# Investigating the Resistance of a Wire

# Investigating the Resistance of a Wire

**Length:** 2214 words (6.3 double-spaced pages)

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More ↓Planning

--------

Aim

The aim of my investigation is to investigate how length affects the

resistance of a wire. Resistance is the force, which opposes the flow

of an electric current around a circuit so that energy is required to

push the charged particles around the circuit. Resistance is measured

in ohms. Resistance occurs when the electrons travelling along the

wire collide with the atoms of the wire. These collisions slow down

the flow of electrons causing resistance. Resistance is a measure of

how hard it is to move the electrons through the wire.

Plan of the method to be used:- The resistivity of a wire can be

determined using the equation P= RA/L Where: R:- Is the resistance of

the wire in ohms and can be determined using the equation R=V/I where

V is voltage in volts and I is current in amperes. L:- is the length

of the wire used in metres. A: - Is the cross-sectional area of the

wire in metres square and can be determined using the equation A=

Ï€(d/2 x10 Â³)Â² where d is the diameter of the wire in mm. I will plot a

graph of length on the x-axis against resistance on the y-axis. From

the relation R = PL /A which corresponds to the straight line equation

y=mx+c the graph should be a straight line passing through the origin

where m is the gradient of the straight line graph that corresponds to

P/A. Since the cross-sectional area of the wire can be found by

measuring its diameter. Therefore the resistivity of the wire can be

calculated.

Apparatus list:-

t Battery 1.5V

t Switch

t Metre Rule

t Voltmeter

t Ammeter

t Wire 100cm (under test)

t Crocodile clips

t Connecting wires

t Micrometer

t Sellotape

Apparatus

Range

Sensitivity

Metre Rule

0-100 cm

0.1 cm

Micrometer

0-25 mm

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0.01 mm

Ammeter (Digital)

0-1 Amp

0.01 A

Voltmeter (Digital)

0-2 Volts

0.01 V

Variables

Factors which must stay constant to keep the experiment a fair test

t The battery must remain constant,

t The wire must be the same thickness along the whole length of wire,

t The temperature must be constant or the resistance will increase as

the temperature increases,

t The equipment should be kept the same so any errors are constant and

are systematic.

The Variable factor

t The factor that I am going to vary is the length of the wire from

30-100cm.

Detailed Plan

I will set up the circuit as shown in the diagram that I have drawn. I

shall start the experiment by taping the wire to a meter ruler so that

I can measure 100 cm of wire accurately. This will make it easier and

more precise as I will not have to keep on holding the wire then

putting the crocodile clips on. I have chosen to use a meter ruler

because the lengths that I will be measuring are to big for a smaller

ruler and the meter ruler can be accurate to +0.1cm. I will make sure

that the metre rule is actually one metre long and not one or two

centimetres shorter. The wire must be carefully tightened at both ends

to try to minimise the kinks or twists in the wire. I will switch on

the circuit so a constant current will flow through the circuit. I

shall then record the corresponding voltage reading that will be

displayed on the digital voltmeter. I will repeat this procedure using

different lengths ranging from 30-100cm and 10cm between each reading

by moving the crocodile clips 10cm closer together. I have chosen a

range of eight as to plot an accurate graph, I will need at eight

points to mark on the graph if I want to make precise and reliable

results, to see if there are any patterns and trends. After recording

the corresponding voltage readings for each length and tabulating them

I have decided to repeat the whole experiment twice again so that I

can take the average voltmeter reading for each length. Using a

micrometer screw-gauge I will measure the diameter of the wire at 3

different positions along the wire and then calculate its average

diameter from the 3 values. I will then plot a graph of the length of

the wire against average resistance and use it to calculate the

resistivity of the wire as mentioned in my plan where the average

resistance can be calculated using the relation R=V/I

Errors in the Experiment

1. If the temperature of the wires or room rises there will be a

greater resistance as the atoms in the wire will be moving making the

electrons need more energy to move along the wire. To minimise this

error I will conduct all the readings on the same day to prevent room

temperature rises and will switch off the circuit to stop the wires

heating up.

2. The placing of the crocodile clips is exactly on the mark to

prevent less or extra length of wire being used which would directly

increase or decrease the resistance. I will solve this problem by

using a ruler with clearly identifiable markings and placing the wire

on the rule above the scale.

3. Faulty connectors and wires would lower the current flowing through

the wire I will eliminate this by performing a preliminary experiment

so I will be able to check if there's a lower current than predicted.

4. Twisted wire that would increase the length of wire, stretching the

wire along the ruler will solve this.

Preliminary Experiment

I am going to conduct a preliminary experiment to find out which

diameter of nickel chromium wire was optimum to tests its resistivity.

