To investigate how length affects the resistance of a length of wire
Aim
The aim of my investigation is to investigate how length affects the resistance of a length of wire
The resistance of a wire depends on certain factors. Some of these variables are listed below:
* Length of wire
* Diameter of wire
* Temperature at which wire is at
* The material of which wire is made out of
* The potential difference across circuit
* Cross sectional area
These must be kept constant (except the length of the wire). The three major factors are explained bellow:
) Temperature When the temperature of a metal increases the resistance of that metal increases. This is because when the temperature increases the atoms of the metal vibrate more vigoursly because of the increase in energy. This means that the electrons have more difficulty getting through the wire as they collide with the atoms which are in their pathway. This increases the amount of collisions therefore there is more resistance. However it is hard to keep the temperature exactly the same as the room temperature might change from day to day. It is essential to use a low voltage because it means a low current that will not heat up the wires. If a high voltage is used the energy would be in form of heat which would make the experiment unfair. The investigation will be done at room temperature. The temperature cannot be investigated because it is hard to control the range of temperature needed without the correct apparatus.
2) Length of wire The larger the length of the wire, the larger the resistance. This is because there are more atoms from the metal so there is more chance that the electrons would collide with one of the atoms therefore there is more resistance. The length of wire will be variable throughout the investigation. Electrons have a longer distance to travel when the wire is longer, so there are more collisions .The length of the wire will make a difference to the resistance. This is because when you have a long wire, the electrons have to squeeze together for longer to be able to pass through the wire than they do in order to be able to pass through a short wire.
3) Type of material Different materials have different resistances because the materials' atomic structures are different so some metals have low resistances and some have high resistances. Therefore it is important to keep the material the same throughout the experiment unless a different material is used to check if the conclusion or theory works for all materials. If different materials are used throughout the investigation, it will affect the results. For example if sometimes copper is used and sometimes nichrome is used, the results where copper is used will be of a low resistance because of the material and not because of the diameter of the wire. Throughout the experiment Constantan will be used. The type of material will affect the amount of free electrons that are able to flow through the wire. The number of free electrons depends on the amount of electrons in the outer shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase of the number of electrons. If the particles in the material are tightly packed together, the electrons will have more collisions and therefore more resistance.
4) Diameter/Cross sectional area A good example to illustrate this where two cars are traveling down a dual lane road side by side. As soon as the road changes to become a single lane road, it is impossible for the cars to travel side by side and one must stop and resume behind the other car. This same can be said for electrons in a wire, the larger the diameter/cross section, the more electrons are able to travel trough the wire at the same time.
All these factors must be kept constant to make the investigation fair. The same apparatus must be used throughout the investigation. It is also important to take three repeat readings and find the mean so if one result is very inaccurate, the others will average it out.
All materials, solid, liquid or gases are made up of atoms. The atoms themselves consist of a central bit, called the nucleus, made up of particles called protons (which have a +ve electrical charge) and neutrons (which have no charge) Orbiting around the nucleus are electrons which are very tiny and have a -ve electrical charge. One can think of the electrons orbiting in layers like the rings of an onion, and it's the ones in the very outside layer, the outer shell, that are the most important when thinking about conduction.
In metals, the outermost electrons are held only very weakly to the atom and often wander away from it and go to the nearby atom or one a bit further away. These wandering electrons are called conduction electronsand the more of these there are, for a given volume of metal, the better the metal will be as a conductor of electricity. When you connect a battery across a wire, one end becomes +ve and attracts the conduction electrons, which drift towards that end of the wire. But the electrons have obstacles to face because the metal atoms are ...
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In metals, the outermost electrons are held only very weakly to the atom and often wander away from it and go to the nearby atom or one a bit further away. These wandering electrons are called conduction electronsand the more of these there are, for a given volume of metal, the better the metal will be as a conductor of electricity. When you connect a battery across a wire, one end becomes +ve and attracts the conduction electrons, which drift towards that end of the wire. But the electrons have obstacles to face because the metal atoms are jiggling about because of their thermal energy and so the electrons collide with them and are knocked all over. It's this difficulty that the electrons have in moving along the wire that we call resistance.
