Resistance Investigation

By Priyesh Patel 11P

Aim

An electronics factory needs resistors of 5 ohms and 15 ohms for a new electrical device.

My task is to investigate how the resistance of a piece of wire depends on length and to find the length of the wire needed to make the required resistors, using only 4 volts.

Introduction/Planning

A selection of different wires made from constantan and nichrome and the usual laboratory apparatus will be available for me.

Wire A – Constantan wire of approximate diameter 0.3mm

Wire B – Constantan wire of approximate diameter 0.4mm

Wire C – Constantan wire of approximate diameter 0.3mm

A constantan is an alloy whose resistance stays fairly constant when it becomes hot. In fact the resistance changes by less than 0.5% even when the temperature rises by a few hundred degrees. Nichrome, along with other metals, is an alloy whose temperature does change appreciably when it becomes hot.

Before starting my coursework, I have to find the variables in the experiment, safety aspects etc. I found that a number of things affect the resistance of a wire. Below is a list of factors and reasons why they affect the resistance of a wire. From this list of factors I have to make sure that these factors remain constant or excluded from the experiment. We are only investigating length but the other variables may change our outcomes.

In electricity, resistance is the ratio of the potential difference (p.d. or voltage) across a conductor to the electrical current, which flows through it as a result. The unit of measurement is the ohm (O), this being the resistance of a conductor requiring a potential difference of 1 volt across its ends to produce a current of 1 ampere. For a given metal conductor at constant temperature the value is the same whatever the current (Ohm's law), but rises if the temperature rises. Any conductor possessing resistance gives off heat when a current flows through it. Joule’s law describes this effect.

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.

Ohm’s law: The current flowing through a metal is proportional to the potential difference across it, provided that the temperature remains constant.

We are going to use metals, which obey ohm’s law, metals which give us a constant value for resistance (gradient).

Resistance (Ω) = P.d across the wire (V) / Current through the wire (A)

Current flows in an electric circuit in accordance with several definite laws.

The basic law of current flow is Ohm's law, named for its discoverer, the German physicist Georg Ohm. Ohm's law states that the amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive force impressed on the circuit and inversely proportional to the total resistance of the circuit. The law is usually expressed by the formula I = V/R, where I is the current in amperes, V is the electromotive force in volts, and R is the resistance in ohms Ohm's law applies to all electric circuits for both direct current (DC) and alternating current (AC), but additional principles must be invoked for the analysis of complex circuits and for AC circuits also involving inductances and capacitances.
A series circuit as on page 5, is one in which the devices or elements of the circuit are arranged in such a way that the entire current (I) passes through each element without division or branching into parallel circuits.
When two or more resistances are in series in a circuit, the total resistance may be calculated by adding the values of such resistances. If the resistances are in parallel, the total value of the resistance in the circuit is given by the formula:

In a parallel circuit, electrical devices, such as incandescent lamps or the cells of a battery, are arranged to allow all positive (+) poles, electrodes, and terminals to be joined to one conductor, and all negative (-) ones to another conductor, so that each unit is, in effect, on a parallel branch. The value of two equal resistances in parallel is equal to half the value of the component resistances, and in every case the value of resistances in parallel is less than the value of the smallest of the individual resistances involved. In AC circuits, or circuits with varying currents, circuit components other than resistance must be considered.
If a circuit has a number of interconnected branches, two other laws are applied in order to find the current flowing in the various branches. These laws, discovered by the German physicist Gustav Robert Kirchhoff, are known as Kirchhoff's laws of networks. The first of Kirchhoff's laws states that at any junction in a circuit through which a steady current is flowing, the sum of the currents flowing to the point is equal to the sum of the currents flowing away from that point. The second law states that, starting at any point in a network and following any closed path back to the starting point, the net sum of the electromotive forces encountered will be equal to the net sum of the products of the resistances encountered and the currents flowing through them. This second law is simply an extension of Ohm's law.

