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Resistivity Coursework

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Introduction

Mohammed A.Z. Ali

Resistivity Coursework

Theory suggests that the resistance of a wire is found with this formula:

R=ρL/A

R = Resistance

ρ = Resistivity of wire

L = length of wire

A = cross-sectional area

I will now perform an investigation to confirm the legitimacy of this formula and confirm a value for ρ in a Nichrome wire.

Planning

A4c: Fully labelled Diagram

image12.pngimage08.pngimage06.pngimage07.pngimage04.pngimage05.pngimage00.pngimage01.png

A4d, A6d: Comprehensive list of Apparatus including Instrument Ranges

Variable power supply unit

Analogue ammeter, accuracy 0.01A, range 0 to 1.0A

Analogue Voltmeter, accuracy 0.1V, range 0 to 5V

Copper leads x5

Crocodile clip x2

Nichrome Wire (diameter=4.57 x 10-4m)

Ruler, accuracy 0.001m, range 0 to 1.000m

A2c: Safety

Confirm the Initial power supply is at 0 volts other wise huge voltages will most likely cause unnecessary heating in wires including the Nichrome not only a hazard but may compromise my readings.

Make sure my practical investigation is free of all or any obstructions; any unnecessary wires may cause a short circuit leading to damaging the power supply unit, ammeters and voltmeters.

A4b, A6a: Identifying Variables and Constants

The variables in this investigation are voltage (V), resistance (R) and length of Nichrome wire (L). Resistance and length are directly proportional to each other. Constants are current (I)

...read more.

Middle

max x 0.6max = 4.00Vmax

Hence I require of a voltmeter ranging 0 to 5V. Therefore the maximum heat per second produced is given by

P max= I 2 max R max = 0.60 2 max x 6.67max = 2.40 W max

Which is a very low power rating, this quality should sustain a constant temperature of the resistor.

Implementation

B6d, D2a: Sources of Significant Error

I expected a problem with crocodile clip connection and wires they took up extra area of the wire causing inaccuracies in measurement

B8a, D2c: Actions Performed to Minimise Errors

  • Ammeter and Voltmeters with appropriate ranges (0 to 1.00A,0 to 5.0V)
  • Low current to minimise heating the wire(0.30A,0.60A)
  • Turning off the power supply between readings to corroborate a constant temperature

Arranging Evidence

C8a: Statement of established theory

The graph should be a straight line through the origin where resistance(R) is proportional to length (m).

The gradient R = ρ / A x L therefore ρ and A are constants similar to the to the line formula, y = m x,

ρ = (gradient x π d 2) / 4

C8b: the graph of R / Ω against L/m, is a straight line through the origin. R is directly proportional to L

C8c: Gradient = ΔR / ΔL = 6.67Ω / 1.000m= 6.67

...read more.

Conclusion

D4d: Reliability of Conclusion

Actual value of ρ = 1.08 x 10-6 Ωm

My value of ρ = 1.09 x 10-6 Ωm

As a result Δρ= 0.01 x 10-6 Ωm

% error in ρ = 0.01 x 10-6 / 1.08 x 10-6 x 100% = 0.93% this is an insignificant difference. My conclusion is legitimate as my graph is a straight line through the origin, I have also found that L is an independent variable and R is dependant on L. As a result, when length is increased, the resistance also increases. In addition my value for ρ is in close proximity to the true value of ρ and my prediction agreed with my results. In addition I finally conclude that the formula is genuine and works

D6a: Sources of Systematic Errors

I have no systematic error as you can see my line goes straight through the origin

D6d: Proposals for Improvement

  • Point contacts as a replacement for crocodile clip connections to increase accuracy to length (L)
  • Use digital meters in replacement for analogue meters to find more accurate values for voltage and current resulting in a exact value of resistance
  • Extend length of wire and assess if the resistivity of the wire behaves the same
  • Record voltage every 0.05m up to the max length of the wire
  • Switch off power supply longer to ensure a consistent temperature
  • Extend my investigation to wires made of different metal alloy wires

...read more.

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Here's what a teacher thought of this essay

4 star(s)

This is a well written report that has an appropriate structure.
1. There is a running commentary that should be removed.
2. The conclusion is very brief and does not attempt to explain the patterns that have been found.
3, The evaluation should suggest further research opportunities.
****

Marked by teacher Luke Smithen 05/09/2013

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