The current density (electric current per unit area, J=I/A) can be expressed as
The number of free electrons, assuming one per atom, is
From the standard form of Ohm's law and resistance in terms of resistivity:
The next step is to relate the drift velocity to the electron speed, which can be approximated by the Fermi speed:
The drift speed can be expressed in terms of the accelerating electric field E, the electron mass, and the characteristic time between collisions.
The conductivity of the material can be expressed in terms of the Fermi speed and the mean free path of an electron in the metal.
PLAN
Problem:
Altering the number of cells or the voltage supplied from the power pack can change the amount of current flowing through a wire. However, the amount of current will also depend upon the resistance of the wire. The resistance, in turn, depends upon certain characteristics of the wire itself.
Task:
To investigate if and how a wires length affects the resistance.
Variables:
- Current -> outcome variable.
- Length of wire.
- Thickness of wire -> Cross sectional area.
- Potential difference (Pd).
- Material of wire.
- Temperature.
Prediction:
I predict that the length of the wire will be directly proportionate to the resistance. I.e. if the length of the wire is doubled the resistance will also double.
The formula for the relation between the length and resistance of a wire (for more information refer to the research section):
R = V / I
Where:
R = resistance.
V = Potential difference (Pd) across the conductor (wire).
I = current.
Apparatus:
The apparatus that I will use:
- Steel wire with a cross sectional diameter of 0.5mm ands a length of 1 metre.
- Power pack – A/C variable current and voltage.
- Voltmeter. (Connected in parallel.)
- Ammeter. (Connected in parallel.)
- Metre rule – To measure contact distance.
- Wires to create the circuit.
The apparatus was set up as follows:
Method:
- Gather all equipment required.
- Make sure all of the equipment is working correctly.
- Cut one metre of wire and attach it securely to a surface.
- Connect the circuit – as shown in the diagram.
- Ensure the circuit is working correctly.
- Ensure the ammeter and voltmeter is displaying correct results.
- Perform a trial run of the experiment.
- Perform the experiment -
- Turn on the power source.
- Record the readings displayed on the voltmeter and ammeter.
- Measure decrease in current & potential difference.
- Move the contact points on the wire 100mm closer together.
- Record the readings given.
- Repeat steps 8 -10 until the contact points are in contact with each other. (10 moves – length of wire = 1 metre. 10 x 100mm moves.)
- Repeat the experiment to ensure accurate results and reliability in the method.
Length (M)
Amps (I)
Volts (V)
R = V (Ω)
---
I
V
A
Safety:
There are many hazards when working in a laboratory. In the series of tests that were performed there were also many hazards:
- High voltage electricity was use in the experiment. Dew care and attention were always a top priority when performing these experiments.
- High temperatures: some of the wires used in the experiment grew very hot. We had to be careful not to touch them.
- Potential for crowding as there were many people.
Fair Test:
To make sure the experiments performed were fair only a few variables were allowed to be changed.
- The distance between the two contacts was the main variable. This variable we had control over, other variables such as the temperature of the wire, we could not control.
Everything else remained constant.
- I made sure the apparatus was working correctly.
- I performed a trial before the real experiment to ensure that the equipment was set up correctly.
- The final experiment was performed 3 times to ensure accurate and reliable results. (The most accurate set of data was used.)
Reliability:
To ensure that the results are reliable and accurate I will perform the test three times and use the most reliable set of data. I didn’t perform the test more that thrice because it would have taken to long. Also I believe that performing the experiment thrice will provide accurate and reliable results.
Trial: I performed a trial test before performing the series of tests. I did this to ensure that apparatus was performing correctly and to a high level of accuracy. I also did this so I could perform the series of tests more efficiently. Another reason was to help me decide on the observations and measurements to be made in the series of tests that followed.
The Trial was conducted at room temperature (in this case 19°c).
Results of Trial:
Obtaining Evidence
I used a wide range of equipment and materials to obtain the evidence required for this experiment. I managed their surrounding environment to ensure that I obtained accurate results.