The application of Ohm's law to circuits in which there is an alternating current is complicated by the fact that capacity and inductance are always present. Inductance makes the peak value of an alternating current lag behind the peak value of voltage; capacitance makes the peak value of voltage lag behind the peak value of the current. Capacitance and inductance inhibit the flow of alternating current and must be taken into account in calculating current flow. The current in AC circuits can be determined graphically by means of vectors or by means of the algebraic equation,

in which L is inductance, C is capacitance, and f is the frequency of the current. The quantity in the denominator of the fraction is called the impedance of the circuit to alternating current and is sometimes represented by the letter Z; then Ohm's law for AC circuits is expressed by the simple equation I = V/Z.

We know that all instruments have an error on its measurement, so the way to work out the percentage error is:

Percentage error = (error / measured value) × 100

Conduction in metals

In metals, atoms contain protons, nucleus and lose electrons which orbit around the nucleus. Below, I have investigated conduction in metals and how they affect resistance.

METAL LATTICE (Electrons move in a random direction.)

METAL LATTICE (Electrons with power pack in a particular direction.)

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This is a preview of the whole essay

We know that all instruments have an error on its measurement, so the way to work out the percentage error is:

Percentage error = (error / measured value) × 100

Conduction in metals

In metals, atoms contain protons, nucleus and lose electrons which orbit around the nucleus. Below, I have investigated conduction in metals and how they affect resistance.

METAL LATTICE (Electrons move in a random direction.)

METAL LATTICE (Electrons with power pack in a particular direction.)

Variables

Length: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this, the length increase should be proportional to the resistance increase.

Thickness: If the wire’s thickness 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 fewer collisions.

The number of free electrons changes from one material to another. The size of the ions changes from one material to another, this affects the current and therefore affects the resistance.

The arrangement and size of the atoms change from one material to another.

So if there is a kink in the wire this will change the thickness of the wire.

Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.

Material: The type of material will affect the amount of free electrons, which are able to flow through the wire. 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 number 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.

Testing resistance with different numbers of resistors, using AC power supply.

In series.

So, as the length of wire increases, so does the resistance.

In parallel.

Whilst doing this test I found that it is not necessary to do the experiment in the parallel set up, as the diagrams show above, the circuits, which have only one resistor are the same in both parallel and in series and they show this via the results. I also found that when the thickness of the wire increases, the resistance decreases. So, the two main factors that affect resistance are, thickness and length. I could carry out a fair test on these two factors, but for the temperature of the wire I would not be able to carry out a fair test because it is extremely difficult to produce and control the range of temperatures needed without the correct equipment.

In this investigation, I have decided to make repeat the experiment 3 times, as this will exclude any anomalous readings.

This is because in the test we did earlier, I found that

I need to check that the both the voltmeter and the ammeter had its scale to start at 0, otherwise I will obtain inaccurate readings.
I have to avoid the parallax error which is if I do not look at the ammeter from straight on I will read off the meter at the wrong point because I have looked at it from an angle. This will also give inaccurate readings.
I have also learnt that all instruments have an error associated to it, and so I need to use the percentage error formula to work out the errors in the instruments.
The voltmeter and ammeter error which is associated to it can be calculated but halving its scale division. I need to know this when reading off the scale. This is because for example if the needle stops at a point in between the scale division then I have to know what to round it up to, which is always the highest instead of just counting it as actually half of the scale division.
I have found that the error for the voltmeter 0.1.
I have found that the error for the ammeter 0.025.
I’ve also found that the error for the meter rule, I’ll be using to measure the wire is 0.5.
All of these errors need to be taken into account in order to acquire precise results.

Safety is an important factor as we are working with electricity, the main safety precautions are:

Handle the power supply carefully.
Only use a voltage of 4 volts, as any higher would make the wire overheat.
Be careful when handling live wires.
Do not work in wet areas, make sure table surface is dry.
Make sure no wires are exposed / damaged, as this is a hazard.
You must not take a measurement at 10cm or below, as the wire will burn out.

The wire I am using in this investigation is constantan and this metal obeys Ohm’s law. If at the end of the experiment this component produces a straight line then we know that it obeys Ohm’s law.

