How the area of a wire affects resistance
Planning
Background Physics:
What is resistance?
Electricity is conducted through a conductor. In this case it is the wire. Resistance is the word used to describe the opposition to the flow of current. The more free electrons there are, the better the conduction and the lower the resistance is. For example gold is a better conductor then aluminium, therefore it is a better conductor . The more atoms vibrate, the more resistance there is. The free electrons are given energy, as a result they move and collide with the surrounding electrons. This happen throughout the whole wire. This happens because electricity is passing through the wire This is how the electricity is conducted. Resistance is the result of energy loss in the form of heat. If the cross-sectional area doubles, the resistance halves. Resistance is caused by electrons bumping into ions. If the length of the wire is doubled, the electrons bump into twice as many ions so there will be twice as much resistance. If the cross sectional area doubles, there will be double the amount of ions bumping into electrons into each other. This means that also there will be twice as many electrons getting through twice as many gaps.
Ohm’s Law
V=I/R is the famous equation and law. This law states that the current through a metallic conductor (wire) at a constant temperature is proportional to the potential difference (Voltage). The size of electric current flowing trough a conductor, depends on the voltage across it, and the resistance of a conductor. If the voltage increases the current increases.
Possible Input Variables
Wire area
Wire thickness
Wire length
Applied voltage
Material
Taught connections
Cross-sectional shape
Insulated
Density of wire
Coiled or not
Temperature
Preliminary Experiments
Applied I and V which is measured with a digital voltmeter and ammeter. I will find out the Resistance by the formula using R=V/I.
Wire area. It is difficult to change the area. A possible solution would be to add wires and twist them together.
Coiled or not? It has not got an obvious affect. The Voltage and Current didn’t increase or decrease.
Temperature. My idea was to set up a water bath to keep the wire at a same temperature at every point. I could experiment with temperatures from 20°C-100 °C (room temperature to the boiling point of water)
Wire length. Is very easy to set up. There is a very large range of results.
Chosen Input variable
I chose wire area as my variable because it is has a better variety of results. I will have 8 wires with the same cross sectional area. It would be to expensive using different cross sectional sizes of wire. I will put the wire parallel to each other an twist them at the end to increase the area of the wire.
My chosen output variable is resistance because that is what I am looking for in the wire.
Fair Test
In the experiment I am not going to change anything ( wire length and applied voltage). The only thing I will change is the area of the wire (input variable). I will use the same equipment throughout the test, to make sure it is a fair test. If I would use different equipment it may give me different readings. I am using a safety resistor, so that the current is the same and that the wire will not overheat. It would not be a fair test if the wire would heat because it would give my different sets of results at different temperatures. It could also be a safety hazard if the wire overheats.
Method
- Cut eight wires of the same cross sectional area in 35cm length (only 30cm of wire measured because I have to attach crocodile clips on each side
- The equipment is as following: Battery
Ammeter+ Voltmeter
Safety Resistor
8 wires (35cm)
2 crocodile clips
- My circuit will look as following:
The diameter of the wire is 0.376mm and
30cm of the wire will be measured
- Connect the wire with the crocodile clips
- Let electricity pass through the circuit and note down the readings of the ammeter and voltmeter.
- Add more wires to the circuit and continue as planned
- Repeat the process three time to get a wide and accurate result
Prediction
I will expect that if the area of the wire increases the resistance will decrease. I also predict that if the area of the wire doubles, the resistance will double as well. If the cross-sectional area of the wire doubles, the resistance will halve . Resistance is caused by electrons bumping into ions. If the cross-sectional area of the wire doubles there will be twice as much electrons and ions bumping in to each other. There will also will be twice as much electrons getting through twice as many gaps. If there are twice as many electrons getting through, as there is twice the current, the resistance must have halved.
Observation
Test Results
This table shows the Voltage I measured
This graph shows the Current measured
This table shows me the resistance and resistance average I have worked out.
My Graphs are on a separate sheet of graph paper.
Analysis
My graph shows me that if I increase the area the resistance decreases. I have plotted two graphs to give me a range of results and averages in different areas (1/Area and Area m^2). My Area graph looks like a y =1/X graph
To test this I have plotted an average 1/Area. If it is correct then I should get a straight line. When I plotted the graph I had a straight line.
This tells me that the average is proportional to 1/Area i.e. Rave α 1/Area.
The slope is: y/x= 10.5/16= 0.66 Ω m²
I am ignoring the offset on my 1/Area graph
This experiment shows me that resistance is definitely affected by the area of the wire. Looking at my background physics it has worked out like resistors on a parallel circuit. When attaching another wire to the experiment it acts like adding another parallel resistor in a parallel circuit. So if the area of the wire increases the resistance decreases. Also I have learned if the voltage goes down the resistance goes up. This shown by the two graphs I have plotted.
Evaluation
I found this experiment easy to do. I had no anomalies on my graph. This means that the points I have plotted are all in a acceptable arrangement. There were no experimental caused by a faulty connection. There were no safety hazards and the experiment was safe to do.
