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# Investigation of Resistivity of Nichrome wire

Extracts from this document...

Introduction

Physics Assignment 3

Part 1 – Investigation of Resistivity of Nichrome wire

Aim

The aim of the investigation is to determine the resistivity of nichrome wire at varying dimensions. The nichrome wire is of 1 metre at 32 gauge and also of 0.5 metre at 28 gauge.

Resistivity is an electrical measure indicating how strongly a material opposes the flow of electric current. A low resistivity indicates the material readily allows the movement of electrical charge. The standard imperial unit of electrical resistivity is the ohm metre (Ωm).

The electrical resistivity ρ (rho) of a material is measured as its resistance to current per metre length for a uniform cross section and is usually defined by the following:

Where:

ρ is the resistivity (Ωm)

R is the electrical resistance (Ω)

l is the length of the wire (metre)

A is the cross-sectional area of the wire (square metres)

Nichrome is a nickel-chromium alloy commonly used in heating elements. The typical resistivity of nichrome at 293 K is 1.50 × 10−6 Ωm.

Hypothesis

The three factors that affect the resistance of a wire would be the thickness, length and the material type.

Between a thin wire and a thick wire, the latter will have less resistance as there is more area for the electrons to pass through. The length of the wire affects the resistance as of the distance the current must travel.

Middle

1.89

5.0212

1.1151E-06

14

11.21

2.20

5.0955

1.1316E-06

16

13.23

2.56

5.1680

1.1477E-06

Mean

4.9300

1.0948E-06

Sample Calculations

Resistance (Ω)

The resistance was measured using the currents and voltages measured during the experiment. The formula for resistance is:

R = resistance

V = voltage

I = current

R =         V

I

R =         1.92

0.11

R =        17.45

Resistivity (Ωm)

The electrical resistivity of an element is the measure indicating how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electrical charge.

ρ = resistivity

R = resistance

A = cross-sectional area

l = length

ρ = RA

l

ρ = 17.45* 5.8965 x 10-8

1

ρ = 1.0292 x 10-6 Ωm

Resistivity as calculated from the graph:

ρ = RA

l

ρ = 17.213 x 5.8965 x 10-8

l

ρ = 1.01496 x 10-6 Ωm for the 32 gauge

ρ = RA

l

ρ = 5.0434 x 1.1104 x 10-7

0.5

ρ = 1.12 x 10-6 Ωm for the 28 gauge

Uncertainty

The Heisenberg uncertainty principle states that one cannot assign, with full precision, values for certain pairs of observable variables. This would also apply to this investigation where we have uncertainties to the readings taken. All readings would have these uncertainties above and below the reading.

To find the percentage uncertainty we apply the following formula.

% uncertainty =   uncertainty      x 100

The uncertainties of the apparatus are shown below. This can play a major role in any errors or anomalies found.

Metre Ruler         •+0.0005m

Voltmeter         •+0.01volts

Ammeter         •+0.01amps

Metre Ruler

The ruler was used to measure the length of the wire. The end of the wire was held at zero centimetres and the other end was measured and cut.

% uncertainty =•+0.0005 x 100

1

= •+0.1 %

 Length (m) % uncertainty (•+) 0.50 0.2 1.00 0.1

Voltmeter

The voltmeter was used to measure the voltage of the wire connected to this circuit.

32 Gauge                                            28 Gauge

 Voltage Recorded Percentage Uncertainty %(•+) 1.92 0.52 3.43 0.29 5.46 0.18 7.24 0.14 9.04 0.11 10.72 0.09 12.68 0.08 14.71 0.07 Voltage Recorded Percentage Uncertainty %(•+) 1.45 0.69 3.00 0.33 4.51 0.22 6.25 0.16 7.72 0.13 9.49 0.11 11.21 0.09 13.23 0.08

Conclusion

The calculated resistivities for the 28gauge gave similar values. Here the mean value from the obtained current and voltage was 1.095 x 10-6 Ωm, where as the resistivity calculated from the gradient of the graph was 1.12 x 10-6 Ωm. Although these values looking different they are of the standard form of negative 6, meaning they are very small numbers, and therefore this slight difference is minute. Again this resistivity for the 28 gauge in comparison to the resistivity for the 32 gauge is the same, where very small decimal places are slightly out.

This investigation led to determining a good value for the resistivity by using two wires of different dimensions. The accepted value for the resistivity of nichrome is 1.50 × 10−6 Ωm. This in ratio to the values obtained is as follows:

32 Gauge        1.0149 x 10-6 Ωm : 1.50 × 10−6 Ωm

0.6766 : 1

28 Gauge         1.095 x 10-6 Ωm : 1.50 × 10−6 Ωm

0.73 : 1

This shows that the values obtained are very close to that of the accepted value. To improve the accuracy of the results the experiment should be repeated. In doing so, some variables should be kept constant i.e. the length, gauge or temperature so that an average can be obtained.

Bibliography

http://www.8886.co.uk/ref/standard_wire_gauge.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

http://en.wikipedia.org/wiki/Electrical_resistivity

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