The output variable is "resistance." There are several ways of working out the resistance, but the best and most accurate way is to first measure the current and voltage using the ammeter and voltmeter. About five readings for each length or thickness would be advisable. This could be done by connecting a variable resistor to the circuit and then obtaining five values of current and voltage. Next, drawing a graph of current (x) against voltage (y). The five results are plotted and a line of best fit is drawn.

To find out the resistance, the gradient of the line is calculated (constructing a triangle and then doing voltage/current). One way which is possible but not accurate, is for each set of values of the current and voltage, calculating the resistance and then taking an average. However, this is not advisable.

George Ohm discovered that the e.m.f. of a circuit is directly proportional to the current flowing through the circuit. This means if you triple one, you triple the other. He also discovered that a circuit sometimes resisted the flow of electricity. He called this resistance. He then came up with a rule for working out the resistance of a circuit:

R = V / I

V - Voltage (V)

I - Current (A)

Resistance is stated as being the ability of an object to resist the flow of current. The value depends on the resistivity of the substance from which the object is made and its shape. We know, that if the length of a piece of wire does affect the resistance it will mean that as the length increases, it is harder for the electrons to flow as freely as when it was short. To explain why the electrons cannot flow, as freely we need to look at how electrons generally move.

Electrons moving in an object hit atoms and give them energy. This continues throughout a circuit. If the atoms are close together in a confined space, then the electrons will take far less time to hit each one, then if they were spread out. The energy is transferred at a faster rate and therefore in the current is more efficient. This all means, that in a short piece of wire, electrons can move fast and effectively from atom to atom, but in a long piece it is much harder for them because the atoms are so spread out. Electricity travels by the easiest path.

If the cross-sectional area of the wire doubles there will be twice as many ions and twice as many electrons bumping into them, but also twice as many electrons getting through, as there is twice the current, the resistance must be halved.

We know, that for a material to work efficiently in a circuit, it needs to be a good conductor. We already know that copper is a good conductor because it is used in a lot of circuits for connecting wire. This is because it has a large number of electrons free inside it that can move easily from atom to atom so the current flows efficiently. Overall, the resistance of a wire due to its material is related to whether that material is a good conductor, whether it has a lot of free electrons or not.

Devices specially made to provide resistance are called resistors. Placed in a simple circuit, they each reduce the current flow. A length of thin nichrome wire makes a simple resistor. The diagram below shows a variable resistor also known as a rheostat. This is used for varying the current flowing in a circuit. Moving the position of the sliding contact changes the length, and therefore the resistance, of the thin coiled wire through which the current has to flow as it passes between terminals A and B.

Electrons bumping into ions cause resistance. If the length of the wire is doubled, the electrons bump into many more ions so there will be more resistance. Therefore, as you increase the length, the resistance increases.

If the cross-sectional area of the wire increases, more electrons will get through the gap meaning a greater current, therefore a decrease in resistance. Therefore, as you increase the cross-sectional area, the resistance decreases.

First, pieces of nichrome wire 22 s.w.g, 26 s.w.g. And 30 s.w.g. Was taken. The voltmeter and ammeter readings were taken when the wire was 10cm.

A simple circuit was set up as and the current and voltage passing through the wire was measured using the ammeter and voltmeter. The results were recorded in the table below:

The results obtained show that as you increase the cross-sectional area, the resistance decreases. The preliminary work was done just to give me an idea of what I am supposed to achieve in the real investigation. Only a few readings were taken for the preliminary work.

If the length is doubled, the electrons bump into twice as many ions so there will be twice as much resistance.

1 x Power Pack,

1 x Voltmeter,

1 x Ammeter,

Wires for connecting the circuit,

2 x Crocodile clips,

Nichrome wire with varied thickness,

Rheostat,

Graph Paper,

Calculator,

Meter rule,

Safety goggles.

First, set up the apparatus as shown above in the diagram. Turn on the power pack making sure the voltage setting is not more than 2 volts.

d.c current is used. The nichrome wire is set at 20cm in length. This is the constant length used for investigating the thickness of a wire. The nichrome wire used is at 22 s.w.g. The crocodile clips are placed either end of the wire at 20cm. The ammeter and voltmeter readings are recorded. The rheostat is varied so that a different reading is shown on the ammeter and voltmeter. This is done until "five" readings are recorded.

This process is repeated for each of the thickness of the wire from 22 s.w.g. to 30 s.w.g. making sure the length is constant at 20cm. The voltage on the power pack is kept low as possible so the wire doesn’t burn (i.e. keeping it in the range of 1 - 2 volts.) This is repeated until all of the thicknesses of the wire have been tested. In total, for each thickness, you should have five readings.

Next, the nichrome wire used for investigating length is 24 s.w.g. This thickness is kept constant. The wire is set at 10cm and five readings from the ammeter and voltmeter are taken and recorded. Next, the wire is set at 20cm and the same is done. This is repeated until the wire has reached 50cm in length.

The results are recorded in a table and the following graphs are drawn:

1. On a pair of axis, the ammeter and voltmeter readings are plotted for each thickness. A line of best fit is drawn. The gradient is calculated and this is equivalent to the resistance. In total, there should be five lines of best fit on this pair of axis, one for each thickness.

