To investigate how the resistances of a metal alloy (constantan) is affected by the length of the wire and by different amounts of voltages.

Ohm’s Law

          “As charged particles try to make their way round a circuit they encounter resistance to their flow eg. they collide with atoms in the conductor. More resistance means more energy is needed to push the same number of electrons through part of the circuit.”

This resistance is measure in ohms,

The equation for this is

 R = V/ I

The equation suggests that if you were to plot a graph you would end up with this result. However because by putting a current through a circuit you inadvertently heat up the wire we don’t usually end up with this result. This happens because when the atoms are heated they gain kinetic energy which leads to more collisions inside the metal, these collisions turn the kinetic energy into heat energy and inturn heat up the wire.

What factors affect the resistance of a material?

a) Length - the further electrons have to travel through material, the more collisions they will have so the higher the value of resistance.

b) Area - a bigger area means that in any 1 second more electrons will be able to travel through a piece of wire. More electrons mean more current which means less resistance.

c) Material - If you swapped all the copper wire in a circuit for wood you’d notice a lot less current and a lot more resistance in the circuit. The ability of a material to conduct is called resistivity.

d) Temperature - but we’ve covered that above.

so

R        l

R        l / A

R       P

These can all be combined to give

R = pl / A

And also

P = (R * A) / l

 

Variables

 

Input:

• Length of wire, and thus the resistance of the wire *
• Material of wire.
• Diameter of wire. *
• Starting temperature of wire.

 

Output:

• Voltage across wire.
• Current in circuit.
• Temperature of wire.
• The resistance of the wire. †

The variables marked with a * will be varied, the other input variables will be kept constant. The output variable marked with a † will be calculated.

 

Predictions

 

• The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal. Therefore, more energy is going to be lost in these collisions (as heat).
• Also increasing the diameter of the alloy will decrease the resistance, because a bigger area means that in any 1 second more electrons will be able to travel through a piece of wire. More electrons means more current which means less resistance
• An increase in heat of the wire will lead to an increase in resistance this is because the fixed electrons have more energy and in turn move around more creating a higher chance of collisions between free electrons and fixed electrons.

 

Method

 

The following circuit was constructed to perform the investigation:

 

1. Set up the aperatus as shown in the diagram.
2. Measure the amount of wire start at 1m then moving own by 10cm each time.
3. Attach crocodile clips to each end of the desired length of wire.
4. turn on the power supply starting with a voltage of 5V.
5. Adjust the variable resistor until the desired voltage is shown in the voltmeter.
6. Measure the current shown in the ammeter every 0.1V.
7. After measuring the current from 0.1V up to 1V move the crocodile clip down 10cm from the previous point.
8. Turn off the power supply for 30 seconds to allow the wire to cool down (when the wire is hot the resistance is higher).
9. After the 30 seconds repeat step 5 until 0cm.
10. Write up results into a results table

Results

Evaluation

Now that I have completed my experiment there are certain things that I was unaware of at the beginning of my experiment that I would alter if I were to repeat the experiment. For instance the wire had some kinks in it that when you uncurled the wire for measuring didn’t straighten out, this meant that the measurements taken during the experiment were not as accurate as they could have been. However because this flaw was constant through the experiment, because we used the same piece of wire with the same amount of kinks in throughout this didn’t effect the results on a great scale. If you were to repeat the experiment again using different pieces of wire for different lengths it could adversely affect the results, leaving you with an untrue picture at the end f the experiment.

        Also as I continued to take down results I realized that even though I was leaving the wire with 30 seconds to cool down in-between different lengths it still remained hot as I continued to write down results. If I were to repeat the experiment I would allocate a greater amount of time to take results and in turn more time to allow the wire to cool between results instead of having to continue the experiment with the warm wire.

Another problem was that arose was the equipment I had to use, it was unreliable and took me some time to find enough working components to complete the circuit. If I were to repeat the experiment I would use more up to date equipment which would lead me to more accurate results.

And finally the last thing I would add to my experiment to improve it would be to collect more results. This would enable me to draw a more accurate graph of my results and then in turn allow me to reach a better conclusion.