Wires of different lengths will have to be tested to prove that resistance is in proportion to length. This should merely involve testing different lengths of one type of wire. There is no range perimeter to how long the lengths could be but it is uncertain that they will surpass 1 meter.
Wires with different diameters need to be tested to prove that the resistance of a wire is inversely proportional to its area. The only widths of wire that can be accessed are 0.90mm, 0.45mm, 0.56mm and 0.32mm.
The experiment will obviously require an electrical circuit as the resistance of a wire in tan electrical circuit is being calculated. To calculate the resistance of the wire using Ohm’s Law, both an ammeter and a voltmeter will be required:
Resistance = Voltage/Current
The wire will be attached in a circuit in series so that the current flows directly through it. Power will need to be supplied through a DC power pack that enables the power to be changed easily and accurately.
Charges
The charge is the amount of electricity traveling through a circuit.
The symbol for charge is Q
The unit for charge is Coulombs
A capacitor is a device that stores charge
Charge (Q) = Current (I) x Time (t)
Current
This is the flow of electrons round the circuit. This is measured in amps (I).
Voltage
This is the driving force that pushes the current round. This is measured in volts (V)
Resistance
This is anything in circuit that slows the flow of current down. This is measured in ohms (Ω). Ohm’s Law shows that: Voltage (V) = Current (I) x Resistance (R) , so if the voltage increases then less current will flow, if the resistance is constant.
Potential Difference
It is the voltage across the terminal of cells, where the current is taken from it. P.d. is measured in volts.
Voltmeter
It is connected in parallel with resistors in the wire in a circuit.
Ammeter
It is connected in series to measure current.
Symbols
Cell: Switch:
Voltmeter: Resistor:
Ammeter: Rheostat:
Resistors
Resistors (made of the length of nichrome wire) can be used to reduce the current in a circuit.
A Variable Resistor or Rheostat
A variable resistor or rheostat is used to vary the current in a circuit.
Ohm’s Law
At a constant temperature the potential difference or voltage across the conductor is directly proportional to the current flowing through it.
Resistance (R) in ohms (Ω)
Current (I) in ampere (A)
Voltage (V) in volts (V)
Resistors in Series:
Resistors in Parallel:
Note:
- When resistors are connected in series the total resistance increases whereas it decreases in parallel.
- When two resistors are connected in parallel then the total resistance can be calculated by the formula R= R1 R2/ R1 + R2
The modal of charge:
All materials have some resistance to a flow of charge. A p.d. across the material causes free charges inside to accelerate. As the charges move through the material, they collide with the atoms of the material which get in their way. They transfer some or all of their kinetic energy, and then accelerate again. It is this transfer of energy on collision that causes electric heating.
The longer a wire, the greater the resistance. This is because the charges have further to go through the material; there is more chance of collision with the atoms of the material. In fact the resistance is proportional to the length of the wire, or R α I
Also, the thicker a wire is, the smaller its resistance will be. this is because there is a bigger area for the charges to travel through, with less chance of collision. In fact the resistance is inversely proportional to the cross-section area of the wire, or R α 1/A
This relations are illustrated in the figure:
Cross Sectional Area
The cross-sectional area of a conductor (thickness) is similar to the cross section of a hallway. If the hall is very wide, it will allow a high current through it, while a narrow hall would be difficult to get through due to it's restriction to a high rate of flow. The animation at the left demonstrates the comparison between a wire with a small cross sectional area (A) and a larger one (A). Notice that the electrons seem to be moving at the same speed in each one but there are many more electrons in the larger wire. This results in a larger current which leads us to say that the resistance is less in a wire with a larger cross sectional area.
Length of the Conductor
The length of a conductor is similar to the length of a hallway. A shorter hallway would allow people to move through at a higher speed than a longer one.
Temperature
The temperature of a conductor has a less obvious effect on the resistance of the conductor. Higher temperature means more vibrations. Imagine a hallway full of people. Half of the people (the electrons) are trying to move in the same direction you are and the other half (the protons) are evenly spaced but stationary in the hallway. This would represent a cold wire. Since the wire is cold the protons are not vibrating much so the electrons can run between them fairly rapidly. As the conductor (hallway) heats up, the protons start vibrating and moving slightly out of position. As their motion becomes more unpredictable they are more likely to get in the way and break up the flow of the electrons. As a result, the higher the temperature, the higher the resistance.
