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investigating the relationship between the diameter and the current in a wire at its melting point

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Introduction

Craig Painter

Investigation Report

Aim

Theory

        Resistance is a property of a particular component in an electrical circuit. Resistance is dependant on the dimensions of the sample of material. Resistively is not a property of a particular sample but a property of a material. It is the resistance of unit cross-sectional area per unit length.

        (Introduction to Advanced Physics, David Brodie, pg 412)

Resistivity, ρ, of a material = resistance of unit cross-sectional area per unit length.

Resistance is measures in Ω

Resistivity is measured in Ωm.

image07.png

image08.pngResistivity

image14.pngResistance

image15.pngCross-sectional area of wire

image16.png Length of wire

This can be rearranged to give:

image17.png

Cross-sectional area of a wire is = image18.png

        (http://bdaugherty.tripod.com/KeySkills/formulas.html)

Putting the 2 equations together gives:

image19.png

The above formula is equal to:

image20.png

This formula is in the form y=mx+c.

Aim

The aim of this work is to investigate the relationship between the resistance in a wire in relation to its cross-sectional area.

Variables

Variable

Independent/ Controlled/ Dependant

Voltage Supply

Controlled

Current through the Wire

Dependant

Resistor Value (if any)

Controlled

Length of Wire

Controlled

Diameter of Wire

Independent

Voltage across the Wire

Dependant

Prediction

The theory suggests that

image20.png

So the gradient of the graph should be a straight line of. This should go through the origin. The Resistance should be directly proportional to image09.png

All of the variables will be measured or known.

Method

Preliminary experiment

Determine a length for the Wire  

The longer the length of wire the larger the resistance.

...read more.

Middle

0.66

The above table shows how an increase in current through a wire increases the resistance of the wire. This is due to the heating effect the current has on the wire. The table above shows that currents greater than 0.6Amps have a significant heating effect such that the resistance of the wire is changed.

Determining a current to use

From the experiment on the effect of heat I have decided to use a current of 0.6 amps. This is because it is the largest current I can use without it heating up the wire and affecting the resistance. I decided to use the largest current before the heating effect changed the resistance as it will give a larger change in the resistance of the test wires which will make it easier to record and will give smaller uncertainties.  

Determining a resistor value to use (if any) to protect the circuit.

I decided to use a variable resistor so that it can easily be changed to give the desired output current.

Determining an Ammeter and Voltmeter to use.

I have decided to use 2 digital multimeters’ to measure the Voltage across the test wire and the current through the wire. I have chosen to use these as the uncertainties are lower than any analogue Voltmeters and Ammeters available for me to use.

Determining a power supply to use

I have decided to use a battery pack power supply as the voltages can be easily varied.

SWG 

dia. (inches) 

dia. (cm) 

14 

.080 

.203 

16 

.064 

.163 

18 

.048 

.122 

20 

.036 

.0914 

22 

.028 

.0711 

24 

.022 

.0559 

25 

.020 

.0508 

29 

.0136 

.0345 

35 

.0084 

.0213 

A table showing conversions from SWG to cm.


Instructions

  1. Set up the circuit shown below. Using 2 multimeters to measure the current through the test wire and the voltage across the test wire. Leave a gap in the circuit for the 1m test wire.
  2. Measure 1m of tin plated copper for every different diameter to be used in the experiment.
  3. Put the 1m test wire into the circuit using 2 crocodile clips.
  4. Put a voltage across the test wire and a current through it. Measure both of these and record the results.
  5. Put the next diameter of test wire into the circuit and repeat the test. Repeat this for every diameter of wire to be used.

Below is the circuit I will use.

image10.pngimage06.pngimage04.pngimage05.pngimage02.pngimage03.pngimage00.pngimage01.png

Equipment List

        1 metre rule

        2 digital multimeters

        Variable resistor

        4mm leads

        2 crocodile clips

        Battery Pack

        Selection of test wires

Results (Test 1)

Wire thickness/SWG

Voltage/Volts

Current/Amps

Resistance/Ω

14

0.0066

0.60

0.011

16

0.0088

0.60

0.015

18

0.0126

0.60

0.021

20

0.0206

0.60

0.034

22

0.0300

0.60

0.050

24

0.0485

0.60

0.081

25

0.0590

0.60

0.098

29

0.1241

0.60

0.21

35

0.3800

0.60

0.63

...read more.

Conclusion

My experiment has several anomalous results. These are the first, second, third, seventh and eighth results taken. These results are a larger percentage away from the line than my maximum uncertainties suggest they should be.  

It is possible that because the final result is so far away from the others on the graph that it has caused the line of best fit to be skewed and it may be that with more results within the specific range the line of best fit may be more accurate and therefore cause the anomalous results to be within the percentage uncertainty.  

Improvements

  • To improve my experiment I could have used more precise voltmeters and ammeters, ammeters and voltmeters with more precision would have decreased the uncertainties for each measurement and therefore given me more accurate results.
  • I could have also used a 2metre rule to measure the pieces of wire as this would not involve putting 2 separate rules together and could have decreased the percentage uncertainties in the measurements. Alternatively I could have used a long tape measure to take measurements larger than 2 metres.
  • When measuring the thicker wires they were very difficult to get completely straight. To reduce the uncertainties caused by this I could have taped the wire to the rule at different points to help keep it straight.
  • I could have used a larger selection of different diameter wires. This would have produced a graph with more results plotted on it, therefore the line of best fit would have been more accurate.

...read more.

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