Investigate how the resistance of a wire is affected by the length of the wire.

 

Part P planning

Variables

 

Input variables:                                                              

• Length of wire.
• Material of wire.
• Width of wire.
• Starting temperature of wire

I am going to change the length of the wire because this is the easiest variable to change and to maintain. 

Preliminary work 

In order to decide upon the voltage and lengths of wire to use in the final experiment, the following rough trials were carried out:

12 Volts wire often overheated at shorter lengths

10 Volts off the ammeter scale still overheats at shorter lengths

 8 Volts of the scale of the ammeter overheated at 10-20 cm’s

 6 Volts overheated at 10cm still off the scale

 4 Volts occasionally off the scale overheating mildly

 2 Volts had mild overheating but was on the scale.

After performing these rough trials, it was decided that 2V would be used in the proper experiment, as it provided results from 0cm up to 100cm and the higher voltage provided no additional ease of measurement.

            Furthermore, it was also decided to allow the wire to cool between experiments as considerable heat was noticed at lower lengths and, as mentioned above, an increase in temperature results in an increase in resistance. By allowing the wire to cool between experiments a fair test could be assured.

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). Furthermore, doubling the length of the wire will result in double the resistance. This is because by doubling the length of the wire one is also doubling the collisions that will occur, thus doubling the amount of energy lost in these collisions.

 

MethodThe equipment needed for my investigation consists of:

• Variable DC power pack,

• Ordinary wires,

• 2 crocodile clips,

• 1 meter rule,

• 1 meter length of wire.

 

The following circuit was constructed to perform my investigation:

 

 

 

 

 

 

 

 

 

 

 

 

 Procedure

One metre length of 0.21mm diameter (steel) wire is fixed to a metre rule. Then ;

1. The first crocodile clip is clipped to the wire at the 0cm position on the metre rule.
2. The second crocodile clip is clipped to the relevant position depending on the required length of wire.
3. The power supply is turned on. The voltage and current are then read off the ammeter and voltmeter, and recorded.
4. The power supply is then turned off and the second crocodile clip is moved to the next position along the meter rule.

 The rectangle with ‘R’ in represents the ruler with the wire stretched across it. I will attach one half of the circuit to one end of the wire using a crocodile clip and have a crocodile clip on the other end and able to slide up and down connected to the other half of the circuit making sure the connections remain constant. I will take readings from the ammeter and voltmeter at 10 cm intervals and then work out the resistance by using the formula above.

The above steps are completed for each length and then the entire investigation is repeated for accuracy.

 

 

Safety

 

In order to perform a safe experiment, a low voltage of 2V was chosen so that overheating was not a danger. Furthermore, lengths lower than 10cm were not tried, which also helped to avoid overheating except for the 0 reading which used direct contact of the crocodile clips.

 

 

 Part O obtaining evidence

        Below are two tables detailing my experiment’s results. The first table is the first run, and the second is the repeats table. The final table is the average resistance for each length I tested at.

Repeats

I calculated the average resistance of both sets of results to give me a better understanding of the experiment.

Analysis.

Luckily through my experiment I found no bad and particularly anomalous points and was pleased with my procedure. My results show a direct proportional link so my results are directly proportionate the longer the length of the wire the higher the resistance. This proves my prediction correct.

Evaluation

Having performed the investigation, the following conclusions were drawn:

 

• As predicted, an increase in length resulted in an increased resistance. This can be clearly said for both experiments tested.
• Both wires show a strong trend of a straight line, i.e. the length of the wire is shown to be directly proportional to the resistance – double the length and the resistance doubles.

My experiment I thought had a good procedure however some things could have gone wrong below:

• In my experiment the length of wire for that particular measurement may not be not correct. it is possible that the length was shorter, causing a lower resistance, and it is possible that it was longer, causing a higher resistance. The solution to this is to measure the lengths more carefully and ensure that the wire is pulled tight against the metre rule.
• For a particular result, one or more of the connections could have been faulty, causing extra resistance at the connections. A solution to this would be to, before each experiment, connect the connections together without the wire in place and measure the resistance then. If it is higher than it should be then the connections could be cleaned.
• Whilst extremely unlikely, it is conceivable that the power supply was providing a different voltage for some of the results. This is unlikely to be a problem in this investigation but it might have been an issue had we used batteries instead.

 

NB:      If one were to assume that Ohm’s Law applies, then another possible explanation could be that at some points (more likely in the lower lengths), the wire was not allowed to cool completely so that the temperature was higher for that measurement. Whilst unlikely (due to the two sets of results), this would cause a higher resistance as explained previously.

For further work one could change this by maintaining the temperature of the wire at a constant temperature throughout each experiment I could do this by submerging the wire in a cold substance for example refrigerated fire resistant gel. Also one could eliminate the areas of Human error by using a computer to measure and record the results and also maintain quality control in the form of a fairer test. I could also eliminate the stretching go the wire by using a new piece each time I collect my results.