I am going to use a constantan wire because it is a metal, which obeys Ohm’s law. Also in this investigation I will be using a power pack, and I will set the voltage to 4 volts. If I chose the maximum of 12 volts, it would burn out the complete circuit, as well as this there would be a temperature increase. On the other hand if I use a smaller voltage, I would get smaller readings, making my results inaccurate and the percentage error high.

The only thing I am investigating is length and so the variables:

Thickness
Temperature
And material used, have to remain constant, only the length of constantan will vary.

In this investigation I will be using a series circuit, as this is laid out in the same way as the parallel circuit, but only when using one resistor. As you can see on page 4, both experiments in series and in parallel circuit with one resistor, we have the same result. The thickness of the wire in the parallel circuit affects the resistance. I will only be changing the length of the wire and not the thickness, as I only want to only want to test the length and want all other variables to remain constant, in order to finish with a fair test.

Prediction

I predict that if the length increases, then the resistance will also increase in proportion to the length. I think this because the longer the wire the more atoms and so the more likely the electrons are going to collide with the atoms. If the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. And also, because I know that all instruments have an error associated to it, it is likely that the thickness of the constantan wire has a varied thickness. My graph should show that the length is proportional to the resistance, and anomalous readings will obviously be found due to the changes in thickness.

The diagrams below show my prediction and should explain it more clearly:

Because the length of the wire A is only half the length of the wire B, there should be half the number of collisions between the electrons and the atoms.

The wire B is twice the length of the wire A and so there should be twice the number of atoms resulting in twice as many collisions and a predicted doubling of the resistance.

I also know that if the wire’s thickness 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 fewer collisions.

The number of free electrons changes from one material to another. The size of the ions changes from one material to another, this affects the current and therefore affects the resistance.

So if there is a kink in the wire this will change the thickness of the wire.

Preliminary Experiment

In order to start the experiment, we have to take part in a preliminary experiment. The apparatus I needed in order to do this were as below:

Electric Wires
2 Crocodile clips
Metallic conductive wire: constantan (cut at 200 cm)
1 Voltmeter
1 Ammeter
1 Power pack.

The apparatus was set as shown above. We took 6 results, from one length of wire; we took down each of the following:

The length, measured in centimetres. (Cm)
The current, measured in amps. (A)
The voltage, measured in volts (V) and then,
The resistance, measured in ohms. (Ω)

Before doing the experiment we had to make sure that the experiment would be safe, so we made sure we went by the safety rules.

We selected an ammeter, voltmeter, power pack and electric wire in order to take the voltage and current in order to figure out the resistance of the wire so that we could get an idea of how our results would come out, and which instruments will give us the most accurate readings.

Throughout the experiment, we made sure that we kept it as fair as possible. We kept the room temperature constant, we made sure that the wire did not heat up and we kept the voltage on the power pack constant.

6 results were taken with the wire, the table below shows the results, including the Voltage and the Current of each length of each wire.

We then each converted our results to find the resistance running through the wire. In doing this we used the equation V = IR, where (V) is the voltage, (I) being the current and (R) the resistance. In the case of our results, we had to use the formulae R = V divided by I.

Preliminary results

Preliminary Research

Conductivity of metals

Metals have a high density of conduction electrons. The aluminium atom has three valence electrons in a partially filled outer shell. In metallic aluminium the three valence electrons per atom become conduction electrons. The number of conduction electrons is constant, depending on neither temperature nor impurities. Metals conduct electricity at all temperatures, but for most metals the conductivity is best at low temperatures.

In electricity, resistance is the property of an electric circuit or part of a circuit that transforms electric energy into heat energy in opposing electric current. Resistance involves collisions of the current-carrying charged particles with fixed particles that make up the structure of the conductors. Resistance is often considered as localised in such devices as lamps, heaters, and resistors, in which it predominates, although it is characteristic of every part of a circuit, including connecting wires and electric transmission lines.