Length of wire:
If I increase the length of the wire (keeping the thickness and the material of the wire same) there will be more atoms of the wire colliding with the electrons. This will consequently increase the resistance of the wire. However if the wire was shorter, the free electrons will not collide with the atoms as much as it did when it was longer. So now I can conclude that resistance is directly proportional to length and that if the length of the wire doubles its resistance doubles. If I draw a graph representing current against voltage for different lengths of wire, then it will look like this:
The shortest wire of these will be the steepest in the graph; this is because it has the least resistance and therefore supplied the least voltage. The longest wire will have the greatest resistance and will be represented by the lowest line on the graph.
Material of the wire:
Here I use two different materials for the wires and calculate their resistance. I have chosen copper and nichrome. I will use the same procedure as mentioned before to calculate the resistance and I will set up the apparatus as first mentioned while keeping the thickness and the length of the wires same. If I were to draw a graph representing current against voltage, for this experiment it will look sort of like this:
Thickness of the wire:
Resistance:
Resistance and length:
If I plot a graph to show how resistance varies with length, it will show me something similar to this predicted graph:
The graph passes through the origin, which concludes that , however much I increase the length, the resistance will increase by the same amount.
Resistance decreases if the cross-section area is increased. An example can help to get a clearer picture; a narrow wire has fewer paths existing for the electrons to move through. While a larger wire has many more paths they could take. This makes conduction easier.
It can be shown that the relationship between the cross-section area, A and resistance is R α 1/A OR R α K/A
Where k is a constant that depends on the length and type of material. If I plot a graph to show how resistance varies with area, this will be shown:
Unlike the graph for length, the line doesn’t pass through the origin. However: R α 1/A means that a graph of R against 1/A will show direct proportion.
If I plot a graph to show how resistance varies with 1/Area, I will get this:
Free electron conducting in metal
Conductors:
Conductors ( e.g. copper, aluminum ) are those substances which easily allow the passage of electric current through them. It is because there are a large number of free electrons available in a conductor. In terms of energy band, the valence and conduction bands overlap each other as shown below. Due to this overlapping, a slight potential difference across a conductor causes the free electrons to form electric current. Thus the electrical behaviour of conductors can be effectively explained by the band energy theory of materials.
Prior test
In order to rely on my results, I take the readings of the current for the increasing and the decreasing currents; giving a prior test.
Material: Length: Thickness:
Experiment
This first trial is to test the accuracy and the realism of the experiment itself. It also shows us that as the temperature has an effect on resistance.
I will use a 100cm long strip of Nichrome wire and attach it to the circuit and the current will be raised and recordings will be taken at different levels.
- Attach 100cm Nichrome wire.
- Turn on the power supply and raise the current.
- Take reading from the voltmeter.
- Continue raising the power recording voltmeter readings.
This above procedure will require the following equipment given below:
- 100cm Nichrome wire
- Ammeter 0 to 200 mA
- Voltmeter 0 to 20 volts
- Rheostat
- Crocodile clips
- Battery
- Switch with key
- Connecting wires
By adjusting the rheostat the voltage are increasing in steps of 0.15 V to 0.50 V. Each time noting down the corresponding ammeter readings. I do this to make sure the readings of the ammeter while increasing and decreasing the voltage are the same almost with a slight variation, therefore making sure that no heating has taken place. I will then note down the ammeter readings while decreasing the voltage in steps of 0.50 V to 0.15 V, and I’ll take the average current readings as this will improve the reliability of my experiment. I will use a table similarly to the one drawn and record my readings and calculate the resistance.
Material: Nichrome Wire Length: 100cm Thickness: 0.45mm
Average = 5.70
And now I will draw a graph representing current against voltage, and then I will take the line of best fit from which I will take the gradient and check whether the results I have obtained graphically matches the results in the table.
Obtaining Evidence
In this part of my task, I will show all my graphs and results that I have obtained after carrying out the experiments. I have done the same process as I have planned earlier.
