Resistance= 1/Area.
This can be explained using the formula
R = V/I
Where there is 2 x the current, and the voltage is the same, R will halve. I did some research and it says 'that doubling the area will therefore halve the resistance' - in other words the resistance of a wire is inversely proportional to its area.
As the electrons in an electric current move around a circuit, they bump into the atoms in the wires through which they pass. Atoms of different elements obstruct the electrons by different amounts. For example, electrons pass easily through copper wire, but much less easily through tungsten wires. We say that copper has a lower resistance than nichrome or tungsten.
This is why copper is used for the connecting wires and cables in electrical circuits.
When an electric current passes through thin nichrome or tungsten wire, the electrons cannot flow easily. They collide with the atoms in the wire, which vibrate more quickly. This causes the wire to warm up. If the resistance of the wire is high and the current is large, the wire may get red hot. Conductors that provide a high resistance are called resistors.
This can be linked to the Ohm’s law which is “The voltage across a metal conductor is proportional to the current through it, provided the temperature stays constant”.
This can be written as:
V x I = VI
Because V is proportional to I, we can say that:
V / I = K (a constant)
Ohm showed that doubling the voltage doubles the current. Treble the voltage will give treble the current, and so on. The larger the resistance, the greater the voltage needed to push each ampere of current through it.
This led to the definition of one ohm:
“A resistor has a resistance of one ohm, if a voltage of one volt will drive a current of one ampere through it”.
The resistance of a resistor is the voltage per unit of current, i.e.
RESISTANCE (ohms) = VOLTAGE (volts) / CURRENT (amps)
R = V/I
Preliminary Experiment
Length of wire as a factor
Aim:
The purpose and aim of this investigation is too see how the length of a wire affects the electrical resistance.
Prediction:
I predict that, as the length of the wire increases the resistance will also increase because it is directly proportional. Therefore if the length of the wire doubles, the resistance will also double.
This was also reflected in my preliminary work, and so I can use this to base my prediction upon, and to prove that my prediction is correct.
Hypothesis:
Electrons bumping into ions on the conductor’s atoms cause resistance. If the length of the wire is doubled, the electrons bump into twice as many ions so there will be twice as much resistance.
This is assuming that the temperature is kept constant and that the material is kept constant. We can include this in our final analysis equations (of the graph and results) by adding a constant (K).
Variables:
Independent
- Length of wire
Dependant
- Resistance
Control
- Voltage on power pack
- Width of wire (SWG)
- Temperature
- Wire Material
Apparatus:
Power Pack (D.C)
Voltmeter
Ammeter
5 x Crocodile Clip Wires
Constantan wires with various lengths (10-100cm in intervals of 10cm)
Meter Ruler
Method:
I have chosen to use normal thickness (28 SWG) Constantan wire because from my preliminary results I found that this wire had a high resistance, because it has a high resistance it will be easier to measure any change in resistance, and therefore get accurate results.
To collect the data for my graph I have chosen to take a range of 10 lengths, from 10cm to 100cm.
Seeing that as I have chosen a range of 10 as to plot an accurate graph I will need at least 10 points to mark on the graph.
I have also chosen to take 3 repeats at each length and then take an average. I have chosen this so that if I have any anomalous results they will not show alot when I plot the averages on the graph.
The lengths that I have chosen are as follows : 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm, and 100cm.
I have chosen these lengths because they are easily measured by the meter ruler and give a good range of results. Below is a circuit diagram of the circuit I am going to use in my main experiment, set up the apparatus as shown below;
In my main experiment instead of using an ohmmeter I have chosen to use an ammeter and voltmeter, from which I will record all my results.
This is what to do once you have connected all the components of the circuit in the above fashion and connected all the wires to the mains power supply in order to create a flowing circuit. Remember to set up the voltmeter in parallel to the length of wire and to connect the ammeter in series. Once the apparatus has been set up to form a circuit like the one above;
- Tape the wire securely to the meter Ruler tightly on both ends, do this so that the reading for the length will be more accurate, and also so there will be no bends in the wire to make it heat up and give an incorrect reading for the resistance.
- Connect the circuit to the end of the ruler (at 100cm) and take down the reading from both the ammeter and the voltmeter. Switch offal the circuit (via the power pack) every time you re-take these readings, this will insure the wire gets a break, does not overheat, and thus we will have more accurate results.
- Do this again for all the lengths (going down in 10cm) until you reach 10cm.
