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# Resistance of a wire

Free essay example:

As Level Physics Coursework

Investigating the resistance of a wire over set distances

Ashley Thornton

PLAN

For this investigation I looked at all the factors that could affect the results of my experiment. These are the Material of the wire. Different materials conduct in different conductivities. The better conductor the wire material is the more electric current will flow therefore the resistance will decrease. Wire Length is also another determining factor of wire conductivity, as a general rule the longer the wire is the further the current of electrons will have to travel meaning that the current will drop due to the larger amount of wire creating more resistance. Thickness of the wire, the thicker the wire I think will add more resistance because there are more metal ions in the wire to have collisions with electrons causing more resistance in the wire. Wire temperature after the experiment has been tested/is undergoing testing. The temperature has the same detrimental effect that a thicker wire does causing more collisions and causing greater resistance to the flow of current. I will be testing overall for the resistivity of the wire over different distances of wire.

AIM

My aim is to investigate the resistance of a wire over set distances incrementing every 50mm. There is little equipment needed and uses little equipment that can cause calculation errors meaning incorrect results. Also instead of testing for different thicknesses this allows me to use 1 wire and simply change the distance over which it is tested. It will also give clear and concise readings that can be trusted and used for comparing/observing trends. I chose not to measure the width of the wire and presume that the wire is of the stated thickness of 28 swg Nichrome wire. For this experiment I will assume that the wire is perfectly round at 0.38mm diameter.

FORMULA’S

Charge is measured in coulombs and charge is the amount of current that flows every second. Electric current is measured in AMP’s (A), Charge in COULOMBS (C)

1 Volt of P.D = 1 Joule per coulomb

i = Q / t

Current can only flow in fully complete circles, there are two different types of circuits called parallel and series. The experiment I set up is a series circuit so that the current is either Fully ON or Fully OFF. All electrical current has energy stored as Potential energy, the voltage transferred in a circuit is measured as energy delivered by each coulomb of electricity. This is Potential difference (P.D), potential difference is the measure of voltage difference between two points within a complete circuit.

Current is recorded by using an Ammeter to find out the Amperes in a circuit, Voltmeters are used to measure P.D. I will need to use both of these to measure the Current and Voltage when carrying out my experiment. Ammeters are connected in series with the wire and the Voltmeter in parallel. Resistance of a wire relates to the amount of current able to flow. The larger the resistivity of my wire the less current will pass through. To calculate resistance the following formula is used:

R = V / I

When resistance is measured the unit is given in Ohm’s. 1 ohm (Ω) means 1 Volt is needed across my wire to sustain a 1Amp current, they are all related.

PREDICTION

Through my own knowledge gained I know that as the lengths of the wire increases so will resistivity. The electrons travelling through the wire have a larger distance to cover thus less current will pass through the wire. I predict that as the wire distance increases so will the resistivity. If the distance tripled, I predict that so will the resistivities assuming that the wire is the same diameter all the way along and perfectly round. The resistance is directly proportional to the distance.

Resistance (ohms)

Length (m)

PRELIMINARY TESTING

Before starting the testing on my final experiment I created a small preliminary test to quickly test for trends/accuracies or potential problems that could occur. It would be easier to solve them before starting the main experiment. I tested different thicknesses of wires from 28/30/32 swg Nichrome wire thickness. I also tested the supply current wasn’t too much/too little. This was a test to see if there were also any learning curves to overcome, this would help make the test fair before there could have been discrepancies in the final experiment. When choosing the wire I used a Micrometer to ensure that I had the correct thickness of wire and that it was reasonably accurate thickness of wire. The micrometer measures to the .00 mm to ensure precise accuracy at very small thicknesses. During the preliminary tests we started with supply voltage on 5volts, this caused the wire of 28swg to get very hot and curl up at very high temperatures eventually snapping the wire. Instead of using a thicker wire we chose to drop the voltage down in increments of 0.25 Volts and decided the best voltage to use was 3volts. This supplied sufficient and reliable results and didn’t damage any of the equipment. During the test I also found that results varied due to leaving the wires to cool sometimes and testing 3 different distances back to back quickly. So in the final experiment I will leave the wire to cool for 30seconds between each change in distance. The Independent variable (I.V) will be altered using the crocodile clips to change the distance selected of the wire. The wires will have been premeasured out to the distances 0-500mm with each increment of 50mm.

