# How does the length of a wire affect its resistance?

October 22, 2017 September 1st, 2019 Free Essays Online for College Students

Resistance is the measure of how hard it is to get a current through a component in a circuit at a particular potential difference. Varying the resistance in the circuit can control the current through a circuit.

The greater the resistance the harder it is for the current to flow and the move energy that is converted to heat and light. Resistance is measured in Ohms (?).

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Electricity is conducted through a wire, which also means in a wire, by free electrons. The amount and number of these free electrons depend entirely on the more material, meaning that the more free electrons there are, the better the conductor. Electrons that are free are given energy as a result of moving and colliding with other nearby free electrons. This also happens across a length of wire, which means therefore, that electricity is conducted. Resistance is the results of energy loss and heat. This involves the collisions between the free electrons and also the fixed particles of the metal, free electrons and other impurities from the metal. These electrons continually collide, and therefore these collisions result in converting some of this energy that the free electrons are carrying into heat. Therefore, the wire becomes hot.

In 1826, Georg Ohm discovered that:

“The current flowing through a metal wire is proportional to the potential difference across it (providing the temperature remains constant)”.

“Ohms Law” is a simple formula, which can be used to calculate resistance, potential difference (voltage) or current in an electrical circuit.

Potential Difference (Volts) = Current (Amps) ï¿½ Resistance (Ohms).

So in order to calculate resistance the formula is rearranged as below:

Resistance (Ohms) = Potential Difference (Volts) / Current (Amps).

Factors affecting resistance

There are four main factors affecting resistance:

* As temperature increases, the resistance of a wire increases. This is because as the temperature rises, the particles of the wire move about, therefore the electrons have a higher restriction, resulting in a high resistance.

* The type of material also affects resistance, as different wires will have different resistances. I will be using copper for this investigation is a good conductor.

* As cross-sectional area increases, the resistance decreases. This is because the higher the width of the wire, the more space that the electrons will have to move about, resulting in no collisions as there will be a lot of free space.

* As the length increases of a wire, the resistance increases also.

A variable resistor or rheostat is used to vary the current in a circuit. As the sliding contact moves, it varies the length of wire in the circuit.

Safety

Within this investigation safety measures will have to be addressed:

* I not touch the wire, as it may be hot as the current flows through it, and may burn the skin.

* I will not inhale any toxic fumes as the wire burns, as it may be dangerous.

Fair test

To make this investigation a fair test, and taking all the factors that affect resistance, I will have to keep some factors the same throughout the experiment so that the results will be fair and accurate.

* Firstly, the temperature will have to be kept the same and constant throughout the investigation, as the temperature increases, the resistance of a wire increases. This is because the temperature the particles of the wire move about, therefore the electrons have a higher restriction, resulting in a high resistance.

* Secondly, the width of the wire will have to be kept the same throughout the investigation, as the width of wire may affect the final results, so they have to be kept the same throughout so the experiment is fair. This is because the higher the width of the wire, the more space that the electrons will have to move about, resulting in no collisions as there will be a lot of free space.

* Thirdly, the type of wire must be kept the same throughout the investigation so that the results will not be affected with the change of type of wire.

The only variable within the investigation will be the length of wire used. By changing the variable of the wire, this will enable to see whether resistance is affected, whether it increases or decreases.

Prediction

I predict that when I change the length of wire, the resistance will change. As in the preliminary experiment, different wires have different resistances but also the length of the wire will affect its resistance. I think that when there is more length of wire, the resistance will be high in comparison to when there is less wire, the resistance will be much smaller. This is because the current and electrons will have more wire to pass through so the resistance will be high, whereas when there is less wire, the current can flow through easier, having a lower resistance.

Research and Preliminary experiment

I firstly carried out a preliminary experiment, using three different sets of wires, to see whether they have different resistances, but also to familiarise myself with the experiment.

Types of wire:

* Copper wire

* Nickel Chrome

* Constantine

Equipment used

* Power pack

* Ammeter

* Voltmeter

* Wires

* Crocodile clips

Safety

* Be aware of the hot wire as fingers or hands may be burned

* Heat proof mat

Prediction

I predict that different wires have different resistances.

Method

* Cut up 30 cm of each wire in length.

* Set up the circuit with ammeter in series and voltmeter in parallel.

* Measure the voltage across each wire and current through the circuit.

