Resistance Investigation: Essay, Research Paper

Physics Investigation Of Resistance Aim: to investigate how the electrical resistance of a wire changes in relationship to it´s length. Prediction: I think that as the length of the wire increases so to will the resistance of it. I also believe that the rate at which the resistance of the wire increases will be directly proportional to the length. The graph to show this should therefore look something like this:Reason: with electricity, the property that transforms electrical energy into heat energy, in opposing electrical current, is resistance. A property of the atoms of all conductors is that they have free electrons in the outer shell of their structure. All metals are conductors and have an arrangement in similar form to this:

As a result of the structure of all conductive atoms, the outer electrons are able to move about freely even in a solid. When there is a potential difference across a conductive material all of the free electrons arrange themselves in lines moving in the same direction. This forms an electrical current. Resistance is encountered when the charged particles that make up the current collide with other fixed particles in the material. As the resistance of a material increases so to must the force required to drive the same amount of current. In fact resistance, in ohms(R) is equal to the electromotive force or potential difference, in volts (V) divided by the current, in amperes (I) – Ohm´s law.

As the length of the wire is increased the number of collisions the current carrying charged particles make with fixed particles also increases and therefore the value for the resistance of the wire becomes higher. Resistance, in ohms (R) is also equal to the resistivity of the wire, in ohm-meters (ñ) multiplied by the length, in meters (l) divided by the cross sectional area, in square meters (A).

The material and cross sectional area of the wire is constant throughout the experiment. Therefore it is clear from the formula that the resistance should be directly proportional to the length. Key factors: in this experiment we will only change one factor, the length of the wire. This should effect the resistance of the wire in the ways stated above. Fair test: in this experiment we are only changing one factor – the length of the wire, the factors that we are going to keep the same are as follows: We must keep the surrounding room temperature the same or the particles in the wire will move faster (if the temperature is increased) and this will therefore have an effect on the resistance. The cross sectional area of the wire must be kept constant throughout as well. This is shown in equation (2) where the cross sectional area is a factor that effects the resistance. The material of the wire must also be kept the same as different materials have different conductivity. The last two factors will be kept the same by using the same wire all of the way through the experiment. The current that we pass through the wire is to be kept the same, also. If this is changed the temperature of the wire might change in a way that is not constant making the results more confusing. Apparatus:

1. Wire, over 50 cm long

2. Rheostat

3. Power supply

4. Six connecting wires

5. Two crocodile clips

6. Voltmeter

7. Ammeter Plan:

1. Connect circuit as shown in the diagram.

2. Adjust rheostat until the ammeter reads .3 A.

3. Record voltage on voltmeter

4. Repeat the experiment with the following lengths of wire, connected between the two crocodile clips:

- 10 cm

- 15 cm

- 20 cm

- 25 cm

- 30 cm

- 35 cm

- 40 cm

- 45 cm

- 50 cm

5. Use Ohm´s law to find the resistance of the wire, equation (1). Diagram:

Safety: this is not a very dangerous experiment but despite this you must always handle electricity with care, keep the current low, handle with dry hands etc. Accuracy: to keep this experiment as accurate as possible we need to make sure, firstly, that the length of the wire is measured precisely from the inside edge of the crocodile clips, making sure that the wire is straight when we do this. We must also make sure that the wire is straight when we conduct the experiment. If it is not, short circuits may occur and bends and kinks in the wire may effect the resistance, also. The reading that we take of the voltage should be done fairly promptly after the circuit is connected. This is because as soon as a current is put through the wire it will get hotter and we want to test it when heat is effecting it the least, i.e. at the beginning. Preliminary: upon testing to see if the experiment would work I found no problems with the plan I described earlier. I was able to get the following results: LENGTH

(cm)CURRENT

(A)VOLTAGE

(V)RESISTANCE

(=V/I(Ù))

