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Transcript
[Type the company name]
Resistance vs. CrossSectional Area
IB Physics HL
Adam Pfoertsch
[Pick the date]
Abstract
As a student, one is expected to know mathematical formulae by heart, how to take them apart,
rearrange them and know what changes what. However, when put into practice, certain equations
might not fit perfectly anymore, which is why nothing beats experimenting and putting models to the
test. In this experiment I wanted to figure out if the equation for finding resistivity in a material is
precise compared to a real life counterpart. By putting a current through several pieces of aluminum
wire and then comparing the results to each other. I expected the results to show that the larger the
cross-sectional are of a wire, the less resistant it is, therefore letting more voltage flow through it.
Expectations
What I expected was that as the cross-sectional are of the wire increases, the resistivity of it
𝐿
decreases. According to 𝑅 = 𝑝 𝐴 with p being the resistivity constant of the material, L being the length
in meters, and A being the cross-sectional area in cm2. Since A is inversely proportional to R, when A
increases, this means that R should decrease. Also, if A decreases, R should proportionately increase.
With my data however, I used a different formula to find R, instead I used 𝑉 = 𝐼𝑅 but since I am finding
𝑉
𝐼
R I simply moved the I over to make𝑅 = . With this, I can now find R because I collected V and I in my
data collecting.
Variables
ο‚·
ο‚·
ο‚·
ο‚·
Current (Amps) – Independent
Voltage – Dependent
Material/Length of wire – controlled
Power Supply strength - controlled
Materials
ο‚·
ο‚·
ο‚·
ο‚·
A power supply that can independently control Voltage and Amps
2 crocodile clips with preferably close to zero resistance
Aluminum wire
A Multimeter
Procedure
1. Make sure the power supply is off before connecting any wires to it
2. Cut three pieces of Aluminum wire to 30 cm
3. Connect the crocodile clips to each a plus and negative port and connect them to the aluminum
wire making sure the circuit is closed properly
4. Set the multimeter to Voltage and make sure the cables are in the right ports
5. Turn on the power supply with both knobs at zero
6. Connect the ends of the multimeter to the crocodile clips at the aluminum wire.
7. Turn the voltage knob up all the way. The displays should still show zero
8. Slowly turn the current knob up, watching the voltage on both the supply meter and the
voltmeter
9. Measure each readable value (Amps, Volts on Power supply/Voltmeter) at .5 Amp steps
10. Combine two pieces of aluminum wire together and repeat steps 8 and 9
11. Repeat with three pieces of aluminum wire
Figure 1: Schematic of Experiment
Power supply
Crocodile Clip
Aluminium Wire
Data
Table 1: Measurements with 1 (one) piece of Aluminum Wire
Current
(Amps)
Volts
Volts
Resistance
(Power (Multimeter) (Ω)
Supply)
0.50
0.1
0.0110
0.0220
1.00
0.2
0.0245
0.0245
1.51
0.3
0.0366
0.0242
2.00
0.4
0.0516
0.0258
2.51
0.5
0.0645
0.0257
3.00
0.5
0.0531
0.0177
Table 2: Measurements with 2 (two) pieces of Aluminum wire
Current
(Amps)
0.51
1.00
1.50
2.00
2.49
3.00
Volts
(Power
Supply)
0.1
0.2
0.3
0.4
0.5
0.6
Volts
Resistance
(Multimeter) (Ω)
0.0097
0.0203
0.0310
0.0431
0.0566
0.0686
0.0190
0.0203
0.0207
0.0216
0.0227
0.0229
Diameter:
1.20mm
Diameter:
4.38mm
Table 3: Measurements with 3 (three) pieces of Aluminum Wire
Current
(Amps)
0.50
1.00
1.50
2.00
2.50
3.00
Volts
(Power
Supply)
0.1
0.2
0.3
0.4
0.5
0.6
Volts
Resistance
(Multimeter) (Ω)
0.0108
0.0212
0.0316
0.0427
0.0533
0.0638
0.0216
0.0212
0.0211
0.0214
0.0213
0.0213
Diameter:
7.5mm
Figure 2: First Trial
0.0800
0.0700
Voltage
0.0600
0.0500
0.0400
0.0300
0.0200
0.0100
0.0000
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
2.50
3.00
3.50
Current (Amps)
Figure 3: Second Trial
0.0800
0.0700
Voltage
0.0600
0.0500
0.0400
0.0300
0.0200
0.0100
0.0000
0.00
0.50
1.00
1.50
2.00
Current (Amps)
Figure 4: Third Trial
0.08
0.07
Voltage
0.06
0.05
0.04
0.03
0.02
0.01
0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Current (Amps)
Figure 5: Combined Graphs
0.0800
0.0700
0.0600
1 wire
Voltage
0.0500
2 wires
0.0400
3 wires
0.0300
Linear (1 wire)
Linear (2 wires)
0.0200
Linear (3 wires)
0.0100
0.0000
0.00
0.50
1.00
1.50
2.00
2.50
Current (Amps)
Calculations:
𝑅=
𝑅=
.0110
.50
= .0220Ω, 𝑅 =
.0097
.51
= .0190Ω, etc.
𝑉
𝐼
3.00
3.50
Analysis
While at first the data may seem inconclusive, upon further inspection one can see that the
resistance does change depending on the three wires. While only one wire has the highest resistance of
the three, the second trial and third trial are both lower than each, fully confirming my expectations.
While they are only very minimal differences, this is also expected since a piece of aluminum wire 30 cm
long cannot possibly have a high amount of resistance, compared to maybe an inch thick steel wire.
However, the first trial contains one data point that does not match up to the rest, which also throws off
the trend line by a lot. This last point should be ignored because it is most likely either a recording error
or measuring error. Otherwise, the two other data lines seem probably and realistic.
Evaluation
This experiment could have been improved in several ways to enhance it. First, while a sufficient
number of data was collected, more could have always been better. While we do get to see that there is
a difference, more data points would have enabled a more precise way to distinguish them. For example,
instead of collecting data every .5 amps, data could be collected every .25 or even every tenth of an amp.
This way, a change would be discoverable more easily than with current data.
Additionally, instead of only using up to three pieces of aluminum wire, more could have
definitely been used. With another 3 thicknesses of wires, more change could have been noticeable and
would have strengthened the idea of thickness decreasing resistance. However, only so many wires fit
into one crocodile clip, so another way of connecting the two would have to be conceived, which might
change some of the variables, and change the data.
Uncertainties, as with every experiment, also remains a slight problem here. While the power
supply can only display voltage to a tenth, this problem was solved by hooking up the multimeter to the
circuit, which can display up the a thousandth of a volt. If we had instead relied on the power supply
read out, we might have gotten completely different data, data that might not have confirmed the
model, or even showed information that is not expected in any way.
Conclusion
In conclusion, this experiment fully confirmed the initial hypothesis and even the model given to
students in the textbook. By having tested that cross-sectional area does influence resistance in an
inverse way, we are now more confident when using the formula in solving theoretical problems that it
will confirm if we did it in practice.