My experiment will be based on these:
- Length (same thickness and different lengths)
- Thickness (same length and different thickness)
- Resistors in series
- Resistors in parallel
Different Lengths
Material: Nichrome Wire Length: 100cm Thickness: 0.45mm
Material: Nichrome Wire Length: 75cm Thickness: 0.45mm
Material: Nichrome Wire Length: 50cm Thickness: 0.45mm
Material: Nichrome Wire Length: 25cm Thickness: 0.45mm
Resistance from graph
Lengths:
100cm
Gradient = y/x
= 24.00/0.20
= 120
Resistance = 1/120 = 0.0083 x 1000
= 8.33
75cm
Gradient = y/x
= 30.75/0.20
= 153.75
Resistance = 1/153.75 = 0.0065 x 1000
= 6.50
50cm
Gradient = y/x
= 24.10/0.10
= 241
Resistance = 1/241 = 0.00414 x 1000
= 4.14
25cm
Gradient = y/x
= 22.00/0.05
= 440
Resistance = 1/440 = 0.00227 x 1000
= 2.27
Different Thickness
Material: Nichrome Wire Length: 100cm Thickness: 0.90mm
Material: Nichrome Wire Length: 100cm Thickness: 0.45mm
Material: Nichrome Wire Length: 100cm Thickness: 0.56mm
Material: Nichrome Wire Length: 100cm Thickness: 0.32mm
Resistance from graph
Thickness:
0.90mm
Gradient = y/x
= 42.20/0.10
= 422
Resistance = 1/422 = 0.00236 x 1000
= 2.36
0.45mm
Gradient = y/x
= 23.65/0.20
=118.25
Resistance = 1/118.25 = 0.00845 x 1000
= 8.45
0.56mm
Gradient = y/x
= 40.68/0.20
= 203.4
Resistance = 1/203.4 = 0.00491 x 1000
= 4.91
0.32mm
Gradient = y/x
= 22.60/0.20
= 113
Resistance = 1/113 = 0.00884 x 1000
= 8.84
Series
Material: Nichrome Wire Length: 100cm and 75cm Thickness: 0.45mm
Material: Nichrome Wire Length: 100cm and 50cm Thickness: 0.45mm
Resistance from graph
100cm and 75cm
Gradient = y/x
= 25.15/0.40
=62.87
Resistance = 1/62.87 = 0.01590 x 1000
= 15.90
100cm and 50cm
Gradient = y/x
= 23.55/0.30
= 78.5
Resistance = 1/78.5 = 0.012738 x 100
= 12.73
Parallel
Material: Nichrome Wire Length: 100cm and 75cm Thickness: 0.45mm
Material: Nichrome Wire Length: 100cm and 50cm Thickness: 0.45mm
Resistance from graph
100cm and 75cm
Gradient = y/x
= 26.10/0.10
= 261
Resistance = 1/261 = 0.003831 x 1000
= 3.83
100cm and 50cm
Gradient = y/x
= 29.05/0.10
= 290.5
Resistance = 1/290.5 = 0.003442 x 1000
= 3.44
Analyzing Evidence
Here in this part of my experiment I will prove that my hypothesis and my obtained results obey the ohm’s law. This is where the results from my graphs and the results I have already obtained earlier will be compared; talking about its proportionality.
Variation in length:
When the length of the wire boosts, the amount of atoms present in it also boosts. The variation of these atoms block the passage of electrons passing through the wire. A slower flow of electrons will therefore lead to less current passing through the wire hence the longer the wire, the longer the electrons have to travel, so they come across more collision. From this statements I predict that the resistance increases with the length of the increasing wire.
Hypothesis:
It is expected that the resistance should increase in proportion to the length. The resistance should be considerably higher for the 100cm length than it is for the 50cm length. Theoretically the resistance for the 100cm length should be 2 times that of the 50cm length. The reason for this was explained earlier. Resistance will increase with length. Resistance is proportional to length.
In this table below I will show the results I have obtained from the graph and the table:
From the above table I have concluded that resistance increases with length and as the length doubles, the resistance doubles about with it. The column R/L is roughly constant. This supports my hypothesis that resistance of a wire is directly proportional to its length. The even increase of resistance with length can be explained by the clashes that take place in a wire as current flows through it. When the current flows through a wire, the free electrons collide with the atoms of the wire. The longer the wire the more collisions occur. And this will result in an increase in the resistance. However, the shorter the wire, less the collision, hence less resistance. I will show the relationship between length of a wire and its resistance on a graph, from the values of the above table. And this will confirm my conclusion that length is directly proportional to its resistance.