The spread of electric energy in the form of heat, even though small, affects the amount of electromotive force, or driving voltage, required producing a given current through the circuit. In fact, the electromotive force V (measured in volts) across a circuit divided by the current I (amperes) through that circuit defines quantitatively the amount of electrical resistance R. Precisely, R = V/I. Thus, if a 12-volt battery steadily drives a 2-ampere current through a length of wire, the wire has a resistance of 6 volts per ampere, or 6 ohms. Ohm is the common unit of electrical resistance, equivalent to one volt per ampere and represented by the capital Greek letter omega. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor.

The resistance of a conductor, or circuit element, generally increases with increasing temperature. When cooled to extremely low temperatures, some conductors have zero resistance. Currents continue to flow in these substances, called superconductors, after removal of the applied electromotive force.

The reason that the length is proportional to the resistance is to do with free electrons. The free electrons constantly flow around the circuit, as fast as they can. The ions in the circuit though, get in their way, and the electrons and ions collide causing resistance. This is what causes resistance. By increasing the length of the wire, we are adding more ions to the circuit therefore increasing the chance that they will collide.

Analysis and relation to preliminary experiment

According to my research, the resistance of a wire generally increases as the temperature of the wire increases. This means that if the heat of the wire does increase, than the results we be inaccurate and therefore the experiment will have to be repeated. That is why it is essential to keep the wire at a constant.

It also tells us that the resistance of a wire is directly proportional to its length and that the resistance depends on the material of the conductor. That is why it is we are going to repeat the experiment - to see which reading was most accurate to my scientific prediction.

To decrease the chances of getting anomalous results I am going to use a micrometer screw gauge, to work out an accurate measurement of the constantan’s thickness.

The micrometer screw gauge.

The method of measurement is:

Work out the value of a division on the spindle scale.
Using the ratchet, close the jaws of the instrument full. The zero on the spindle scale should coincide with the horizontal reference line. If not, note the zone error.
Using the ratchet, close the jaws on the object to be measured until it is gripped.
Note the reading of the highest visible mark on the sleeve (in this case 6.5mm).
Note the division on the spindle scale, which coincides with the horizontal reference line (in this case 0.41).
Add the two readings and add or subtract the zero error to get the correct reading (in this case 6.91).

All experimental measurements are subject to some errors, other than those caused by carelessness (like misreading the scale). The most common errors, which occur, are parallax errors, zero error and reading errors. When starting a reading, therefore, a number of significant figures should be quoted which give an estimate of the accuracy of the readings. I will take 10 readings, and I will repeat the experiment 3 times giving me a range of results, I will investigate the length starting with 20cm and increase by 20cm and finally finishing with 200cm. I will then compare the 3 results against on another, and this will help us see any anomalous readings. Hopefully, I shall find that the difference between the first and last readings should be proportional according, to my scientific knowledge. I am going to plot 2 graphs and I will pick the best results and plot that on graph paper, then I am going to work out the average resistance of the three results and plot that on another sheet of graph paper. I am not plotting it on computer because it would be harder to draw the line of best fit and explain anomalous results.

Main experiment

So, I can now move on to the actual experiment, I am going to use the same apparatus I used in the preliminary experiment, which are:

Electric Wires

2 Crocodile clips
Metallic conductive wire: constantan (cut at 200 cm)
1 Voltmeter
1 Ammeter
1 Power pack
2 metre rulers
Cello tape and a
Micrometer screw gauge.

But this time, I am going to measure the thickness of the wire at 10 places on the wire, using the micrometer screw gauge. I used wire A, a constantan wire of approximately 0.3mm in diameter. I suggested that we do it at every 20 centimetres. I used the method on page 11 and the readings I got were as below:

The Method

First, I had to get the apparatus.
I then placed the equipment on a dry surface, as we were using electricity.
I set up the apparatus in the same way set in the preliminary experiment, (In series) as below:

I then made sure that the voltage was set to 4 volts.
I took account of the safety regulations and I started the experiment.
I started to measure at 20 cm, and increased by 20cm after each reading until I got 10 readings, from 20 cm to 200cm.
Then, I repeated this experiment 2 more times
I recorded all my readings on a table.

Obtaining Evidence/Results

The results I found were as below:

Experiment 1

Experiment 2

Experiment 3

I used the formula:

Resistance =

Where in symbol form it is:

Where R is resistance, V is voltage and I is current.

