We will use a 1.5V battery and constantan wire. The wire will have a diameter of 0.234mm
which will be checked by a micrometer screw gauge.
The results will be observed and the resistance recorded. There are two ways to find the
resistance
- Ohmmeter (multimeter)
- Voltmeter and Ammeter
We will use the second as it is more accurate. This will then be repeated for the next length
(see table). Once they have all been recorded the tests will be repeated. This time, to ensure
that they are reliable we will use a 3V battery. The wire has a fixed resistance so when the
voltage changes, the current will change, still giving the same resistance.
We will then calculate the resistance using the following equation -
Resistance = Voltage / Current
R = V / I
We found this equation from a previous experiment where we investigated how the current
through a resistor changed when the voltage was varied. This gave us a straight line which
showed this relationship.
Once all the results have been calculated and recorded we will draw a graph showing how
the resistance varies with the length of the wire.
The dependant variable will be the resistance and the controlled variable will be the length of
the wire. The thickness of the wire will be kept the same because if it was increased there
would be a larger area for the electrons to flow through, so more current could flow at a
time, reducing the resistance. If you double the diameter you would square the total area,
and therefore ¼ the resistance.
The material will be kept the same because if it was changed there might be a different
number of free electrons to flow round the circuit, the atoms might be larger so the electrons
are more likely to collide with them, or they could be arranged differently making it
easier/more difficult for the electrons to get through.
The temperature will be kept the same, because when it is heated up the atoms get more
energy and vibrate more, making it harder for the electrons to get through and lose more
energy. This increases the resistance. There will be some heating effect if left a long time due
to the resistance, so when recording results we will disconnect the circuit as soon as they
have been taken to stop it heating too much.
We will keep the equipment the same and the wire will be measured by a meter stick to
ensure accuracy.
Results
A Table to show how the resistance through a piece of
wire varies with length
Test 1
Test 2
Test 3
Length /
Voltage
Current
Resistance
Voltage
Current
Resistance
Voltage
Current
Resistance
Average
cm
across
through
through wire /
across
through
through wire /
across
through
through wire /
Resistance /
wire / V
wire / A
ohms
wire / V
wire / A
ohms
wire / V
wire / A
ohms
ohms
50
1.31
0.22
5.95
2.35
0.40
5.86
3.30
0.56
5.89
5.90
60
1.33
0.18
7.30
2.41
0.34
7.08
3.44
0.48
7.16
7.18
70
1.35
0.16
8.44
2.46
0.30
8.20
3.55
0.43
8.25
8.30
80
1.36
0.14
9.71
2.52
0.26
9.69
3.60
0.38
9.47
9.62
90
1.37
0.13
10.54
2.57
0.24
10.70
3.70
0.34
10.88
10.71
100
1.38
0.10
13.80
2.60
0.21
12.38
3.45
0.29
11.90
12.69
These were the results from our preliminary work which was done on software on the
computer.
Length of wire /
cm
Voltage across wire /
V
Current through wire /
A
Resistance /
ohms
20
0.87
1.26
0.69
40
1.05
0.89
1.18
60
1.15
0.69
1.67
80
1.22
0.56
2.18
100
1.26
0.48
2.63
This supports my prediction.
Conclusion
Our graph shows that, as the length of the wire is increased, the resistance of the wire
increases. We know this because the line has a positive gradient of 1.2, which means it
increases in equal steps. The line is a straight line which tells us that length is directly
proportional to resistance.
Or length a resistance.
They are directly proportional because if you double the length, there would be twice as
many atoms for the electrons to collide with, so it would lose twice as much energy. This
means there would be half the current so the resistance doubles.
e.g.
Wire, length = 20cm
Wire, length = 40cm, resistance doubled.
This supports the theory I used to make my prediction and the outcome matched my
predicted outcome.
Evaluation
We know our data is reliable because we repeated it three times using different voltages to
ensure there was no fault with our circuit. We also switched the circuit on and off quickly to
prevent it heating up, which would increase the resistance. They supported our predicted
results and the results from our preliminary work. They are enough to help us reach a safe
conclusion.
There is one anomalous point on our graph, which is when the length was 100cm. This could
have been because it was the last experiment so the wire got slightly warmer. When the
wires get hotter, the atoms vibrate more, so it is harder for the electrons to get, through and
they lose more energy, so the resistance increases. It could also have been because the wire
wasn’t measured correctly, for example if there was a twist in the wire that we didn’t notice,
which would increase the length. This means there would be more atoms for the electrons to
collide with so the resistance would increase.
The points are very tightly scattered, with only one or two points being off the line, and they
are still quite close, showing that our results are reliable.
To improve this method and prevent errors we could use a water bath to keep the
temperature constant. The wire would be placed in the water bath and then tested.
To make sure the wire was accurate, new wire would have to be used, and made sure it
was flat. It would then be measured using a metre rule to measure to the centimetre.
Our results supported my conclusion and allowed me to make a firm conclusion. They were
reliable, close to the line of best fit and supported our preliminary work.