Results
The resistance is clearly increasing as the length of the wire increases. And when the length of the wire doubles, its resistance also doubles. The results shown in graph is exactly what is anticipated to happen as stated in the hypothesis. From the table above we can see that as the length doubles, the resistance also approximately doubles. In the last column R/L if found to be constant somewhat, therefore making it obey the ohm’s law R α L
The predicted graph drawn between R and L looks like this:
Variation of thickness
This experiment is needed to confirm that the resistance of a wire is inversely proportional to its diameter. If the cross-section of a wire is enlarged this means that the area on which the electrons move will be enlarged. Thus suggesting that there will be no clouds of electrons and atoms. The current can travel easily with nothing increasing the resistance. Likewise if the wire is narrower the obstruction will be crossed by the electrons will be lesser and therefore the current will decrease.
Hypothesis
It is expected that the thinnest wire will have the highest resistance because a thicker wire offers less resistance to current than a thinner one of the same material. This is because current consists of electrons flowing through the metal of the wire. The electrons hop from atom to atom in the metal in reaction to the electric field in the circuit. A conductor with a larger cross-section allows more electrons to intermingle with the fields. Because there is more current with a given voltage, a conductor in this case the Nichrome wire with a larger cross-section has lower resistance.
It is rather apparent in the table above that resistance decreases with the increase in the thickness of a wire. R x A is to some extent constant. And this supports my calculations that the thicker the wire, the lesser its resistance. This concludes that the resistance of a wire is inversely proportional to its thickness: R α 1/A. This is because of the fact that the electrons flowing through the wire bump with other atoms of the wire. If the wire is thicker, then there will be more space for the electrons to move freely. And this results in a lower resistance.
The following graph will point up the relationship between resistance of a wire and its thickness. Here the values from the table of resistance and the area is taken, and this will substantiate my conclusion.
1/A
Series Circuit
In this experiment using series circuit a Nichrome wire of length 170cm is connected in series with the connection of the combined wires of length 100cm and 75cm together. Here I have to prove that the resistance is same for both wires. So if the electrons travel in the same distances, the collision of electrons with the atoms of the wire will be the same and so the resistance of the wire will be the same.
Results:
When the resistors are connected in series, the total resistance will be the sum of the individual resistors. And also when the lengths are similar the resistance of the wire in the series circuit, is the same as that is a single circuit.
Parallel
I take a wire of a 100cm and connect it along with a 75cm length of wire in a parallel circuit. I must prove that the resistance in both the wires are the same. Since the channels provided by both the wires are the same, thus electrons will travel in the same way across both the wires making the resistance the same.
Series Circuit
Series circuit are the simplest type of circuits. They have all their components (lamps, cells, switches, etc.) connected in one loop of wire. As it only consists of one loop it therefore has just one current. has
Disadvantage of Series Circuit
Series circuit have two drawbacks when compared with parallel circuits. One is that if one component in a series circuit fails, then all the components in the circuit fail because the current has been broken. And the second disadvantage is that the more components there are in a series circuit, the greater the circuit’s resistance.
Parallel Circuit
Parallel Circuit have two advantages when compared with Series circuit. The first advantage of Parallel Circuit is that a failure of one component does not lead to the failure of the other components. This is because a Parallel Circuit consists of more than one loop and has to fail in more than one place before the other components fail. And the second advantage is that more components may be added in parallel without the need for more voltage. Lastly , we already know that the more components connected in a parallel, the more the energy is used.
Resistivety
Conclusion
The achievement of each experiment has been good. The results from every experiment have gone as expected in the hypothesis and have followed all of the earlier information that is shown in the introduction. The results have been in finishing the aims and predictions of each experiment and the investigation as a whole.
The following objectives have all be successfully fulfilled:
-
Resistance is proportional to length: The results of this experiment proved that resistance increases in proportion to length. As the length of the wire is increased, the resistances also increases. Also, I get a straight line out of my graphs which indicates that they are in proportion.
-
Resistance is inversely proportional to area: The results of this experiment without a doubt proved that resistance is inversely proportional to area. As the thinner the wire is the higher its resistance will be, concluding that resistance is inversely proportional to area.
-
Resistance in series circuit: The results of this experiment proved that in a series circuit the resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance value of the individual resistors: equivalent resistance of resistors in series is R = R1 + R2
-
Resistance in parallel circuit: The results of this experiment proved that in a parallel circuit the resistors are arranged with their heads connected together , and their tails connected together. The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistors in parallel is the same. The total resistance of a set of resistors in parallel is R = (R1 x R2)/R1 + R2
General Evaluation of Investigation and Improvements
The accuracy of my results shows the success of the investigation. Without precisely exact results, the investigation would be worthless. The results shown in this investigation are true and are believed to be correct. There are many way in which this investigation could have improved. One way to improve the dependability and accuracy of the results is would be to do again the experiment a number of times so that a true average could be obtained. The experiments were repeated to obtain an average but they were only repeated once. Now if I had more time I could have extended my research many times as so to get a more precise average.
