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# Physics - Resistivity

Extracts from this document...

Introduction

## AIM

The aim of the experiment I am conducting is to find the resistivity of a 24 watt light bulb. This will be conducted through a series of experiments which will be followed by some calculations using formulas such as:

Or

ρ is the resistivity (measured in ohm metres, Ω-m)

R is the electrical resistance of the material (measured in ohms,Ω)

is the length of the piece of material (measured in metres, m)

A is the cross-sectional area of the material (measured in square metres, m²).

There are other equations that could be used to work out electrical resistivity, such as:

E is the magnitude of the electric field (measured in volts per metre, V/m);

J is the magnitude of the current density (measured in amperes per square metre, A/m²).

Finally, electrical resistivity is also defined as the inverse of the conductivityσ (sigma), of the material, or:

Electrical conductivity or is a measure of a material's ability to conduct an electric current. This is because resistivity and conductivity are reciprocals.

I aim to use the first equation to work out resistivity by re-arranging it, like so:

So if I can measure ‘R’, being resistance, ‘A’ being cross sectional area and ‘l’ being length of a light bulb, I can use the latter equation to work out the resistivity of the light bulb.

## RESISTIVITY

The resistance of a wire depends on quite a few factors; these will affect the wires in many different ways, such as temperature increasing resistance. The length of the wire will make a difference. This is because when you have a long wire, the electrons have to ‘squeeze’

Middle

## IMPLEMENTING

This is how my final circuit looked; I have included the EMF of the power supply and the power of the lamp in this diagram.

After conducting my first repeat, I got the following results:

 EMF Voltage across bulb        (V) Current across bulb        (I) Resistance of bulb (V/I) 12 10 1.96 5.10 12 9 1.85 4.86 12 8 1.73 4.62 12 7 1.62 4.32 12 6 1.5 4.00 12 5 1.36 3.68 12 4 1.23 3.52 12 3 1.07 2.80 12 2 0.9 2.22 12 1 0.69 1.45 12 0 0 ∞

On the second repeat I got the following results:

 EMF Voltage across bulb        (V) Current across bulb        (I) Resistance of bulb (V/I) 12 10 1.55 6.45 12 9 1.46 6.16 12 8 1.36 5.88 12 7 1.26 5.56 12 6 1.16 5.17 12 5 1.04 4.81 12 4 0.92 4.35 12 3 0.78 3.85 12 2 0.63 3.17 12 1 0.4 2.5 12 0 0 ∞

On the third repeat I got the following results:

 EMF Voltage across bulb        (V) Current across bulb        (I) Resistance of bulb (V/I) 12 10 1.55 6.45 12 9 1.45 6.21 12 8 1.38 5.80 12 7 1.28 5.47 12 6 1.18 5.08 12 5 1.06 4.72 12 4 0.94 4.26 12 3 0.82 3.66 12 2 0.66 3.03 12 1 0.51 1.96 12 0 0 ∞

On the forth repeat I got the following results:

 EMF Voltage across bulb        (V) Current across bulb        (I) Resistance of bulb (V/I) 12 10 1.51 6.62 12 9 1.43 6.29 12 8 1.34 5.97 12 7 1.25 5.60 12 6 1.16 5.17 12 5 1.05 4.76 12 4 0.94 4.26 12 3 0.81 3.70 12 2 0.68 2.94 12 1 0.52 1.92 12 0 0 ∞

## ANALYSING

So I can see the general trend of my results, and spot any anomalous data, I have drawn a simple I-V graph, which includes all my repeats.

As you can see from this graph, my repeats 2 to 4 are very similar but my first repeat isn’t.

Conclusion

The actual limitations of my experiment that I couldn’t control were things like, external temperature, obviously the limitations of the equipment I used couldn’t control the environmental temperature around the experiment, so I haven’t taken into account any change in temperature as it is out of my control so I couldn’t do anything about it. Also the accuracy and precision of my voltmeter and ammeter would have an effect on my results, this would cause a systematic error and so my graph’s gradient and thus calculated resistance would still be the same. There could also be random fluctuations in the school’s power supply, or in my power pack, which could result in a temporary random error in my results. I don’t think this happened though, as all my data was very similar, excluding the first repeat. Apart from these factors I think my results are reasonably accurate and precise, they were what I predicted and my 2nd, 3rd and 4th repeats proved to be precise.

I think next time I conduct this experiment; I could do it in a controlled atmosphere, so environmental factors, like temperature and pressure don’t have as much of an effect.

The actual value of resistivity for tungsten is  0.0000000528 Ωm at room temperature. The value I got for this according to my results is: 0.0000054 Ωm. This difference would be because of the level of control and accuracy that I had over my equipment and environment. I think that to do this experiment and get the results nearer the standard value of resistivity for tungsten I would need to have this control over the environment, I would need to do more repeats, I would need to take a lot of other factors into account and I would need to use expensive voltmeters and ammeters, that will provide a better accuracy and precision.

This student written piece of work is one of many that can be found in our AS and A Level Electrical & Thermal Physics section.

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