The choice of diameters I have are; 0.30, 0.45 and 0.55mm. I performed

the experiment using the same apparatus listed above and in the same

set-up.

Diameter of nickel chromium mm

Current Amps

Voltage Volts

Resistance Ohms

0.30

0.18

1.69

9.4

0.45

0.18

1.26

7

0.55

0.18

1.03

5.7

I am going to use the 0.45 mm wire as the resistance is a integral

number so will be easier to calculate with to find the resistivity of

the wire. I also wanted to do this experiment to familiarise myself

further with the method; if I had any problems I could correct them

there and then. This would mean I would obtain precise and reliable

results in my main experiment when investigating the connection

between the length of the wire and the resistance of the wire.

Safety

I am going to only use a voltage of 1.5 volts so the wire will not

burn.

Be careful when the wire is connected, as it will get hot.

Be careful when cutting the wire.

Make sure the circuit is off when removing the wire from the circuit

to be measured.

Justification of Procedures

Length of the wire: - At the beginning when I did a preliminary

experiment I was using crocodile clips instead jockey keys to connect

the wire to the circuit. Although the crocodile clips made it easier

for me to measure the length of the wire I found it very difficult to

keep the wires in these clips since it kept slipping out so the wire

wouldn't get connected successfully to the circuit. I therefore

decided to use jockey keys because these keys made it easier for the

wire to be measured accurately using a meter ruler. I decided to chose

8 different lengths between 30-100cm because these lengths will give

me accurate results and that 8 readings are sufficient enough for me

to plot a straight line graph and draw a good line of best fit through

the points. Micrometer screw-gauge: - I decided to measure the

diameter of the wire at 3 different positions on the wire. I then

calculated the average diameter from the 3 measurements taken to

enable me to measure the diameter of the wire as accurately as

possible. Switch:- I have decided to use a switch in the circuit to

prevent the wire from overheating by breaking the circuit once a

result has been obtained. If the wires' temperature increases the

resistance will increase also, causing me to gain an anomalous result.

Justification

I am going to conduct the experiment in this way to get a resistance

(R), value across a length of nickel chromium wire. This R value along

with the length (L) will allow me to plot a graph of R= P L

Resistivity (P) Area (A)

A

Y=m x +c making the gradient P allowing me to find P as I know the

values of R, L, and A.

A

Results

Length of wire cm

1.) Voltage Volts

2.) Voltage Volts

3.) Voltage Volts

Average Voltage V

Current Amps

Resistance Ohms

100.0

1.21

1.24

1.24

1.23

0.18

6.83

90.0

1.10

1.11

1.11

1.11

0.18

6.17

80.0

0.98

0.99

0.99

0.99

0.18

5.50

70.0

0.86

0.87

0.87

0.87

0.18

4.83

60.0

0.73

0.74

0.74

0.74

0.18

4.11

50.0

0.61

0.62

0.62

0.62

0.18

3.44

40.0

0.49

0.50

0.49

0.49

0.18

2.72

30.0

0.36

0.37

0.35

0.36

0.18

2.00

Results of testing the diameter of Nickel Chromium

0.45

0.45

0.46

0.46

The average diameter of the nickel chromium found by using a

micrometer is 0.455 or 0.46 mm to two decimal places. I will use 0.46

mm in the equation Area = Ï€ (D x 10 Â³)Â² 2

Conclusion/calculations

Resistivity formula R=PL

A

Formula found from graph R= P L +0

A

Y= m x +c

Gradient = Y = 5.8 = 6.9 Î©/m

X 0.85

Area = Ï€ (0.46 x 10 Â³)Â² Area = 1.66 x 10

2

P = Gradient P= Gradient x Area

A P= 6.9 x 1.66 x 10

P= 1.14 x 10

P= 114 x 10 Î© m

From my graph on the previous page, I can see that the resistance of

the wire is directly proportional to the length of the wire. I know

this because the Line of Best Fit is a straight line through the

origin showing that if the length of the wire is increased then the

resistance of the wire will also increase in proportion to each other.

The line of best fit is a straight and it goes though (0,0) if there

is no length, there is no resistance proving that the resistance of

the wire is directly proportional to the length of the wire.

The length of the wire affects the resistance of the wire because the

number of atoms in the wire increases or decreases as the length of

the wire increases or decreases in proportion.

The resistance of a wire depends on the number of collisions the

electrons have with the atoms of the material, so if there is a larger

number of atoms there will be a larger number of collisions that will

increase the resistance of the wire. If a length of a wire contains a

certain number of atoms when that length is increased, the number of

atoms will also increase.