Now that I have assessed how the experiment will go I am quite confident the experiment will now produce more accurate results, I will ensure this even further by repeating each test 3 times with 30seconds cool down between each test. This will be much more time consuming but will ensure that I get accurate results. I will take the average of the 3 results by adding them up and dividing by 3. In the final experiment I found that there may be an equipment error in the power pack causing +- 0.005V fluctuations in the set voltage although this shouldn’t affect my experiment as the power pack has a dial function to set the voltage. This is quite an inaccurate way to do, so we must check the readings using a Voltmeter.

APPARATUS AND SETUP

• Power pack – 3volts
• Crocodile Clips + wires
• 28 swg Nichrome wire
• Wood plank to ensure wire doesn’t burn the lab desk
• Meter ruler, 30cm ruler
• Micrometer
• Ammeter
• Voltmeter

METHOD

On the wooden plank, place the meter ruler and measure as accurate as possible from 0-50cm in increments of 5cm. Then take the 30cm ruler with mm measurements and make these marks on the planks of wood 100% accurate distances. Ensure that the wire is tight and will not sag pre-experiment – giving extra accuracy compared to it not being a tight wire. At each 5cm Point I will take a thickness reading of the wire using the micrometer to assess how accurate the thickness of the wire is – if it has different thicknesses in different parts of the wire. When starting the experiment always remember to leave 30seconds for the wire to cool between each distance change or rerun.

Start with both crocodile clips touching each other at one end of the wire. This will give the smallest amount of resistance shown in the circuit. Then add 50mm to each measurement working up to 500mm. After each distance has had the current measured at 3V supply voltage 3 times move up to the next distance, repeat until 10 results have been gathered. (10 results average).

Safety Precautions –

Due to the nature of my experiment there are no obvious risks to health apart from burning yourself on the wire if you touch it whilst hot. I have thoroughly assessed all aspects of my experiment and deem only a few items to be of very minimal risk.

These risks are covered mainly by common sense but listed here as a reminder:

• Never operate equipment, which you are not familiar with or competent to use.
• Always switch off equipment after you have finished using it or between each measurement to allow the wire to cool.
• Never use faulty equipment, report it immediately to a member of staff.
• Keep gangways clear of obstructions. If you need to keep bags or other articles with you, store them so as not to cause a trip or other hazards.
• Keep electrical devices away from sinks and keep all liquids clear.
• No types of safety goggles or gloves are required for this experiment as it doesn’t involve anything moving but only hazardous to touch (burning potential) But avoiding touching the wire will prevent this, although the burn from the wire wouldn’t be very severe if it did happen.

RESULTS

 Current in Amps (A) Length (mm) Voltage(V) Repeat #1 Repeat #2 Repeat #3 Average of Current (A) Resistance (ohms) 00 3.0 4.15 4.16 4.30 4.20 0.71 50 3.0 2.33 2.44 2.35 2.73 1.09 100 3.0 1.79 1.80 1.93 1.84 1.63 150 3.0 1.39 1.45 1.45 1.43 2.09 200 3.0 1.30 1.25 1.19 1.24 2.41 250 3.0 1.17 1.14 1.12 1.14 2.63 300 3.0 0.99 0.84 0.97 0.93 3.22 350 3.0 0.80 0.88 0.81 0.83 3.46 400 3.0 0.74 0.66 0.68 0.69 4.34 450 3.0 0.48 0.54 0.48 0.50 6

R = V / I

Rearranges to V / I = R

R being the resistance, what we are trying to find out.

E.g. 3V / 4.20amps = Resistance

Resistance = constant (resistivity) ×length

Area of cross-section

You can calculate the resistance if you know the resistivity, I will calculate the resistance of the wire at 25cm point (250mm).

