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
1*Ammeter(0-5A)
1*Voltmeter(0-5V)
6*connecting wires(copper)
1*Rheostat(to act as fixed resistor)
1*ruler
Blu-Tak
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