QETA009 Electrical Principles
9.1 Resistivity and Temperature Coefficient
Name .................
Formulae
  R
A
R = R [1 + α(T − T )]
T
r
r
(Tr is the temperature at which the coefficient is given)
R = R [1 + αT] (simplified form, used if coefficient is given at 0°C)
T
0
Resistivity of Copper 1.68E-08 @20°C
Temperature Coefficient of Copper is 0.0039 Ωs/Ω/°C at 20°C
Exercise
1) Express in terms of square metres the cross sectional area of a wire of csa
10mm2.
One square meter is 1,000,000 square millimetres so one mm is one
millionth of one m2
1 mm2 = 0.000001m2 (i.e. 1e-6m2) so 10mm2 is 10e-6m2
2) Given a piece of 10mm2 csa copper wire 18m long work out the resistance if
the resistivity of Copper is as above.
R = ρL/A
(1.68e-8 *18)/10e-6 = 0.0302Ω
3) Given a piece of 6mm2 csa copper wire 58m long work out the resistance.
R = ρL/A = (1.68e-8 * 58)/ 6e-6 = 0.l62Ω
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4) Work out the resistance of a piece of 1mm2 csa copper wire 200m long.
R = ρL/A = (1.68e-8 * 200)/ 1e-6 = 3.36Ω
5) If a piece of copper wire has a resistance of 22Ω at 0°C what is its resistance
at 120 degrees C?
R = R [1 + α(T − T )]
T
r
r
R = 22[1 + 0.0039(120 − 0)] = 32.29Ω
T
If a piece of copper wire has a resistance of 22Ω at 20°C what is its resistance
at 120 degrees C?
R = R [1 + α(T − T )]
T
r
r
R = 22[1 + 0.0039(120 − 20)] = 22.39Ω
T
6) If a piece of copper wire has a resistance of 11Ω at 0°C what is its resistance
at 15°C?
R = R [1 + α(T − T )]
T
r
r
R = 11[1 + 0.0039(15 − 0)] = 11.643 Ω
T
7) If we have a piece of wire 100m long and a csa of 10mm 2 what is the
resistivity of the material if the resistance of the sample is 0.85Ω?
ρ = RA/L =(0.85*10e-6)/100 = 8.5e-8
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8) If a piece of copper has a resistance of 0.55Ω at 20°C what is its resistance at
100 degrees C?
R = R [1 + α(T − T )]
T
r
r
R = 0.55[1 + 0.0039(100− 20)] = 0.862Ω
T
9) Express in terms of square metres the cross sectional area of a wire of csa
15mm2.
15e-6m2
10) Explain the term Negative temperature Coefficient with respect to resistors.
If a resistance has a negative temperature coefficient then its resistance
decreases with increasing temperature.
11)
Resistance Ω
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
Temp °C
In the chart above, state if this line demonstrates Positive or Negative
Temperature Coefficient and, from the line, work out the value of the
Temperature Coefficient for the resistor that this chart represents.
This is chart for a PTC and its temperature coefficient is 6/15 = 0.4
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12) Describe, using diagrams, how you would determine a rough value for the
Temperature Coefficient of a resistor. Draw a sketch of the equipment that you
would assemble to do this and write the method for the experiment below.
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13) Look at the table below and decide if the two components shown are NTC or
PTC
14) Using the figures from the table above roughly estimate the value of
resistance for the 100Ω Thermistor when the temperature is 50°C
15) State why this kind of estimation is less reliable for a NTC Thermistor
The curve for an NTC component is not linear so estimations made
without the curve are invalid.
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