* Use Ohms Law to calculate the resistance.

* Compare the resistance of wires.

Results

Type of wire

Current (Amps)

Voltage (Volts)

Resistance (Ohms)

Copper

5.0

0.1

0.02

Constantine

2.8

0.5

0.18

Nickel Chrome

0.9

0.1

0.11

Copper has the highest resistance, meaning that it is harder for the current to pass through, whereas Nickel has the lowest resistance as current passes through easily.

The reason I chose to use copper in the real investigation, is because copper is a good conductor, so I will be able to monitor the resistance.

Plan

Apparatus:

* Power pack (Batteries)

* Ammeter (to measure the current)

* Voltmeter (to measure the voltage)

* Wires

* Crocodile clips

* 100 cm copper wire

* Heat mat

* Metre ruler

Method

* Firstly, I set up the apparatus as shown in the diagram above.

* I did not use power packs, whereas 1.5V of batteries were used. This is because it will give a direct current. A power pack was not also used as the high voltage heated up the wire and therefore was very dangerous, so batteries were a safer option.

* I placed the crocodile clips on the ends of the wire so that 100cm could be measured.

* I recorded the current and the voltage for 100cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 90 cm so this length of wire could be measured.

* I recorded the current and the voltage for 90cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 80 cm so this length of wire could be measured.

* I recorded the current and the voltage for 80cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 70 cm so this length of wire could be measured.

* I recorded the current and the voltage for 70cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 60 cm so this length of wire could be measured.

* I recorded the current and the voltage for 60cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 50 cm so this length of wire could be measured.

* I recorded the current and the voltage for 50cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 40 cm so this length of wire could be measured.

* I recorded the current and the voltage for 40cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 30 cm so this length of wire could be measured.

* I recorded the current and the voltage for 30cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 20 cm so this length of wire could be measured.

* I recorded the current and the voltage for 20cm of wire from the voltmeter and ammeter.

* I then moved the crocodile clips to 10 cm so this length of wire could be measured.

* I recorded the current and the voltage for 10cm of wire from the voltmeter and ammeter.

* This was carried out three times for each length of wire so as the result could be much more accurate and an average could be calculated for the resistance.

Obtaining Results

Below are the results of how wire affects the resistance. Three different sets of results were collected, than an average result was calculated for the resistance. The resistance in each table was multiplied by 100 so as the results will be easier to calculate a trend in a line graph.