Resistance involves collisions of the current-carrying charged particles with fixed particles that make up the structure of the conductors. A resistor is a material that makes it hard for electrons to go through a circuit. Without resistance, the amount from even one volt would be infinite. Resistance occurs when electrons travelling along the wire collide with the atoms of the wire.
The unit of resistance is Ohms and the symbol is:
The higher the resistance, the lower the current. If there is high resistance, to get the same current a higher voltage will be needed to provide an extra push for the electricity.
Some metals have less resistance than others. Wires are always made out of copper because copper has a low resistance and therefore it is a good conductor. The length and width of a wire also has an effect.
A variable resistor alters the amount of current flowing easily, which makes it very useful for speed control or light dimming.
An LDR's (Light dependant resistor) resistance will increase as light becomes brighter. But a thermistor's resistance will increase as the component accumulates heat energy. Bellow are the symbols for these different types of resistor. I will be using a variable resistor in my circuit.
An ammeter is used to measure current in Amperes. A voltmeter is used to measure the voltage (V). I will be using both of these devices in my experiment. Their symbols are shown bellow:
Ohm's law
In 1827, a German physicist discovered relationship that the amount of steady current through a large number of materials is directly proportional to the potential difference, or voltage, across the materials. Thus, if the voltage V (in units of volts) between two ends of a wire made from one of these materials is tripled, the current I (amperes) also triples; and the quotient V/I remains constant. The quotient V/I for a given piece of material is called its resistance, R, measured in units named ohms. The resistance of materials for which Ohm's law is valid does not change over enormous ranges of voltage and current.
Ohm's law may be expressed mathematically as V/I = R.
That the resistance, or the ratio of voltage to current, for all or part of an electric circuit at a fixed temperature is generally constant had been established by 1827 as a result of the investigations of the German physicist George Simon Ohm.
Alternate statements of Ohm's law are that the current I in a conductor equals the potential difference V across the conductor divided by the resistance of the conductor, or simply I = V/R, and that the potential difference across a conductor equals the product of the current in the conductor and its resistance, V = IR. In a circuit in which the potential difference, or voltage, is constant, the current may be decreased by adding more resistance or increased by removing some resistance. Ohm's law may also be expressed in terms of the electromotive force, or voltage, E, of the source of electric energy, such as a battery. For example, I = E/R.
With modifications, Ohm's law also applies to alternating-current circuits, in which the relation between the voltage and the current is more complicated than for direct currents. Precisely because the current is varying, besides resistance, other forms of opposition to the current arise, called reactance. The combination of resistance and reactance is called impedance, Z. When the impedance, equivalent to the ratio of voltage to current, in an alternating current circuit is constant, a common occurrence, and Ohm's law is applicable. For example, V/I = Z.
With further modifications Ohm's law has been extended to the constant ratio of the magneto motive force to the magnetic flux in a magnetic circuit.
Resistance values in electronic circuits vary from a few ohms, W, to values in kilohms, kW, (thousands of ohms) and megohms, MW, (millions of ohms). Electronic components designed to have particular resistance values are called resistors.
Bellow is a graph to show the relationship between current and voltage (with temperature as a constant):
Current (A)
--Resistance
Voltage (V)
Non-ohmic conductors do not necessarily comply to Ohm's law. One example is a filament lamp. The graph bellow shows that the line is curved as it passes through the origin. This is because as current increases, so does temperature.
Current (A)
--Resistance
Voltage (V)
Another example of a non-ohmic conductor is a diode. This device ensures that the current flows in one direction only. This is because resistance is high on one side of the device and low on another.
Current (A)
--Resistance
Voltage (V)
In a parallel circuit, the more resistors that are added make for more routes for the current to take. A rheostat is used in a circuit to change the current from time to time, used to control volume.
Prediction
I predict that if the length increases then the resistance will also increase in proportional to the length.
I think this because, as I have explained above in my background knowledge, the longer the wire the more atoms and so the more likely the electrons are going to collide with the atoms. If I had a 30 cm wire and a 60 cm wire, the 60 cm wire would have a resistance twice that of the 30 cm wire. Therefore, if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the Length is directly proportional to the resistance.
If the length of the wire is only half the length of the wire on the same type of wire, there should be half the number of collisions between the electrons and the atoms.
