Investigating Factors Which Affect Electrical Resistance
Investigating Factors Which Affect Electrical Resistance
Brief
What effect does varying the length of a wire have on its resistance?
Background Information
Variables involved in this investigation
* Length of wire.
* Material of wire.
* Width of wire.
* Starting temperature of wire.
All of these affect the;
* Resistance of the wire.
* Voltage across wire.
* Current in circuit.
* Temperature of wire.
The Length and Width of a Wire
If the length of the wire is increased then the resistance will also increase as the
electrons will have a longer distance to travel and so more collisions will occur. Due to this, the length increase should be proportional to the resistance increase. However, if the wire width is increased the resistance will decrease. This is because of the
increase in the space for the electrons to travel through means less likelihood of the free electrons having collisions and losing energy. Therefore, length of wire is directly proportional to resistance, and width (cross-sectional area) is inversely proportional to resistance.
The Material of a Wire
The type of material will affect the amount of free electrons which are able to flow through the wire. The more free electrons that there are in a space, the more collisions there will be between them, as the higher the resistance will be as a result.
Resistance
Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, and there is less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and, in this way, electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions result in some energy that the free electrons are carrying being 'lost' (though energy cannot be destroyed or created, only converted) as heat. As the temperature increases, so does the resistance because the more heat energy received by the particles in the metal wire, the more they vibrate, and so the harder it is for free electrons to move through the wire.
The resistance of a length of wire is calculated by measuring the current in amps in series with an ammeter and the voltage across the wire in volts with a voltmeter in parallel. The current is the same all through the wire These measurements are then applied to this formula:
V = I x R where V = Voltage, I = Current and R = Resistance
This can be rearranged to:
R = V/I
Resistance is measured in ohms (?).
Ohm's Law
It is could also relevant to know Ohm's Law, which ...
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The resistance of a length of wire is calculated by measuring the current in amps in series with an ammeter and the voltage across the wire in volts with a voltmeter in parallel. The current is the same all through the wire These measurements are then applied to this formula:
V = I x R where V = Voltage, I = Current and R = Resistance
This can be rearranged to:
R = V/I
Resistance is measured in ohms (?).
Ohm's Law
It is could also relevant to know Ohm's Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). This means that V/ I is constant, so the resistance of a metallic conductor is constant, providing that the temperature also remains constant. The resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, and so are increasing the likelihood of collisions with the free electrons.
Hypothesis
I predict that;
* The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal. Therefore, more energy is going to be 'lost' in these collisions (as heat).
* Doubling the length of the wire will result in double the resistance. This is because when the length of the wire is doubled, the number of collisions that will occur will also double, thus doubling the amount of energy 'lost' in these collisions as heat, which will serve to double the resistance.
Preliminary Work
In order to decide upon the voltage and lengths of wire to use in the final experiment, preliminary trials were carried out. After performing these rough trials, it was decided that a 1V fixed power supply would be used in the proper experiment, as it would provide results for lengths from 30cm up to 100cm without the wire overheating. To increase accuracy, it was also decided to allow the wire to cool between experiments as the wire seemed to be getting hot was noticed at lower lengths and, as mentioned above, an increase in temperature results in an increase in resistance. By allowing the wire to cool between experiments a fair test could be assured. The preliminary experiments also confirmed that the ammeter and voltmeter were compatible with the power supply and that they provided an appropriate degree of accuracy. To ensure that this is a fair test, a fixed power supply will be used, measurements will be taken twice, and the same thickness of wire will be used. A wire will be used that will not overheat at short lengths, which would affect resistance.
Safety
In order to perform a safe experiment, a low voltage of 1V was chosen so that overheating was minimised. Also, lengths lower than 30cm were will not be tried, which will also help to avoid overheating.
Apparatus
* Metre rule marked in centimetres to measure the wire being tested to ensure a fair test
* a Voltmeter and an Ammeter to measure the voltage and current, and hence find the resistance.
* a 1 Volt controlled power supply
* crocodile clips to connect the wire being investigated to the rest of the circuit
* a length of nichrome wire at least 1 metre long
* circuit wires to connect the above items and to complete the circuit.
Method
Construct the circuit below:
. One metre length of wire is fixed to a metre rule.
2. The first crocodile clip is clipped to the wire at the 0cm position on the metre rule.
3. The second crocodile clip is clipped to the relevant position depending on the required length of wire ( the first length tested will be 30cm).
4. The power supply is turned on. The voltage and current are then read off the ammeter and voltmeter, and recorded.
5. The power supply is then turned off and the second crocodile clip is moved to the next position. The wire is left to cool down for 3 minutes.
The above steps are completed for each length and then the entire investigation is repeated for accuracy.
Results
Length of Wire (cm)
Average Voltage (V)
Average Current (A)
Resistance (?)
30
0.7
2.6
0.27
40
0.78
2.2
0.35
50
0.84
.9
0.44
60
0.88
.7
0.52
70
0.92
.5
0.61
80
0.95
.4
0.69
90
0.98
.2
0.8
00
.1
0.88
See also attached graphs - length of wire against resistance, and current against resistance.
Conclusion
Having performed the investigation, the following conclusions were drawn:
* As predicted, an increase in length resulted in an increased resistance. This is because, when the wire is longer, there are more free electrons, and they have to travel further, increasing the chance of them colliding and causing resistance.
* As my first graph shows, the wire shows a strong trend of a straight line, i.e. the length of the wire is shown to be directly proportional to the resistance - double the length and the resistance doubles. This can be seen at 50cm, where the resistance was 0.44?, and the resistance at twice that length, 100cm, was 0.88?. This relationship. E.g. resistance of the wire at 40cms was 0.35? and at 80cms it was 0.69?.
* My second graph show that current is inversely proportional to the length of the wire. Although I had not hypothesised this, it makes sense when considering the relationship between voltage, current and resistance, and then considering the relationship between resistance and length of wire that I have just found. Voltage can be seen as being 'shared' or divided between current and resistance, i.e. V/I =R, and V/R = I. Therefore, any factor which positively affects resistance will negatively affect current.
Evaluation
I believe that my results are appropriately reliable for this experiment, and that they are as accurate as the conditions of the school classroom can allow. I say this because there do not appear to be any anomalous results. My results are the result of taking an average of two experiments, so any inaccurate results that would have made it difficult to see a trend were evened out. If I wanted to increase the degree of accuracy in my results, I could have used more accurate voltmeters and ammeters, and not have rounded my result to 2dp, but I do not think that this very high degree of accuracy is appropriate for this experiment, as the level of accuracy to which my results were taken has provided me with sufficient data to see strong, consistent trends in it.
If there are any anomalous results in my investigation which I have not noticed, they could be explained by Ohm's Law. If, at these points (more likely in the lower lengths), the wire was not allowed to cool completely so that the temperature was higher for that measurement, then this could have caused anomalous results. Whilst unlikely, this would cause a higher resistance as explained previously in my background knowledge.
If I were to extend this investigation, I would like to see how changing other properties of the wire would affect its current, resistance and temperature. I would like to use experiment with using different metals for the wire, and also with using different widths. Another interesting factor to investigate would be how temperature affects other variables of the wire.
Octavia Younger
Sc1: Physics
