# Inversely linear relationship between the two variables, rather

Inversely proportional means that there is not a linear relationship between the two variables, rather if one doubles, the other halves. For resistance measured with an ohmmeter: As predicted, with a low resistance, the ohmmeter was inaccurate, so the final two points must be ignored to be able to read the graph correctly: Here, the points clearly line up, suggesting an inverse proportionality, for reasons detailed above. Overall conclusion: The results and conclusions agree with my prediction: there is an inverse proportionality between resistance and cross sectional area in the wires tested.

The agreement is quite good, except that there are anomalous readings on the graphs, and with them, resistance and cross sectional area do not appear to be inversely proportional. However, ignoring these values, the conclusions completely match the predictions. Evaluating Evidence My results, for the most part, appear to be accurate. Using voltmeters and ammeters to calculate the resistance, only one result was anomalous. It can be seen to be anomalous on the graphs above, as it completely deviates the line of best fit from the way it should look, as in the graph plotted with the manufacturer’s values.

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However, the resistance measured with ohmmeters had two anomalous values. Without these, both graphs showing my measurements appear to be almost the same as the the one with the manufacturer’s values. By looking at my tables, the resistances calculated with the voltage and current are more accurate when compared to the manufacturer’s values than the resistances measured with an ohmmeter. The values measured with the ohmmeter tend to be higher than the other values, but it was already known that the ohmmeter was less accurate than the other method.

Removing the anomalous result, the resistances calculated with the voltage and current line up very much in a straight line, but by comparing graphs, the line is slightly steeper than the one with the manufacturer’s values, indicating that the manufacturer’s given resistances are on average slightly higher than the calculated ones. The method to calculate resistances with the voltage and current appears to be the most consistent and reliable. Firstly, it only produced one anomalous reading, while the ohmmeter method produced two.

Also, when checked in Microsoft Excel, the line of best fit in the graph with the calculated resistances passes through all the points more accurately than the one with the measured resistances. The ohmmeter measured an anomaly on the wire of diameter 0. 71mm. While the same ohmmeter was used, different connecting wires were used for that reading. It could be that these connecting wires were dirty, or damaged, so measured an increased resistance. Both methods recorded the same anomaly with wires of diameter 0.

90mm. The resistance recorded is around half of what is shown in the manufacturer’s values. This points to a problem with the wire being tested. However, this problem is hard to discover, as the wire was checked to have diameter 0. 90mm, and its temperature did not change. It was measured to be one metre long also. The most likely problem is faulty connecting wires again, because there was nothing conceivably wrong with the wire being tested. There are enough accurate results to be quite sure of my conclusions.

Out of the 20 average values taken, only three are not close to the manufacturer’s values. That is an 85% success, but it would have been helpful to take readings with more, different diameter wires, but due to time and material constrictions, this was not possible. However, the method I used was not the best possible. If the wire was straightened out along a ruler, human error could result in the crocodile clips being attached slightly wrong, and they are not very thin at the tip, so exactly a meter is very hard to measure out.

Therefore, obtaining much thinner crocodile clips would help to make results more accurate. Also, using weights to straighten out the thicker wires would stretch them slightly, giving them slightly lower cross sectional surface areas. To avoid this, it would be necessary to purchase the thicker wires not in coils, but in straight lengths, to give more accurate readings. The measuring instruments used were not the most accurate in existence. However, the most accurate equipment is very expensive, and thus could not be afforded for this investigation.

There are many other variables that could affect the resistance of a wire. Temperature is one, and this could be tested by insulating the wire being tested, and submerging it in water baths of various temperatures while taking readings. Testing wires of different materials would show whether wires of the same length and diameter but of different metals have the same resistance or not. Varying the length of a wire being tested would show whether the length of a wire affects its resistance. Rhodri Williams 11X Science Group C Show preview only