100.30.130.43

150.30.200.66

200.30.270.90

250.30.351.16

300.30.421.40

350.30.481.60

400.30.571.90

450.30.602.00

500.30.682.26

Observations Observations: we will observe the reading on the voltmeter change as we change the current to .3 A. we also observe a general increase in the voltage as the length of wire we use gets longer. The rheostat will also be set at different positions for the different lengths of wire that we use. Evidence: to make sure our overall values are as accurate as possible we will repeat our readings 3 times and then take the mean resistance of the 3 readings. We will also be able to spot and discard any anomalies from our results. Results:

Set (i)

Length

(cm)Current

(A)Voltage

(V)Resistance

(=V/I in Ù)

100.30.130.43

150.30.200.66

200.30.270.90

250.30.351.16

300.30.411.36

350.30.481.60

400.30.561.86

450.30.622.06

500.30.692.30 Set (ii)

Length

(cm)Current

(A)Voltage

(V)Resistance

(=V/I in Ù)

100.30.130.43

150.30.200.66

200.30.270.90

250.30.351.16

300.30.421.40

350.30.491.63

400.30.571.90

450.30.612.03

500.30.702.33 Set (iii)

Length

(cm)Current

(A)Voltage

(V)Resistance

(=V/I in Ù)

100.30.130.43

150.30.200.66

200.30.280.93

250.30.341.13

300.30.401.33

350.30.481.60

400.30.571.90

450.30.622.06

500.30.702.33

Average

Length

(cm)Resistance (Ù)-Set (i)Resistance (Ù)-Set (ii)Resistance (Ù)-Set (iii)Mean Resistance

(Ù)

100.430.430.430.43

150.660.660.660.66

200.900.900.930.91

251.161.161.131.15

301.361.401.331.38

351.601.631.601.61

401.861.901.901.89

452.062.032.062.05

502.302.332.332.32 Anomalies: there was only one real anomaly in this experiment and it has been highlighted like this: 000

Analysis Trends: from the graph we can see one very clear trend, which is, as the length of the wire increases so does the resistance of it. Another, more significant thing is that it the increase is constant. This is indicating by the fact that the line drawn is a straight one. One may also note that the gradient of the line drawn is (1.85/40) .04625. Conclusion: I think that from my results I can safely say that my prediction was right. The resistance did change in proportion to the length. This is because as the length of the wire increased the electrons that made up the current, had to travel through more of the fixed particles in the wire causing more collisions and therefore a higher resistance. We can work out what the resistivity of the wire should be from our results using the formula

It is obvious from the formula that R/l is simply the gradient of the graph, thereforeEvaluation I feel that overall our results were quite accurate. This is can be seen when we look at the graph, which shows a straight line with all of the points apart from one being very close to or on that line. The one point that was not that close to the line was a slight anomaly, but it was only slight and did not effect the final gradient of the graph. I have found out that for the wire I was using, the resistivity at 20©C is 4.9 X 10-7 ohm-meter. From this we can then work out the percentage error of our results:

The accuracy for this experiment is, theoretically, ± 15.7%, but as one can see this does not seem to be the case from looking at the graph. The reason for this could have been due to a number of different factors. Firstly the temperature of the wire was not necessarily 20©C when we conducted the experiment and the material of wire may not be as pure as it should have been. The main reason for this was probably due to the equipment that we used being inaccurate. This did not stop us from seeing the trend, though, because the equipment would have been out by a constant amount each time therefore there was a constant error. So the trends that were predicted in the plan still were shown. Most errors in our experiment were encountered in the measuring of the wire. This is because it simply was not very practical to hold a piece of wire straight, whilst holding it next to a ruler and then trying to accurately fix crocodile clips to the right part on the wire. Also I do not feel that the crocodile clips were always fixed securely to the wire with a good connection. This also meant that they were easy to move about on the wire changing the length of it. Errors rarely occurred in the setting of the current and the reading of the voltage. It was just in the preparation area that they did occur. Another example of this is the wire was never totally straight when we started the experiment, which may also, as said earlier on, effect the resistance of it. I do not think that doing any more results in our experiment would have made it any more accurate. I feel that the only way to make it more accurate would be to use a different method – perhaps were we had a bar that did not bend in place of the wire. We could even use a rheostat in place of the wire, because it is essentially a long coiled wire that is connected at different lengths to change the resistance of the circuit

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