Test 1

Length

Current

Voltage

Resistance

Resistance x 100

100cm

1.03

0.10

0.097 to 3sf

9.7

90cm

0.93

0.08

0.086 to 3sf

8.6

80cm

0.94

0.07

0.077 to 3sf

7.4

70cm

0.95

0.07

0.073 to 3sf

7.3

60cm

0.96

0.05

0.052 to 3sf

5.2

50cm

0.96

0.04

0.041 to 3sf

4.1

40cm

0.97

0.03

0.030 to 3sf

3.1

30cm

0.98

0.03

0.030 to 3sf

3.1

20cm

0.99

0.02

0.020 to 3sf

2.0

10cm

1.02

0.01

0.009 to 3sf

0.9

Test 2

Length

Current

Voltage

Resistance

Resistance x 100

100cm

0.91

0.10

0.109 to 3sf

10.9

90cm

0.93

0.09

0.096 to 3sf

9.6

80cm

0.94

0.09

0.095 to 3sf

9.5

70cm

0.95

0.07

0.073 to 3sf

7.3

60cm

0.97

0.06

0.061 to 3sf

6.1

50cm

0.98

0.06

0.061 to 3sf

6.1

40cm

0.98

0.05

0.051 to 3sf

5.1

30cm

0.99

0.04

0.040 to 3sf

4.0

20cm

?1.01

0.03

0.031 to 3sf

3.1

10cm

?1.02

0.02

0.021 to 3sf

2.1

Test 3

Length

Current

Voltage

Resistance

Resistance x 100

100cm

0.88

0.11

??0.123 to 3sf

12.3

90cm

0.91

0.10

0.109 to 3sf

10.9

80cm

0.92

0.10

0.108 to 3sf

10.8

70cm

0.92

0.09

0.097 to 3sf

9.7

60cm

0.95

0.08

0.084 to 3sf

8.4

50cm

0.96

0.06

0.062 to 3sf

6.2

40cm

0.97

0.05

0.051 to 3sf

5.1

30cm

0.99

0.03

0.030 to 3sf

3.0

20cm

0.99

0.02

0.020 to 3sf

2.0

10cm

1.02

0.01

0.009 to 3sf

0.9

Average Resistance

Length

Resistance

Test 1

Test 2

Test 3

Average x 100

100cm

9.7

10.9

12.3

10.97

90cm

8.6

9.6

10.9

9.70

80cm

7.4

9.5

10.8

9.23

70cm

7.3

7.3

9.7

8.10

60cm

5.2

6.1

8.4

6.57

50cm

4.1

6.1

6.2

5.47

40cm

3.1

5.1

5.1

4.43

30cm

3.1

4

3

3.37

20cm

2

3.1

2

2.37

10cm

0.9

2.1

0.9

1.30

From looking at the results, there were a few anomalies. For example, in table 1 for the first current in 100cm, it was 1.03, which was not correct, as the resistance should have increased as the length of wire decreased. From these results I will now create a line graph from the average resistance.

Conclusion

Graph-Analysis

From analysing my graph, I can clearly see as the dependent variable increases the independent variable also increases. This shows a strong positive correlation, as the trend line is positive. As the length of wire increases, the resistance also increases. This shows that the more wire there is, 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). Whereas when there is less wire, there are fewer electrons to collide with each other, or particles of the copper or any impurities in the copper. Therefore the resistance is low when there is less wire.

The line graph shows the line of best fit of a strong trend of a straight line so the length of the wire is shown to be directly proportional to the resistance – double the length and the resistance doubles.

From my prediction, my graph and tables support my prediction. As I predicted that as the length of wire increases, the resistance will also increase. This is because the current will have more wire to pass through so the resistance will be high, whereas when there is less wire, the current can flow through easier, having a lower resistance.

My line graph shows my prediction was correct as the independent variable increases, which is the length of wire; the dependent variable also increases as the resistance increases.

There maybe a few anomalies, but most points go through the line of best fit, with the other points close to it.

Evaluation

From evaluating my evidence, I have come to a conclusion that the length of wire does affect the resistance. This is shown by my tables as the length of wire increases, the resistance also increases.

My graph also supports this, as it is a strong positive correlation as one variable increases, the other variable also increases.

I tried to make my results as accurate as possible by firstly, making sure that it was a fair test as stated earlier in the coursework. Everything was adhered to so as the results could be accurate and concise. The temperature was kept the same, the width of the wire was kept the same and also the type of wire was kept the same.

However, I feel I could have made by results more accurate and reliable to support my prediction and aim. Because I may have a made a few mistakes such as the way the crocodile clips were moved, could have hindered my results, which were the movement of the clips. The voltmeter and ammeter sometimes did not work properly so I had to change them and get a new one, which could have affected my results.

However, as I carried out this experiment on different days, the room temperature may have been different, which may have also affected my results and also hindered my experiment, as there was an anomaly in test 1.

I had difficulties in taking some results as power packs made the wire dangerous, so as then the results could not be accurate enough as the temperature of the wire may affect the resistance.

To improve this investigation, I could have used a variable resistor or rheostat, which is used to vary the current in a circuit. As the sliding contact moves, it varies the length of wire in the circuit.

To make my results more accurate and to also improve this investigation, I could have used a more accurate digital ammeter and voltmeter, so as the results will be exact and will help me to get a more accurate result. I could have also used a well calibrated ruler, so as I could have measured the exact length I wanted, as I may have made errors with this.

To make and investigate the resistance further, I should have used different wires and tested them fully. Whereas in the preliminary I took only one reading of three different wires, as do that I could familiarise myself with the investigation.

I could have also changed such aspects as mentioned in the fair test section, such as changing the temperature to find out also if temperature in any way affects the resistance. I could have also changed and varied the width of the wire, as I have already found out that length of wire does affect resistance and whether the width also affects it. I could have also tested out different wire such as nickel chrome, Constantine as in the preliminary results to find out different resistances of different wires.

I could have also, to make the investigation more accurate by measuring the temperature of the wire to find out whether different lengths of wires have different temperatures so as this may affect the resistance

Overall, I feel the investigation was a success, and I believe I have achieved my aim of finding out how the length of wire affects the resistance. This is, as the length of wires increases, so does the resistance also increases, due to more electrons colliding with each other.

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