Apparatus & Materials:
- Steel wire with a cross sectional diameter of 0.5mm ands a length of 1 metre.
- Power pack – A/C variable current and voltage.
- Voltmeter. (Connected in parallel.)
- Ammeter. (Connected in parallel.)
- Metre rule – To measure contact distance.
- Wires to create the circuit.
Collecting Evidence:
To collect evidence from my experiment I had to decide on the most efficient and accurate way to do so. The procedure of collecting the evidence had to be simple and also safe.
I decided to conduct the obtaining of the evidence in the following way:
- Once the experiment had been set up correctly (see apparatus in the plan section) I made sure that all the equipment was working correctly. I did this by doing a “trail” experiment (see “trial” in “plan” section).
- I conducted the “true” experiment, and recorded measurements given.
- I repeated the “true” experiment again twice and recorded the second set of measurements.
- I used the most accurate and reliable set of data as my final results.
- I displayed the results in a table and a graph.
Results:
(Insert graph here)
Analysing & Considering Evidence
The results from the experiment display and prove many things.
As displayed in the graph, it is clear to see the relationship between a wires length and its resistance is directly proportional.
Conclusion:
The results show that the wires length does indeed affect the wires resistance.
The results prove that the relationship between the length and the resistance is directly proportional (proving my prediction correct.)
There is a formula to display the relationship between the length and the resistance:
R = V / I
Where:
R = resistance.
V = Potential difference (Pd) across the conductor (wire).
I = current.
Here is a graph displaying the direct proportional relationship between a wires length and its resistance.
The results prove that the electrical resistance of a wire is greater for a longer wire, less for a wire of larger cross sectional area, depends upon the material out of which the wire is made.
The resistance of a wire can be expressed as:
The factor in the resistance which takes into account the nature of the material is the resistivity. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.
The results produced from the series of experiment prove Ohm’s law to be correct.
OHM’S LAW
For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor.
The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterised by such a resistance, then the current can be predicted from the relationship:
I conclude that the relationship between a wires length and resistance is directly proportional. Thus proving my prediction correct.
Evaluation
The experiment generally ran very well. It ran smoothly and according to plan, which was designed carefully and accurately.
The experiment was performed three times, “Run 1,” “Run 2” and “Run 3.” The most reliable and accurate set of results with the least anomalies was used in the results table and graph.
After creating the results table I was able to make a graph and plot a line of best fit on it; as there were enough accurate results to plot onto it. All three tests gave very similar results, showing that the test was set up correctly, and shows the results must be accurate. There were few anomalous results on my graph, the results given were accurate.
Also before performing the two tests, a trial test was performed. This was performed to ensure that apparatus was performing correctly and to a high level of accuracy. I also did this so I could perform the series of tests more efficiently. Another reason was to help me decide on the observations and measurements to be made in the series of tests that followed. Another reason of deciding to perform a trial was to see if any changes and modifications needed to be made to the experiments conduction. No major changes needed to be made.
The equipment proved to be working well and the apparatus was set up correctly so the three runs were then performed.
To make the test fairer and more reliable a number of additional things could have been done. For example, repeat the experiment more times to further the accuracy of the results, use a wider range of measurements to ensure trends in results were accurate, more control of the environment would ensure results with higher accuracy, different equipment and apparatus could have been used to ensure trends remain true.
The results show that the wires length does indeed affect the wires resistance.
The results prove that the relationship between the length and the resistance is directly proportional (proving my prediction correct.)
There is a formula to display the relationship between the length and the resistance:
R = V / I
Where:
R = resistance.
V = Potential difference (Pd) across the conductor (wire).
I = current.
Here is a graph displaying the direct proportional relationship between a wires length and its resistance.
The results prove that the electrical resistance of a wire is greater for a longer wire, less for a wire of larger cross sectional area, depends upon the material out of which the wire is made.
The resistance of a wire can be expressed as:
The factor in the resistance which takes into account the nature of the material is the resistivity. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.
The results produced from the series of experiment prove Ohm’s law to be correct.
OHM’S LAW
For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterised by such a resistance, then the current can be predicted from the relationship: