the measurement of length. The most significant measurements involved the measurement of length, voltage and current. The ammeter and voltmeter were checked to see if they were functioning properly. Thus any inaccuracy would be due to the number of decimal places that the ammeter or voltmeter shows readings. The possible error is calculated as follows: 0.1/5*100%=2% for the voltmeter 0.1/5*100%=2% for the ammeter The ammeter and voltmeter gave readings that were to one decimal place. If the readings were to more significant figures the reliability of the data would have increased significantly. Measuring the length accurately was a difficult process which could cause errors in the results of the experiment, especially when dealing with crocodile clips. The cross sectional area of the wire was calculated using the value of the diameter for a 30SWG wire from a data book. This variable was accurate. The conclusions drawn were reliable, as the readings and records demonstrated the direct proportion between length and resistance, and the discrepancies wouldn?t have affected the outcome of the investigation dramatically.(A large number of readings were taken.) In order, to improve the outcome of the results: 1-Digital ammeters and voltmeters could be used. 2- The temperature of the wire would have to be monitored. 3- The length of the wire would have to be changed more accurately and with more care.

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