If the wire is twice as long, there should be twice the number of atoms, resulting in twice as many collisions and a predicted doubling of the resistance.
Fair Test
The wire must be the same thickness,
The surrounding temperature must be constant, or near enough constant, so the experiment should only be done on one day,
The equipment should be kept the same, Only change the length of the wire and nothing else,
The edge of the crocodile clips should be at the edges measured length.
Safety
Handle the power supply carefully.
Be careful when touching the wire, as it may be hot.
Start on the lowest current, so the wire then will not melt or burn instantly.
Be careful when the wire is connected, as it will get hot.
Be careful when cutting the wire.
Make sure the mains to the power supply is switched off when removing the wire from the circuit to be measured. Keep my work area clean and tidy to avoid confusion.
Apparatus
Power Supply, to regulate the mains power supply and bring 240v standard mains down to a safe amount.
Ammeter, to measure the current of the circuit in amperes.
Voltmeter, to measure the voltage of the circuit in volts.
Wire Constantan, to use to test the resistance in the circuit and conduct electricity.
Meter Rule, to accurately measure the length of the wire constantan. Variable Resistor, to provide the resistance so I can take my readings accurately.
Crocodile Clips, to provide safe contact between the components and the wire
Wire clippers, to safely cut the wire when reducing it's length.
Method
. Gather up listed equipment.
2. Take reel of constantan wire and use meter stick and wire clippers to measure and cut 100cm (1m).
3. Clip both ends of constantan wire with crocodile clips.
4. Measure voltage in voltmeter and amps in ammeter. Record reading.
5. Cut wire down to 90cm using meter ruler and wire clippers.
6. Repeat step 3.
7. Do the same for 60cm, 70cm and 80cm lengths in 2, 4 and 6 volts.
Observations
When doing my experiment I made some very interesting observations:
We did the experiment on two different days, which means that the room temperature would have been different. This would have affected my results because I have found out that temperature can have an affect on resistance. The amount of heat being exhibited on the wire could have been during the experiment or even before I begun it while the wire was in storage. Nevertheless, I am certain that the wire was at different temperatures on the two different days.
The power packs I used on the two different days could have varied. The power packs look the same and all have the same markings. So there is a good change that I did not pick up the same power pack on both days. I could not tell weather or not these power packs had anything physically wrong with them (unless I received extremely anomalous results).
The power pack has a analogue dial. I had to manually adjust the knob to regulate the voltage. There is a good chance that I made a human error when turning the knob, which could have resulted in a marginal error in the regulation of the voltage.
During the experiment, I had to break the circuit in order to cut the wire to an appropriate length. This meant that however many electrons were flowing during the time of interruption would have simply stopped as this circuit was connected in series.
Taking a closer look at the crocodile clips, I could see oxidization occurring on a select few. Rust had taken over the inside of one of the clips and this could have affected the amount of resistance given out.
When measuring and cutting the constantan wire, I noticed that there was a little bit of slack, making the wire longer than it seemed. This could have been eliminated simply by holding the wire tight and on a fat surface, but this was over seen.
As I have found out, temperature affects the resistance of the wire. We used the same wire and simply cut it down to size. I noticed that the wire has become increasingly hotter each time we broke the circuit and cut it. Wire can physically expand due to the heat, which would have affected resistance as I have found out.