Resistivity =   resistance × area of cross-section        “(Cross-sectional area of wire =πr2)”

Length                                  = 14.06x10-9m2

Resistivity =   gradient × area of cross-section

Gradient is calculated by taking Resistance

Length

So:  (6 – 0.71) / (0.5 – 0.05)

Gradient = 11.75 Ω/m   x 14.06x10-9m2   =

Graph of averaged results from the graph included I can conclude that increasing the length of a wire increases its resistance. This is clearly shown from the positive correlation line in the graph with a fixed gradient. From my results on the averaged results graph you can clearly see that there 2 anomalies.

EVALUATION

After finishing my experiment and looking over my method and how I worked out certain things, I feel that the graphs should have shown the results to be proportional to the length of the wire. But this wasn’t fitting the trend of my results. After drawing up the graphs and studying the results table, all of the results for average of current are gradually increasing dis-proportionately until 50mm and 0mm where they seemed to have a huge difference in resistivity compared to other distances. This is expected but not to the scale that it occurred. The results we got could have been through human error in testing.

Looking back on the final experiment we did, the crocodile clips were not as accurate as they could have been in measuring precisely the distances. Also, I don’t think that we left the wires for 30seconds between each reading due to time restrictions. This I feel has had a negative impact on some of our results has they had to be collected over two separate sessions. We kept the same power pack but the wires were mixed and most likely causing different wires to be used. BUT we did retest the wire to ensure we had the correct thickness, just the wire could have been worn down. We did a further 3 tests on the wire using the micrometer to get the thickness of 28 swg again. At 10cm, 25cm and 45cm, using more accurate methods than a rather ‘chunky’ crocodile clips will help remove the measurement error. A different method to sorting the cool down period would be to have more time and possibly reduced the number of distance increments tested over. To get the most accurate readings from our ammeter and voltmeter we used digital models to get results to the 2nd decimal point. Temperature surroundings have to be taken into consideration as they are almost impossible to maintain perfectly. Sunlight frequently shone through the windows and this could have easily caused slight but important differences in the wire resistivity. Resistance in the wire can also be increased by very small kinks or lumps in the wire, again the affect is minimal but all the small differences add up.

IMPROVEMENTS TO BE MADE

I am quite pleased that we did the preliminary test and ironed out a few problems, there are some still that need addressing.

1. Instead of crocodile clips use thinner metal strips or pointers to increase accuracy of distance taking.
2. To ensure environment conditions stayed the same I would use an air conditioned room.
3. I could possibly repeat the readings 5 times instead of 3, but 3 is acceptable. The extra 2 repetitions would be to add to the accuracy although it is not deemed absolutely necessary.
4. Longer lengths of wire than 50cm could be used to see for further correlation of results on distances 50cm+
5. Leave a bigger gap than 30seconds between each reading say 1minute, this is impractical due to time restrictions but is a sacrifice for more accuracy.
6. To ensure environment conditions stayed the same I would use an air conditioned room.
7. Get a more reliable power supply that isn’t old and isn’t analogue. It was hard setting the voltage to the correct setting and needed to be constantly tested with a Voltmeter to ensure accuracy which made the experiment take much longer.

EXTRA INVESTIGATION

There are many different ways to further the experiment, but the most simple and interesting to me would be testing different thicknesses of Nichrome wires. I could use both 30 and 32 swg thicknesses of wires available to me. This would be with the same method, just the difference in wire thickness. It would have to be the same method and setup to allow a fair comparison to be created. As I mentioned before about thickness of wire making lesser resistance due to the amount of electrons colliding with metal ions, this would have an effect on the wires resistance...but to what extent is what I would find out. The thicker the wire the more electrons are available to carry the charge along and the more space available reducing the amount of collisions. I would think that the cross-sectional area of the wire wouldn’t be as directly proportional to the resistivity as the 28 swg wire. The resistance should be inversely proportional to some extent where increasing wire length was x2 resistance the increase of wire thickness would mean DIVIDE by 2 making less resistance.

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