Seeing that I have finished the experiment, I have to move on to plotting the graphs, but first I have to work out the average resistance of the three results tables on page 14. All readings are accurate to 3 significant figures.

I am now ready to plot two graphs; I have decided to plot the resistance in experiment 3, and the average resistance. These are highlighted on the table above.

Analysing Evidence

I have drawn two graphs on the previous pages these consist of the normal readings and the average readings, I have drawn them using the axis:

Length of constantan wire on the x-axis in centimetres.
Resistance on the y-axis in ohms.

I have made these graphs, large because it would then be more accurate, this will help me make note of any anomalous readings and patterns. To get an idea of what the graphs are supposed to look like, I have drawn a line of best fit. This will show which readings are reliable and which are not.

From the graphs, I can see that the resistance of the wire is proportional to the length of the wire. I know this because the Line of Best Fit is a straight line showing that if the length of the wire is increased then the resistance of the wire will also increase.

Although, there are minor mistakes in my graphs, my prediction still satisfies the results, because I stated that when the length increases, then the resistance would also increase in proportion to the length. I said this because the longer the wire is, the more atoms there are and so the more likely the electrons are going to collide with the atoms. I also stated that if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance.

To explain the minorities of anomalous readings, I can say that it was due to many factors. The reason why I had these anomalous readings was frankly due to the fact that there were some variables, which did not remain constant. For example, it seemed to me that the voltage did not stay the same, because when I recorded the voltage in the experiment, I found that it did not remain constant, this may have happened because we were using lots of short wires connected together. Another example is the fact that the crocodile clips were not put exactly on the point needed, I know this because when I placed the crocodile clip at 120cm and 140cm I found that it measured the same voltage and same current. The thickness did not stay constant either, as we know from using the micrometer screw gauge, the wire’s thickness varied from allocated places on the wire from 0.30mm to 0.32mm. This would have made the resistance decrease. This is because of the increase in the space for the electrons to travel through and due to this increased space between the atoms, there were be fewer collisions. I also know that if the wire were not stretched along the ruler then the thickness of the wire would have made the resistance decrease.

Conclusion

In my prediction I said that: if the length increases then the resistance will also increase in proportion to the length.

From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is 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, which 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. This is shown in my diagrams below:

In this diagram the wire A is half the length of the wire B and so has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times.

Also if the length of the wire was trebled or quadrupled then the resistance would also treble or quadruple.

Evaluation

From my results table and graph I can see that my results that I collected are very reliable. I know this because my results table only show a couple of minor anomalous results this shows that the one minor reading had made the average results change. Also on the graph I can see that 2 of the averages plotted are anomalous because all the averages lie along the same straight line, but only the 2 circled show further away from the line than others.

During my experiment I have noticed several modifications I could make to improve on the Investigation if I was to repeat it, once more.

The first of these modifications would be in the circuit that I would use. To be more accurate with my results I would use the following:

Power supply of 4 volts.
A digital ammeter, a device that also measures voltage and resistance.
A needle instead of a crocodile clip.
A wider ranges of wires not just the constantan, as this would give me varied readings.

Instead of connecting the voltmeter to the main circuit I would connect it to the wire, which is being tested. I would do this so that the voltmeter is measuring the voltage of just the wire being tested and not the wires of the main circuit as well.

To also improve on my results I would use a digital instrument to read the voltage, current and resistance, instead of the analogue instruments. I would do this because a digital instrument is a lot more accurate than an analogue because if the needle in the analogue voltmeter, for example, is bent then the readings given off will be false whereas a digital voltmeter does not rely on a needle or any other manual movements and the reading error can be made very easily along with the parallax error, on which we have to avoid.

The next modification I would make would be to use pointers instead of crocodile clips or maybe even a needle, I would do this because pointers or needles would be more accurate. The pointers/needles would be more accurate because the tips have a much smaller area on its tip than the crocodile clips giving a more accurate measurement of the length of wire.

As well as making these modifications I would also improve my Investigation by testing the same wire but different widths of that wire. I would do this to expand on my Investigation.