If the wire is half the length of a certain wire, it would have has

half the number of atoms, this means that the electrons will collide

with the atoms half the amount of times. In addition, if the length of

the wire was trebled or quadrupled, then the resistance would also

treble or quadruple. This is indicated on my graph, with the length

being 100cm and the resistance being 6.83 Ohms. This in theory would

mean that at 50cm there would be a resistance of 3.45 Ohms. From the

graph it is easy to tell that the theory is correct and therefore my

results reliable. From my results table and graph, I can see that my

results that I collected are very reliable and accurate as all the

points lie exactly on the straight line.

Evaluation

My results are very reliable as they all lye on the best fit line so I

can confirm my prediction and support a conclusion. I know this

because outside resources (Textbooks and Britannica) say that 'the

length increases in direct proportion to the resistance.Â´

Possible errors

t The wire had actually increased in temperature due to a change in

room temperature or the circuit had been left on for long periods of

time. I tried to reduce the temperature increase, if any, by switching

off the circuit as soon as possible once I had obtained a result.

t The wire I used was taken off a reel of nickel chromium wire so was

new with no twists or kinks and could be very taught once taped on the

ruler. During the placing of the wire on the ruler a few bends had

been made in the wire, these would be straightened easily and only

added a negligible increase in length.

t Placing the jockey keys on the exact length of wire being tested was

difficult because the ends of the keys had a very small area. They

often slipped down the wire so the wire I tested was actually a few

millimetres longer/shorter this meant I needed to repeat the test once

I'd noticed this change in length.

t The apparatus I used might have been faulty due to loose connections

but I would have noticed the discrepancy in results when I conducted

my preliminary experiment as I used the same apparatus.

Percentage Errors

All experiments conducted have a certain error on them, as not all

apparatus is 100% accurate. The apparatus I used has a certain

percentage error found by using the equation:

Percentage Error = Sensitivity x 100

Reading

t Metre Rule

Error = 0.10 x 100

30

= 0.33%

t Micrometer

Error = 0.01 x 100

0.46

= 2.17% in millimetres

= 8.69 % as the cross sectional area is squared

t Ammeter

Error = 0.01 x 100

0.18

= 5.56%

t Voltmeter

Error = 0.01 x 100

1.23

= 0.81 %

Total error = 15.39%

The most sensitive measurement was the reading on the micrometer as it

could be + 8.69% due to the squaring of the cross sectional area. This

means that my average diameter could be + 8.69%.

Diameter found

Error

Minimum Value

Maximum Value

0.46 mm

8.69 %

0.42 mm

0.50 mm

Numerical Error = Diameter x 8.69 = 0.04 mm

100

The resistivity of nickel chromium that I found using the equation R =

PL has a total error of 15.39 % so the resistivity could actually be a

different value. A

Resistivity found

Total Error

Minimum Value

Maximum Value

114 x 10 Î©/m

15.39 %

965 x 10 Î©/m

13.15 x 10 Î©/m

The error in numerical value has a + 175 x10 Î©/m. Found by Error =

Resistivity x 15.39

100

I had no systematic errors as my best fit line found on my graph runs

through the origin (0,0). Random errors are:

t I found that the experiment was quite easy to set up, as it was

simple and uncomplicated. The only problem I can see is the

calculations once all the results have been obtained as very small

numbers are used and a simple mistake can lead to a wrong answer being

produced.

t Temperature increase

t Battery running out (current reduced)

t Faulty apparatus

I had no anomalous results as all the points lye exactly on the bast

fit line. This proves I conducted the experiment very well making sure

all the apparatus I used was working and of good quality. I also made

sure all my tests were done fairly by keeping all the variables

constant except the length of wire and I tried to do the experiment to

the best of my ability. I also gained a good set of results by testing

the lengths from 100-30 cm then 30-100 cm so using the average would

solve any difference in voltage results. I found no need to repeat any

lengths as my first and second set of results were very close to each

other. I wanted to repeat the experiment for a third time to make sure

there were no anomalous points that may have been found twice.

If I were to conduct the experiment again I wouldn't change the way I

performed it at all because my results were so accurate. If I were to

perform the experiment again I would choose a different variable such

as:

t Wire diameter :

I think that if the wire diameter is increased the resistance will

decrease. This is because of the increase in the space for the

electrons to travel through. Due to this increased space between the

atoms there should be less collisions. I would also test to see if

diameter if also directly proportional to resistance.

t Material :

I think that the type of material of the wire will affect the amount

of free electrons, which are able to flow through that wire. This is

because the number of electrons depends on the amount of electrons in

the outer energy shell of the atoms, so if there are more or larger

atoms then there must be more electrons available. If the material has

a high number of atoms there will be high numbers of electrons causing

a lower resistance because of the increase in the number of electrons.

Also if the atoms in the material are closely packed then the

electrons will have more frequent collisions and the resistance will

increase.