Results (Shown repeated 3 times for each length)
2 Volts
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
0.71 0.69 0.72
0.23 0.24 0.22
3.09 2.87 3.3
90 cm
0.65 0.66 0.67
0.25 0.24 0.23
2.6 2.75 2.91
80 cm
0.60 0.59 0.61
0.25 0.26 0.24
2.4 2.27 2.54
70 cm
0.58 0.57 0.58
0.28 0.26 0.27
2.1 2.19 2.15
60 cm
0.56 0.56 0.56
0.29 0.29 0.29
.93 1.93 1.93
4 Volts
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
.45 1.45 1.45
0.46 0.46 0.46
3.15 3.15 3.15
90 cm
.22 1.23 1.21
0.44 0.43 0.45
2.77 2.86 2.69
80 cm
.26 1.26 1.26
0.51 0.51 0.51
2.47 2.47 2.47
70 cm
.01 1.01 1.01
0.47 0.47 0.47
2.15 2.15 2.15
60 cm
0.94 0.94 0.94
0.51 0.51 0.51
.84 1.84 1.84
6 Volts
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
2.5 2.6 2.4
0.81 0.86 0.82
3.09 3.25 3.93
90 cm
2.33 2.33 2.33
0.84 0.84 0.84
2.77 2.77 2.77
80 cm
2.21 2.21 2.21
0.90 0.90 0.90
2.46 2.46 2.46
70 cm
2.04 2.03 2.05
0.95 0.96 0.94
2.15 2.11 2.18
60 cm
.89 1.90 1.88
.01 1.00 1.02
.87 1.90 1.84
To eliminate any major anomalous results, the above results have been averaged out by adding each set together then divided it by 3. The average results are shown in table form bellow:
2 Volts (Average Results)
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
0.71
0.23
3.09
90 cm
0.66
0.24
2.75
80 cm
0.60
0.25
2.48
70 cm
0.58
0.27
2.15
60 cm
0.56
0.29
.93
4 Volts (Average Results)
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
.45
0.46
3.15
90 cm
.22
0.44
2.77
80 cm
.26
0.51
2.47
70 cm
.01
0.47
2.15
60 cm
6.94
0.51
.84
6 Volts (Average Results)
Length of Wire
Voltage (V)
Current (amps)
Resistance (ohms)
00 cm
2.55
0.81
3.09
90 cm
2.33
0.84
2.77
80 cm
2.21
0.90
2.46
70 cm
2.04
0.95
2.15
60 cm
.89
.01
.87
Analysis
From the graph, 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 that passes near enough in the region on the origin, showing that if the length of the wire is increased then the resistance of the wire will also increase. This means that resistance is directly proportional to length. For example, if the length is 40cm, and resistance is 2, then if length is doubled to 80cm, resistance also doubles to 4.
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.
The results satisfy Ohms Law, stated in my scientific knowledge, and that if you double length, you double the number of atoms in it, so doubling the number of electron 'jumps', which causes resistance. The results support my prediction as well:
"I predict that if the length increases then the resistance will also increase in proportional to the length."
No matter what the voltage is of the circuit, the resistance will remain the same, or will be in the same region. Again, this can be explained by Ohms Law: using the formula R= V/I, where there is 2X the current, and the voltage is the same, therefore R will be halve.
The results from the graph give a clear indication of how the resistance compares to the wire length. There is a very strong positive correlation.
The theory behind this is explained in the prediction. In any given metal wire, there are a number of atoms and free moving electrons. Electricity is the movement of these electrons through the wire. Resistance is caused when the free electrons moving through the wire collide with the atoms making their path through the wire more difficult. This means that if there are more atoms in the way to collide with the free electrons the resistance is increased. In a length of wire there will be a number of atoms, and in a wire twice the length, there will be twice the number of atoms. In turn this will lead to there being double the number of collisions between the electrons and the atoms increasing the resistance by 2. This explains why the results were directly proportional. For example a wire that was 10 cm long may have 500 atoms blocking the electrons. Therefore in a wire 20 cm long, there would be 1000 atoms meaning that the resistance had doubled.
The line of best fit clearly shows that the results followed the expected pattern very well. The points are very close if not touching the line. This shows how the results were directly proportional through out, as the gradient remained the same.
In turn, this effectively means that if the wire was trebled or quadrupled then the resistance would also treble or quadruple.
Evaluation
My results have a good standard of accuracy. This is shown by the points being near or on the line of best fit and there were no anomalous results. Therefore my results support a firm conclusion that the length of wire is proportional to the resistance.
I think that three repeats were sufficient. I feel that there were a few inaccurate results but not inaccurate enough to call an anomaly.
I believe that if I had a precisely controlled experiment, the lines on my graph would be on the top of one another. But because of a few factors, this was not possible.
If I were to repeat the experiment, I would make time to be able to do it on one day to eliminate the temperature factor. I would have used a digital display to give precise readings from my power pack (so I would not compromise or increase the voltage in the circuit. I would have used connectors rather than crocodile clips to add further reliability to my results. I would have let my wire cool down before proceeding with the remainder of the experiment.
Nevertheless, I have proven that the length of a wire is directly proportional to the resistance, no matter how many volts you pass through it.