2. Next, on a different pair of axis, The ammeter and voltmeter readings for each length are plotted. A line of best fit is drawn and the gradient calculated. In total, there should be five lines of best-fit, one for each length.

3. After calculating the gradients of each line in graph 1, the resistance for each thickness is recorded and then a graph is plotted of resistance (y) against cross-sectional area (x). The cross-sectional area is found out by using the formula below:

4) The last graph drawn is length of wire (x) against resistance (y). The resistance for each length at 24 s.w.g. is recorded and then plotted. This graph is drawn to find out any relationship between resistance and length of a wire.

The main safety point for this investigation is to keep the current as low as possible. This is done by keeping the voltage setting on the power pack to a minimum. Care should be taken not to heat the wire especially if using Copper wire. Goggles should be worn. If the ammeter reading goes off the scale, the power pack must immediately be switched off and a different ammeter plug should be fitted. When there is any sign of burning of the wire, the circuit should be disconnected. All Laboratory rules apply. The power pack shouldn’t be left on for a long time as this wears out the ammeter and may affect the results.

After completing this investigation successfully, there are a number of points, which can be concluded.

From the thickness investigation, the first thing which can be seen just by looking at the graphs is that as the thickness decreases, the resistance increases. As we know that the wire with 22 s.w.g. is the thickest and the wire with 30 s.w.g. is thinnest. This also means that as the cross-sectional area increases, the resistance decreases. Table 3 shows the results obtained. It shows that my second hypothesis which stated that as the cross-sectional area increases, the resistance decreases is correct.

Next, by looking at graph 3, we see that the cross-sectional area is inversely proportional to the resistance. The line of best fit sort of shows this. The question is if the resistance at 22 s.w.g. is an anomaly or not. The next four results show that they decrease in such a way that if a straight line is drawn, the points are on this line. The general trend which the graph shows is that the resistance is inversely proportional to the cross-sectional area. If we look at graph 5, we see that the graph cross-sectional area against 1/resistance does not show a straight line through the origin. This means that there is no clear relationship between these variables. Seeing below, that mathematically speaking, the prediction is not a true one.

Let us mathematically see if this prediction is true:

k = constant

C = cross-sectional area

Let us find the constant k, for each result:

k = C x R

For 22 s.w.g. k = 0.4 x 0.7

= 0.28

For 24 s.w.g. k = 0.25 x 1.08

= 0.27

For 26 s.w.g. k = 0.16 x 1.27

= 0.20

For 28 s.w.g. k = 0.13 x 1.33

= 0.17

For 30 s.w.g. k = 0.1 x 1.89

= 0.19

This happens because of the electrons that flow through the wire. These electrons travel at a steady space, when they come to a different piece of wire, they have to slow down in order to be able to pass. (This is why the current differs.) While moving through the wire, the electrons need to squeeze together. This is because there is not enough room for them to pass evenly through. The more the electrons have to bump together, the higher the resistance. This is because it will take longer for them to pass from one side of the wire to the other side because the current is slowed down.

The longer the wire, the longer the electrons have to stay squashed together, and so the longer they take to pass through some materials than it is for them to pass through others. The results of this experiment clearly justify my prediction, as I stated the longer the wire the higher the resistance. This occurs due to the amount of atoms in the wire; if the wire is longer, the amount of atoms increase, therefore making it harder for the electrons to pass through the wire, which resists the flow of electrons.

Graph 1 shows that the results for 28 s.w.g. do not pass through the origin. A systematic error is present. This could be because the voltmeter reading before the start was greater than 0V. Graphs 1 and 2 show that lines of best fit are drawn. However, there are some anomalies present, e.g. for 26 s.w.g. in graph 1, there is one point which is away from the line if best fit. More are present in graph 2, e.g. for 40 cm, there are 2 points away from the line.

The experiment I carried out seemed to be fair but it was hard to make it completely accurate because the equipment was not consistent and when the readings were repeated they gave different voltage and amp readings. Even though the resistance turned out the same, the calculations are not entirely fair because the equipment gave two different readings. This did not effect the graph however, so the resistance recorded is still correct.

Overall, the results were very conclusive and I was able to see how each variable effected resistance. I would say that the evidence is reliable. I made sure that it was a fair and safe test. When investigating the thickness, the length was kept constant and vice versa.

Difficulties were achieved when trying to measure a distance on the wire. The wires are not straight and so it is difficult to measure a certain distance. As stated in my conclusion, there are some anomalies present. More repeats at the anomalies would be advisable. A systematic error is also present. This means that a repetition here is very much advisable. The gradient was still calculated however.

If I was to investigate this further, I would measure greater lengths and have more repetitions. Investigating different materials would also be a good variable to investigate. The reason I did not choose this in this investigation is because copper is a good conductor and it gives very low resistance. Type of material can be tested, but is categoric and so does not lend itself to a mathematical analysis.

The equipment used was reliable however, the crocodile clips also conduct electricity. A rheostat was used so that to vary the current and to achieve more results.

However, being humans, mistakes are very popular. We are bound to make some mistakes. Therefore, to have a new set of repeated results would be advisable in the future.

© Akil Kanani