Harry Sedgwick 3/4/08Measure the diameter of a wire by an electrical method

Aim – The termination of the diameter of the wire using an electrical method

Prediction/hypothesis – I predict that the longer the length of wire, the higher the voltage will be and therefore the higher the resistance. From this i can receive my diameter of the wire.

Method and apparatus – Apparatus - 4v battery, analogue amp meter, analogue volt meter, ruler and wire, 5 wires, metal jockey and a power source. Firstly I need to set up the experiment as follows -

Then using the jockey measure the resistance of the wire I will take down 6 readings of amplitude and voltage at certain lengths of the wire, these being – 40, 50, 60, 70, 80 and 90cm. With these results I will make a table of the voltage and amplitude of the wire and from this I can calculate the resistance of the wire using the equation -R = v/I. When I have found the resistance and I know that the resistivity of the wire (1.2 x 10-6Ωm) I can then use this equation - R = p x L/A, to find the diameter of the wire. R = PL/A A = ρ(L/R) πr2 = ρ (L/R) πr2 = ρ (1/gradient of graph) when you have found πr2 then you divide by pie and square root it to find the radius. Finally you times this answer by 2 to find the diameter. If the diameter is the same for each result taken down then this gives an indication that I have completed the experiment successfully and so I will have found an estimate of the diameter of the wire. I find 1/gradient of the graph to get a more accurate reading. Safety – The only safety precaution is to e careful near the power source so that you don’t get electrocuted so you need to be careful when to turn the battery on only when the equipment is set up and ready to use safely.

Observations - Results - L (cm) +/- 0.1cm I (Amps) V (Volts) R (Ω) gradient Diameter (cm)40 0.12 1 8.33 0.142 0.00350 0.12 1.2 10 0.142 0.00360 0.12 1.42 11.833 0.142 0.00370 0.12 1.8 15 0.142 0.00380 0.12 2 16.66 0.142 0.00390 0.12 2.2 18.33 0.142 0.003

Repeat 1- L (cm) +/- 0.1cm I (Amps) V (Volts) R (Ω) gradient Diameter (cm)40 0.12 1 8.33 0.142 0.00350 0.12 1.2 10 0.142 0.00360 0.12 1.42 11.833 0.142 0.00370 0.12 1.8 15 0.142 0.00380 0.12 2 16.66 0.142 0.00390 0.12 2.2 18.33 0.142 0.003

Graph – Resistance/length of wire –

Evaluation/conclusion – This process has been successful because i have completed my aim and showed this by producing a graph with resistance against length of wire. When i plotted this graph there was a positive correlation in a more or less a straight line proving my prediction further. There were not many variables in this experiment so there wasn’t many things that could go wrong even though this experiment overall could be made more accurate. One possible improvement is that i could use digital dials rather than analogue dials so it would be more accurate and i could record results to more decimal places. I could also use a more accurate way of measuring the length of the wire by using a better ruler that measures half millimetres. To conclude I think that this experiment was successful in showing the diameter of a wire with electrical currents because results showed the same calculated diameter each time and the repeats were the same. But this is an estimate so a different method would be appropriate if you need to find the exact diameter.