Write an expression for the resistivity of a metallic conductor showing its variation over
Answers
Explanation:
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The attributes like shape or the cross-sectional area have an impact on the resistance of the conductor, but resistivity is not affected by it. Resistivity is only affected by the change in temperature. The relationship between resistivity and temperature is
Δρ = α * ΔT * ρ0
Where:
Δρ : Change of the resistivity
α : Resistivity, temperature coefficient
ΔT : Change of temperature
ρ0 : Original resistivity
For example, at 20 °C (293 K), the resistivity of Copper at 20 °C is 1.68 * 10-8 , it's temperature coefficient is 0.0039 K-1, its resistivity at 30 °C is 1.75E-8.
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Another Expression for Resistivity Variation with Temperature
As stated above, the resistivity ‘r’ of a conductor is unaffected by its shape and size but is affected by its temperature. Increase in temperature results in an increase in ‘r’ especially in the case of Ohmic conductors. If the given temperature is denoted by ‘T’ then the expression for ‘r’ is:
r(t) = r0 (1 + a DT), where r0 = resistivity at 0oC,
a = temperature coefficient of resistivity.
Also, a = (p – p0) / p0ΔT or
a = 1 / p dp / dT.
For conductors ‘a’ is a positive constant but for insulators and semiconductors it is negative.
We have tabulated below the values of resistivity of certain metals. It will provide you a clear idea of the effect of temperature on resistivity of metals.
Metal
Resistivity (Ω . m) at 20 °C
Temperature coefficient [K-1]
Silver
1.59 × 10-8
0.0038
Copper
1.68 × 10-8
0.0039
Gold
2.44 × 10-8
0.0034
Aluminium
2.82 × 10-8
0.0039
Calcium
3.36 × 10-8
Tungsten
5.60 × 10-8
0.0045
Zinc
5.90 × 10-8
0.0037
Nickel
6.99 × 10-8
0.006
Iron
1.0 × 10-7
0.005
Platinum
1.06 × 10-7
0.00392
Tin
1.09 × 10-7
0.0045
Lead
2.2 × 10-7
0.0039
Manganin
4.82 × 10-7
0.000002
Constantan
4.9 × 10-7
0.000008
Mercury
9.8 × 10-7
0.0009
Nichrome
1.10 × 10-6
0.0004
Carbon
3.5 × 10-5
-0.0005
Germanium
4.6 × 10-1
-0.048
Silicon
6.40 × 102
-0.075
Besides metals, we list below certain insulators with their resistivity:
P.V.C. 5.4 x 1015
Glass 104
Quartz 1012
P.T.F.E 1012
Here, P.T.F.E stands for polytetrafluoroethylene which is used for the insulation of high voltage cables. The values in the above table clearly show that the resistivity of insulators is much higher than that of conductors.