QETA009 Electrical Principles
9.1 Resistivity and Temperature Coefficient
Name
Formulae
The Resistivity of Copper at 20°C is 1.68*10-8
RT = Rr[1 + α(T − Tr)]
If the Reference temperature is 0°C then we can use.
RT = R0[1 + αT]
1) Write down the definition of Resistivity.
Resistivity is a measure of how strongly a material opposes the flow of electric current.
Low resistivity for a material indicates that it readily allows the movement of electric
charge. The SI unit of electrical resistivity is the ohm metre (Ωm). It is commonly
represented by the Greek letter ρ (rho). It is calculated by measuring the resistance
between opposite faces of a one metre cube of the material.
2) Calculate the resistance at 20°C of a piece of copper wire 200m long and of c.s.a. (cross
sectional area) 10mm
R = ρℓ /A
= (1.68*10-8 *200)/10*10-6 = 0.336Ω
Calculate the resistance at 20°C of a piece of copper wire 1000m long and of c.s.a. (cross
sectional area) 1mm
R = ρℓ /A
= (1.68*10-8 *1000)/1*10-6 = 16.8.Ω
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3) Calculate the resistance at 20°C of a piece of copper wire 1000m long and of c.s.a. (cross
sectional area) 0.5mm
R = ρℓ /A
= (1.68*10-8 *1000)/0.5*10-6 = 33.6Ω
Note that the csa of the wire in Q 3 is half that of the wire in Q2 and hence the resistance is
doubled. Both wires are the same length.
4) Calculate the resistance of a piece of wire, which at 0°C is 150Ω, when it is heated to
70°C. The material has a Temperature coefficient of 0.0055. The formula you need is
RT = R0[1 + αT]
RT = 150[1 + (0.0055 * 70)]
RT = 202.5 Ω
5) You have plotted a graph of resistance against temperature for a conductor and the
graph looks as below, work out the Temperature Coefficient for the material.
X Axis is temperature Y Axis is resistance
2250.00
2200.00
2150.00
2100.00
2050.00
2000.00
1950.00
1900.00
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
As temp rises by (44-26) degrees C so Resistance rises by (2200-2050)Ω
Hence temperature coefficient for the material is
150/18 = 8.333 Ω/Ω/°C
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6) Repeat the above for this graph and from the table choose what material this number
represents
110.00
108.00
106.00
104.00
102.00
100.00
98.00
96.00
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Material
Temp Coefficient @20°C α
Silver
0.0038
Copper
0.0039
Gold
0.0034
Aluminium
0.0039
As temperature rises by (35-25)°C so resistance rises by (106-102) Ω
Temperature coefficient is therefore 4/10 = 0.4
Within the limits of the accuracy of our experiment the material we were testing could have
been any on the list above. I am sure however that we would be able to identify the material
just by looking at it as these are four very identifiable elements.
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