# Resistance in a Conductor

The aim of this investigation is to discover the factors affecting resistance in a conductor. I will use what I believe to be the most effective method and experimentation in order to come to a fair conclusion and accurate evaluation. Secondary sources will be used in order to confirm any theories or motives that I may use, and all conclusions will be explained using scientific theory or the results from the experiments that will be carried out. Each experiment will be completed safely, and using the best of my scientific knowledge.

Results will be arranged neatly and analysed carefully. At the end of this investigation I would like to have discovered whether the conductor obeys Ohms Law, in reference to a sound prediction in relation to my conclusion and evaluation.

## Basic Plan

As already said, I am going to discover the relationship between the length (and diameter) of carbon putty and the resistance. This can then be plotted on a graph, using the two factors of voltage and current.

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To discover the relationship between the length of carbon and its resistance, the putty will be placed in the circuit at different lengths, and the current and voltage will be recorded at each of these lengths, and then the following equation can be used:

Resistance = Voltage OR R = V

## Current I

Therefore the resistance can be discovered, however the unit of power used will remain constant this time rather than being altered. Also, to ensure accuracy, different experiments will be set up using a digital multimeter, which converts the voltage and current directly into ohms, making it easier to find the results.

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We will be using both methods in case one of them gives false indications, so that the experiment is reliable.

In order to perform this experiment, a circuit will need to be set up, ensuring that an ammeter is placed in series in the circuit to measure the current (amps), and a voltmeter is placed in parallel in the circuit in order to measure the Voltage (in Volts). Once this circuit is set up, the carbon putty will be rolled to the appropriate length and diameter, and the first result will be taken. We then need to cut off 2 cm from the carbon putty each time, and take another reading. We continue this until the results have ranged from 18cm to 2 cm. We will then repeat this experiment using a different diameter. A graph will then be plotted of length against resistance of the carbon putty, using different diameters of carbon putty on the same sheet of graph paper to show the varying gradients. Read also does length of wire affect current essay

## Safety

I will take precautions whilst performing the experiments to ensure that the procedure is as safe as possible. The safety elements are listed below:-

1. Make sure that there is a low voltage across the conductor. A high voltage may be dangerous.
2. When using the carbon putty, avoid contact with eyes and mouth. Rubber gloves and safety goggles could be used for maximum safety.
3. Take care when using sharp equipment, e.g. Scalpel.

## Variables

For this test to be accurate, I need to draw up a detailed plan in order to obtain the best possible results. I need to take into account several factors on the experiment in order for it to succeed one of the most important being variables. In this investigation there are things that I will need to change, or if you choose, keep constant (the Control Variables) and this that will change as a consequence (dependant variables).

### Control Variables

These are the variables in the experiment which I will change, or if necessary, keep constant to ensure a fair and reliable test. In my experiment, there will be two types of control variables. Firstly, what we will change, and secondly, what we will keep constant. These in turn will determine the relation ship between the length of carbon putty and its resistance, and we may also observe certain other factors.

Firstly, we need to state the control variable that we will change. In this experiment, only one will be present; to discover the relationship between the length of the carbon putty and the resistance. Therefore, in this experiment, we will be using a scalpel or a knife to cut the carbon putty to the required length, using a ruler to do this. This needs to be accurate, since it is a very important factor to ensure reliability.

Secondly we need to state what we need to keep constant throughout the experiment. These are listed below :

• The diameter of the material

This has an effect on resistance, so will need to be kept constant throughout. Although this will change in different experiments, it will remain the same through each individual experiment.

• The type of material

The type of material has an effect on resistance, so must be kept constant.

• The temperature

This also has an effect on resistance. This is the most difficult to control, since the temperature will vary slightly from time to time. We must keep the conditions at room temperature, and keep them as constant as possible.

• Same power pack, ammeter and voltmeter

These will all give slightly different readings, so will need to be kept constant if the results are to be reliable. If the readings differ, our records of resistance will also differ, therefore causing the experiment to be inaccurate.

• Power pack settings

The voltage emanating from the power pack will need to be kept constant to ensure reliability, and so that it is a fair test, otherwise the results could differ.

• How many lengths that will be tested

Since we are repeating the experiment, it is important that the number of lengths recorded are kept constant as each repeat is performed, in order to obtain the same number of results for each length used.

### Dependant Variable

The dependant variable is the change that will occur in the experiment that we are unable to control. In this case, it will be resistance, owing to the change of conditions in the circuit. We will then measure the resistance using a multimeter, and later an ammeter and a voltmeter, using R=V/I (explained later).

## Outline of procedure

The diameter and temperature will be set to a fixed value. The length will then be changed through several different values and the values of current and voltage will be taken to work out the resistance.

The diameter will then be changed, and the experiment repeated. This will be done for several different diameters. To ensure reliability, more than one set of values may be taken for each diameter.