Even if the experiment is to be repeated numerous times, the result would still not be able to be understood as precisely accurate. The performance of the equipment was suitable. The equipments worked well enough to give an accurate answer but with limits.
Few improvements and precautions can be done here and there. Try to minimize possibilities of heating effect by using wide range of length, thickness and voltage values. Try always to have an exact length. And always make sure crocodile clips do not touch any other neighbouring wires while conducting experiment. Parallax errors should be avoided. Always make sure that the experiment is done quickly so that wire does not get heated up.
Imperfections in the circuit: Any essential error in the circuit such as a flawed wire could have caused a change in results particularly as it was not possible to use the same equipment for each experiment. If it was likely to use new/tested equipments and to be able to use the same equipment for each experiment then there may be less existing argument.
Accuracy on length: The only obtainable way for measuring was by ruler and hand. It would be not possible to get accurate length using this method. It was measured to top facility but the border of error could easily have been up to 1cm considering the poor means in which the wire was help in position, by crocodile clips. There a more accurate measuring method should be considered as well as a more helpful method of conductor connecting.
Over all the minor flaws the experiment was very consistent and helpful. There can’t be any other ways than this method for the experiment. It was a very good and easy method for calculating the resistance, which involved the formula R = V/I, which had helped us to substitute the values for a correct result. The experiment was simple, quick and effective. The results and the conclusions obtained were all true.
The investigation was an accomplishment. Every experiment has effectively confirmed the research :
- R = V/I
- Resistance is proportional to length
- Resistance is inversely proportional to area
- ρ = RA/L
In general through my detailed study I have confirmed these facts:
- If the length of a wire doubles, resistance of the wire also doubles.
- If the cross sectional area of a wire doubles, the its resistance will be cut in half.
At this point my research about the factors that affect the resistance of a wire has been completed. However, I would consider a further improvement that will involve a simple filament lamp or a diode.
characteristic of a filament lamp
Apparatus and materials
-
Filament lamp 12V, 24W
-
Power supply, 0 to 12 V dc to supply up to 4 A
-
Leads, 4 mm
-
Millimeters, 2 or 1 ammeter and 1 voltmeter of suitable ranges
-
Rheostat, e.g. 8 ohm rated at 5 A
Safety
Some components may become hot enough to burn fingers.
Procedure
a Set up the circuit as shown below.
The potential difference across the lamp will be shown on the voltmeter or millimeter, set to volts and placed across the lamp as shown and the current on the ammeter.
b Use the variable power supply and the variable resistor to vary the potential difference across the lamp, from 1.0 V to 10.0 V in intervals of 1 volt. Record pairs of potential difference and current values in the table.
You can record results for currents in the opposite direction by reversing the connections on the lamp.
c. Plot a graph of current/A (y-axis) against potential difference/V (x-axis).
The resistance of the lamp at a particular potential difference = potential difference/current.
.
Hypothesis
1 The aim of this experiment is to develop confidence in setting up simple circuits and in taking careful measurements.
2 It is often stated that the resistance of a component is the gradient of a V against I graph. This is not necessarily the case.
3 In the case of a filament lamp it is, in fact, the resistance that increases (rather than the number of charge carriers falling) due to increased lattice vibrations.
For a filament lamp, however, the temperature of the filament is most definitely not constant (it must to get hot in order to give out light!)
The resistance of a lamp's filament (the long, thin, coiled wire) increases dramatically as the current increases. This results in the following graph:
Diodes
For diodes, only tiny currents of a few micro amps (millionths of an amp) flow at low voltages. Putting more than about 1.5 volts across them normally makes them "turn on" allowing current to flow.
This gives rise to a rather curious-looking graph of current against voltage
One special thing about diodes is that if you connect them the "wrong way around" in a circuit, they have a very high resistance, so virtually no current flows (less than a micro amp).
This means a better graph of their behaviour includes a large zero section:
Of course, if you put too high a voltage across them, even the "wrong way", they will blow up as too much current flows!
