How the area of a wire affects the resistance in a circuit
Planning
Background Physics:
What is resistance?
Electricity is conducted through a conductor. Resistance is the word used to describe the opposition between forces. The more free electrons there are, the better the conduction and the worse the resistance is. 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 is how the electricity is conducted. Resistance is the result of energy loss in form of heat.
How do we measure it?
V=I/R V=Voltage I =Current R=Resistance
Ohm’s Law
This law states that the current through a metallic conductor (wire) at a constant temperature is proportional to the potential difference (Voltage). Therefore the Voltage and Current is constant. If the resistance increases the temperature increases, so it stays constant. At higher temperatures the particles move more quickly, increasing the collision of the free electrons.
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 or V by a double cell which is measured by digital volt 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 would experiment with temperatures from 20°C-100 (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 add 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: 2 cell Battery
Ammeter+ Voltmeter
Safety Resistor
8 wires (35cm)
2 crocodile clips
- My circuit will look as following:
- 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
- Make three sets of results through an accurate experiment
Prediction
I will expect that if the area of the wire increases the resistance will decrease. This can be proven by background physics of the past.
Observation
Test Results
This graph shows the voltages I measured
This graph shows the Current I measured
This graph shows me the resistance and resistance average I have worked out. It also includes the formulas for the Area and 1/Area
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 wider 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 reassure 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
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.