## Scientific Theory

Electrons move more easily through some conductors than others when a potential difference (voltage) is applied. The opposition of a conductor to a current is called its resistance. A good conductor has a low resistance and a poor conductor has a high resistance. All conductors resist the flow of electrical charge to a certain degree, however some are better at it than others. The factors affecting the resistance in a conductor are as follows.

1. Resistance increases as the conductor's length increases.
2. Resistance increases as the conductor's cross-sectional area decreases.
3. Resistance varies depending on the type of material being used.

All metals are good conductors. This is because they have a large number of free electrons that can move easily from atom to atom, so therefore a current flows.. A thin wire in a lamp will resist the movement of electrons that is within it. Therefore we can conclude that the wire has a resistance to the current. The greater the resistance, the more voltage that is required to move a current through the wire.

A long thin wire has more resistance than a short thick one of the same material.1 Silver is the best conductor, but copper, the next best, is cheaper and is used for connecting wire in electric cables. Resistance is used to control the amount of voltage and amperage in a circuit. Everything in the circuit will cause a certain amount of resistance.

So therefore resistance is anything within a circuit that will slow or inhibit the movement of electrons, and if you increase the resistance then less current will flow.

"The Physics World" by Ken Dobson explains the effect in a conductor with a high resistance adequately:

"It is like water flowing downhill in a river. If the bed of the river is smooth then the water can flow easily, and more can get through in a given time. But if the bed of a river is rocky the water can't flow so easily. It will move downhill more slowly, and a lot of energy is being wasted-you can hear the noise and see the water being thrown up in the air."

## Measuring Resistance

Resistance is measured in units called ohms (?). For example, a 10? resistor would have twice the resistance of a 5 ? resistor. If the current flowing through a conductor is I when the voltage across is V, the resistance R is defined by:

R = V

I

Or: the resistance is equal to:

p.d. across a wire

Current flowing through a wire

Finding the resistance using the current and potential difference is known as the ammeter-voltmeter method.

Alternatively, if R and I are known, V can be found from

V=IR

Also, knowing V and R, I can be calculated from

I=V

R

Below is a simple test in a circuit, which allows you to measure the current and voltage and to therefore calculate the resistance:

## Ohms Law

Ohm's Law is a set of formulas used in electronics to calculate an unknown amount of current, voltage or resistance. I was named after the German physicist George Simon Ohm, who was born in 1787, and died in 1854.

### Ohms Law is defined as:

"The amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive forces impressed on the circuit and inversely proportional to the total resistance of the circuit."

Or, also:

"The current flowing through a metal wire is directly proportional to the potential difference across it, providing that the temperature remains constant."

For many useful conductors this is a simple rule which connects current, voltage and resistance. Its relationship in this law is that if we double the applied voltage, the current is doubled. If the voltage is halved, so is the applied current. This does not apply for all conductors, but it will work as long as the temperature remains constant across the conductor.

### Although this sounds complex, Ohms Law means:

1. A steady increase in voltage, in a circuit with constant resistance, produces a constant linear rise in current, as shown in this graph: (This conductor obeys Ohms law, because there is a straight line through the origin.)
2. A steady increase in resistance, in a circuit with constant voltage, produces a progressively (not straight line if graphed) weaker current.

The formula can be written as I = V/R, or R = V/I. We can use this formula to make calculations with all values for V for a given conductor. However, the resistance may change is the conductor heats up.

Many laws in physics are stated to be unbreakable, however this is not how Ohms Law is defined. It does not state what must occur, it simply describes the behaviour of materials. This of course applied on to metals, ionic solutions and in some cases carbon. Many conductors do not obey Ohms Law.

### Current-Voltage Graphs: Ohm's Law

The results from completing a circuit where voltage and current can be measured allows the current to be plotted against the voltage for different conductors.

• Metallic Conductors

Metals and some alloys give I-V graphs which are a straight line through the origin, as long as the temperature remains constant. A substance that will give a straight line like this are called ohmic or linear conductors, since I is directly proportional to V. The resistance of an ohmic conductor does not change when the voltage does:

• Semiconductor Diodes

The graph below shows that current passes when the voltage is applied in one direction but is almost zero when it acts in the opposite direction. A diode has a resistance that is only large one way; the other way it is very small. It conducts in one direction only and is a non-ohmic conductor. "GCSE Physics" by Tom Duncan, states that "this makes it useful as a rectifier for changing alternating current (a.c.) to direct current (d.c.).

