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Resistance of Wires

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Introduction

Resistance of Wires

AIM: An experiment to investigate how the length of a wire affects its resistance.  

PLANNING:

I will set up an experiment to investigate how the length of a wire affects its resistance.  I will set up the experiment as follows:image00.png

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METHOD: The apparatus will be set up as above.  A piece of wire will be measured and cut, then inserted between two crocodile clips.  This wire will then be connected in parallel with a voltmeter.  An ammeter will then be connected to the voltmeter and wire, and these will all be connected in a circuit to the cells.  I will measure the current and voltage of the circuit in order to calculate the resistance (see formula below).  I will then repeat the experiment once more (so that I can obtain two sets of results and calculate an average) as to ensure accuracy and reliability.  A suitable number and range of observations will be taken (the highest and lowest limits of lengths of the wire will be determined in the preliminary work).  A brief trial of the range of the lengths will be done in the preliminary work to make sure that it will be suitable for the actual experiment.

The main aim of this experiment is to find out how the length of the wire affects the resistance of the wire.  Since I do not have access to a piece of equipment which directly measures the resistance, the resistance has to be calculated by hand.  This is why I have planned to use two other pieces of equipment which will help me calculate the resistance.  To work out the resistance, the following formula has to be used:

R = V ÷ I

…where R = resistance, V = voltage, and I = current

...read more.

Middle

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As the length of the wire increases, the amount of metal ions in the lattice structure of the wire will also increase, which means that the electrons will find it harder to pass because there is more of the lattice structure for the electrons to pass through.  The probability that the electrons will collide with the metal ions will increase.  This increases the resistance.  If the length of the wire doubles, the lattice structure will also double.  Electrons have to pass through this doubled lattice structure, and the probability that the electrons will collide with the metal ions will double, so resistance also doubles.  Hence I predict that the length of the wire is directly proportional to its resistance.

I predict that the graph will be in this general shape:

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PRELIMINARY WORK:image00.pngimage08.png

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METHOD:  The apparatus was set up as shown above.  I measured and cut one piece of wire from two different thicknesses of wire to determine which to use in the actual experiment: I used 0.32 mm (30 swg – the thinnest wire) and 0.91 mm (20 swg – the thickest wire).  I varied these wire lengths to obtain two sets of results from each wire: 29 cm (the largest length) and 5 cm (the shortest length).  These two extremes in wire thickness made sure that I could make a decision on what thickness would produce a suitable range and extent of evidence from which to be able to draw conclusions from.  The extremes of lengths that were to be in the experiment were determined in the preliminary experiment (long enough to produce a sufficient range, yet remain under 1A) and used in the preliminary check the range produced.  An ammeter will be connected in series with the wire and the cells.

...read more.

Conclusion

From the results collected and looking at the graphs plotted (distribution of points and scatter) as well as the reliability and accuracy of the experiment, a reasonable conclusion can be drawn.  To make a firm conclusion on the experiment, further work will have to be done.  

The check the accuracy and reliability of the points plotted on the graph, a larger number of observations could be taken, maybe at 0.5 cm intervals.  By investigating these lengths, we would be able to get a graph with a better correlation, and predict the resistance of the circuit more accurately.

As for further work, a number of observations could be made on longer than the ones that were investigated.  From this, the shape of the graph could be confirmed, and if any change in shape does occur, this could be investigated more thoroughly.

Another experiment that could be carried out as further work would be to vary the type of wire, within the length ranges used in the actual experiment.  I would set up the experiment as follows:

METHOD: The apparatus would be set up as above.  A piece of wire of a specified material would be measured and cut, then inserted into the crocodile clips.  An ammeter will then be connected in series with the wire and the cells.  The voltmeter will then be connected in parallel with the wire to be tested and I would measure the current and voltage of the circuit in order to calculate the resistance (R = V ÷ I, where R = resistance, V = voltage and I = current).  I would then repeat the experiment once more (so that I would be able to obtain two sets of results and calculate an average) as to ensure accuracy.  I would repeat this procedure with the following materials:

  • constantan
  • copper
  • nichrome
  • carbon
  • iron
  • lead

(I would use a variety of ohmic and non-ohmic resistors in this experiment to find out, when the lengths are varied, which of them has the greatest resistance.)

...read more.

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