- Get 3 readings for each length to make sure you get accurate readings, then find the mean averages for each length.
- Find the resistances (by using the formula R=V/I) and write them down.
- Record all results in a table, then do graphs and charts plotting the lengths against the Current (amps), Voltage (volts), and the resistance (ohms).
Results:
Below is a table of results showing the recordings for currents, voltages, and resistances;
After working out, here is a table showing the mean averages and resistances;
Conclusion:
In my prediction I said that:
”if the length increases than the resistance will also increase in proportion to the length”
From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is proportional to the length of the wire.
The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion.
The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material , so if there is a larger number of atoms there will be a larger number of collisions which will increase the resistance of the wire.
If a length of a wire contains a certain number of atoms when that length is increased the number of atoms will also increase.
This is shown in my diagrams below;
Wire A is half the length of wire B,
therefore because wire A has 20 atoms wire B will have 40.
In this diagram the wire is half the length of the wire below and so has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times.
Also if the length of the wire was trebled or quadrupled then the resistance would also treble or quadruple, and so on.
Therefore my findings and results support my prediction that the length of a wire is directly proportional to it’s resistance.
Analysis:
From the graphs on the previous pages I can see that the resistance of the wire is proportional to the length of the wire. I know this because the Line of Best Fit is a linear straight line showing that if the length of the wire is increased then the resistance of the wire will also increase in proportion.
At length 10cm the resistance read 0.5 ohms, but it then steadily increased to 1.6 ohms as the length increased to 20 cm. It gradually rose along the straight line until at 100cm the resistance was 10.6 ohms.
Cross-Sectional Area (A):
A = ∏(½D)²
= 0.1104 mm²
My graph is in the straight-line form with formula:
“y=mx + c” (where c = 0)
Therefore the equation is:
“y=mx”
I measured the constant gradient of my graph to be:
However the gradient is usually measured as Ω/mm, therefore:
0.106 / 10 = 0.0106 Ω/mm
After looking back at the equation that linked the resistance of a wire with its resistively length and area, which I was explained and analysed in the introduction and background knowledge, I notice that I can write the equation in the form of the straight line “y=mx”, where y = resistance, and x = length.
I will use this to link my result’s values to the equation and find the constant resistance (p).
My graph’s equation was:
“R = ML”
Where M is the constant gradient:
= 0.0106 Ω/mm
Therefore:
Hence once I have substituted the values the formula becomes:
As the gradient is constant, and the area of the wire is constant, the resistivity (p) is therefore also constant, with a value of:
p = 0.0106 Ω/mm x 0.1104 mm²
= 1.177024 x 10-3 ohms.
Cross-sectional area of wire as a factor
Aim:
The purpose and aim of this investigation is too see how the cross-sectional area of a wire affects the electrical resistance.
Prediction:
I predict that as the cross-sectional area of the wire widens and increases the resistance will also increase because it is proportional to the cross-sectional area.
If the cross-sectional area doubles or trebles, so will the resistance accordingly.
Again I can use my preliminary work as a source and a reference to back up my prediction and use as a reference in the conclusion/analysis.
Hypothesis:
Resistance is when the electrons in an electrical circuit bumping into ions on the metal material’s atoms. If the cross-sectional area of the wire is doubled or trebled, the electrons bump into twice or 3-times as many ions so there will be twice or 3-times as much resistance.
Assuming that the temperature is and material is kept constant throughout the experiment. We can put this into our graph’s equations when analyzing and working them out by adding a constant (K).
Variables:
Independent
- Cross-sectional area of the wire
Dependant
- Resistance
Control
- Voltage/Current (Via powerpack)
- Length of wire
- Temperature
- Wire Material
Apparatus:
Power Pack (D.C)
Voltmeter
Ammeter
5 x Crocodile Clip Wires
Constantan wires with various cross sectional areas (SWGs)
Meter Ruler
Method:
In my experiment I have chosen that I will use wires with different SWGs but with the same length of 50cm. I chose 50cm because it has a normal average resistance, which is not an extreme high or an extreme low, and so the results would be fairly normal.
The range of cross-sectional areas that I will be using will be, 26 SWG, 28 SWG, 34 SWG, and 38 SWG.
After much calculation, I have worked out that they have the following cross-sectional areas (A = Cross-sectional area).