• Filament Lamp

A filament lamp, for example a torch bulb, the V-I bends over as V and I increase. This means that the resistance increases as I increases and makes the filament hotter. Therefore the temperature does not remain constant:

• Variation of resistance with temperature:

As a rule, if you increase the temperature you increase the resistance of the metals, and this applies to the filament lamp, but it decreases the resistance of a semi-conductor. The resistance of most thermistors decreases as the temperature rises, and the I-V bends or curves upwards:

This scientific knowledge helped me to understand what would happen, allowing me to make my prediction below, and also write my detailed strategy. This also helped me to understand what the control variables would be, and also what I would need to change in the experiment.

## Prediction

Using the scientific theory obtained I believe I can make some sort of prediction based on the theories of Ohms Law. Also I can confirm the scientific theory of measuring and confirming the factors of resistance within a circuit.

I believe that, since carbon putty contains a conducting material and will allow a current to flow through it, as long as the temperature remains constant the carbon putty will obey Ohms Law. I can confirm this because the putty is not a diode, filament lamp or a thermistor, and therefore the shape of the graph is not predictable unless it applies to one of these categories. However, if the carbon putty obeys Ohms law the prediction graph will show the shape of the final graph produced from the results. I can confirm this because of the following scientific theory:

### Ohms Law is defined as:

"The amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive forces impressed on the circuit and inversely proportional to the total resistance of the circuit."

Or, also:

"The current flowing through a metal wire is directly proportional to the potential difference across it, providing that the temperature remains constant."

I believe that the carbon putty will act in the same way as a metallic conductor, so a graph of current against voltage would so a straight line, therefore a graph of resistance against length would also be directly proportional. A graph of resistance against area would be inversely proportional, making resistance against 1/area directly proportional.

I can simply state that if it does obey Ohms Law the above result will occur. I cannot predict the actual measurements on the graph itself, only the shape it will produce, so any numbers on the graph are to demonstrate direct proportionality only, and not the results I believe will be present. However, I can base the graph on the preliminary results, and the basic numbers used in that context.

I can predict a result to discover how its length affects the resistance of carbon putty. I predict that as I shorten the length of the putty, the resistance will decrease. I can confirm this prediction because the scientific theory written states the following. Also, I believe that if the cross-sectional area of the putty increases, the resistance will decrease making them inversely proportional. I can prove these predictions by the following:-

Electrons move more easily through some conductors than others when a potential difference (voltage) is applied. In a given energy source, the size of the current depends on the resistance. All conductors resist the flow of electrical charge to some extent, however some are more capable of doing so than others.

"All metals are good conductors. This is because they have a large number of free electrons that can move easily from atom to atom, so therefore current flows. A good conductor has a low resistance and a poor conductor has a high resistance. A thin wire in a lamp will resist the movement of electrons that is within it. Therefore we can conclude that the wire has a resistance to the current. The greater the resistance, the more voltage that is required to move a current through the wire."

### There are four factors that affect resistance:

1.  As the length increases, the resistance increases
2. As cross-sectional area increases, the resistance decreases
3.  Copper is a good conductor and is used for connecting wires. Nichrome has more resistance and is used in the heating elements of electric fires
4.  As the temperature increases, the resistance of the wire increases

A long, thin wire has more resistance than a short thick one of the same material.

Therefore one of the factors of resistance is that as the length increases, so does the resistance. Therefore the resistance will decrease as I shorten the length of the putty, and as long as the cross-sectional area remains constant throughout the putty and the temperature remains constant, there will be a decrease that will be directly proportional to the length. This will result in a straight line on a graph that passes through the origin. I can confirm this because if no other factors affect the decrease in resistance, the decrease must be constant. I can draw a prediction graph to show this decrease, however I cannot predict what the resistance will be, as I do not know how the current and voltage will change in order to result in a decrease in the resistance. Therefore only the shape of the graph can be predicted, and not the actual resistance in Ohms.

Below is a sketch to show what my graph should look like.

As you can see, the smaller diameters show a higher resistance, so the gradients will be steeper.

Therefore, it is predicated that the resistance is proportional to the length, but inversely proportional to the diameter.

## Preliminary Testing

In order to conclude what method would be the most suitable to use in the investigation, I need to decide on a particular method that I deem to be the most suitable and the most efficient in order to carry out the experimentation to the best of my ability. I also need to consider appropriate equipment and observe measurements that can be concluded in "Measurements and Observations."

A simple circuit needed to be created, and there were not very many options within that circuit, as this was an essential way of collecting appropriate data. I decided to use a multimeter and a circuit board, that allows precise lengths to be taken, and therefore accurate results. The multimeter creates its own circuit, and can read the resistance through the wire without needing to work calculations between the relationship of voltage and current.

I collected the multimeter, the circuit board, as well as several lengths of wire ( with varying diameters), and constructed a simple circuit by placing the wire at different lengths on the circuit board. There were sockets at either and to what the wire was attached, allowing the wire to be attached to the terminals of the multimeter easily. From the experiment, I collected the results in a table and then plotted a graph from the results using three different diameters of wire.

Updated: Feb 19, 2021