This was achieved by using the equation for cross-sectional area which is:
A = ∏(½D)²
Because of the limitations at my school, only 4 different SWG wires where available to me, and so my graph will have at the most 4 points on it, therefore being not as accurate as if I had for example 10 points.
I will take 3 readings for each current and voltage, and I will work out averages and resistances as I did in the 1st experiment in which we tested for how the length affects the resistance.
I am using the following cross-sectional areas: 0.01824 cm², 0.04301 cm², 0.1104 cm², and 0.16403 cm².
I used these cross-sectional areas because they where the only ones available to me at the time, however they are more than enough to give me accurate and good results because they cover a wide range.
I will set up my apparatus like I did in the previous experiment to test for the lengths, and I will then do the following points;
- Take the wire securely to the meter Ruler tightly on both ends, do this so that the reading for the length will be more accurate, and also so there will be no bends in the wire to make it heat up and give an incorrect reading for the resistance.
- Connect the circuit to the ends of the wire (50cm long) and take down the recordings of both the voltage and current. Turn off the current between each reading to allow time for the wire to cool.
- Do this for each of the wires in order (each width), and record them all.
- Get 3 readings for each width to make sure you get accurate readings, and then find the mean averages for each width.
- Find the resistances (by using the formula R=V/I) and write them down.
- Record all results in a table, then do graphs and charts plotting the lengths against the Current (amps), Voltage (volts), and the resistance (ohms).
Results:
Below is a table of results showing the recordings for currents, voltages, and resistances;
After working out, here is a table showing the mean averages and resistances;
Conclusion:
In my prediction I said that:
”if the width increases than the resistance will also increase in proportion to the width”
From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is proportional to the width of the wire.
The width of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the width of the wire increases or decreases in proportion.
The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material , so if there is a larger number of atoms there will be a larger number of collisions that will increase the resistance of the wire.
If a width of a wire contains a certain number of atoms when that width is increased the number of atoms will also increase.
This is shown in my diagrams below;
Wire A is half the width of wire B,
therefore because wire A has 20 atoms wire B will have 40.
In this diagram the wire is (approx) half the width of the wire below and so has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times.
Also if the width of the wire was trebled or quadrupled then the resistance would also treble or quadruple, and so on.
Therefore my findings and results support my prediction that the width of a wire is directly proportional to its resistance.
Analysis:
From the graphs on the previous pages I can see that the resistance of the wire is
proportional to the length of the wire. I know this because the Line of Best Fit is a straight line showing that if the length of the wire is increased then the resistance of the wire will also increase.
As done in the previous Analysis section, we calculated our results, and analyzed our graphs so that I could implement certain formulae into the experiment that would back up my conclusion.
Please review the Initial research.
Safety
To ensure that the experiments where safe, there were certain precautions that had to be observed.
Because we were handling sharp wires, along with electricity and bare crocodile clips etc…, we had to wear protective clothing. We wore safety goggles, and protective lab coats.
To make sure that there was no hazardous items around that could damage our health, we cleaned the workplaces and kept all equipment at arms length away from us, and we ensured that all materials that could be hazardous to our health were well out of harms way to ensure our safety.
Evaluation
The experiment went fairly well, with good results and graphs obtained all round. We didn’t encounter any problems, and as far as seen so far there were no major problems at all. Many steps could be made to make the results more accurate, and precise.
When measuring the wire lengths for the experiment, we didn’t cut fairly, and we measured out approximate lengths roughly depending on a ruler that was quite a it away. One major improvement that would affect the results a lot would be to make these readings more accurate, this is because the length/width of the wire is THE MAIN variable of the experiment, and so if this is altered even by a extremely small amount, it would make a lot of a difference to the results.
I think both the experiments were fair tests, including the preliminary test, however they could be improved if we repeated the experiment a few more times, because then we would have got a broader range of results, and they would be more accurate.
Safety was a big issue due to the fact that we were using sharp wires and a high volume of electricity, so we wore eye protection and lab coats all of the time.
If I was to repeat this test, I would make sure that I got more than 3 readings per test, so that I can get more accurate results. To improve it even more I would use a broader range of lengths and widths, especially more SWG values for the 2nd test (width as a factor).
Hopefully to go on and investigate the different factors that affect the resistance of a wire, in the near future I will be able to conduct more tests using different factors as variables, including using temperature and pressures of wires, which would make a considerable difference to the overall view of how the rate of a reaction is dependant on factors.