Resistivity and Conductivity - Temperature Coefficients Common Materials
Resistivity is
- the electrical resistance of a unit cube of a material measured between the opposite faces of the cube
Electric Conductor Resistance Calculator
This calculator can be used to calculate electrical resistance of a conductor.
Material | Resistivity Coefficient ^{ 2) } - ρ - (ohm m^{2}/m) ( Ω m ) | Temperature Coefficient ^{ 2) - α - } (per degree C) (1/^{o}C) | Conductivity - σ - (1 /(Ω m)) |
---|---|---|---|
Aluminum | 2.65 x 10^{-8} | 3.8 x 10^{-3} | 3.77 x 10^{7 } |
Aluminum alloy 3003, rolled | 3.7 x 10^{-8} | ||
Aluminum alloy 2014, annealed | 3.4 x 10^{-8} | ||
Aluminum alloy 360 | 7.5 x 10^{-8} | ||
Aluminum bronze | 12 x 10^{-8} | ||
Animal fat | 14 x 10^{-2} | ||
Animal muscle | 0.35 | ||
Antimony | 41.8 x 10^{-8} | ||
Barium (0 ^{o}C) | 30.2 x 10^{-8} | ||
Beryllium | 4.0 x 10^{-8} | ||
Beryllium copper 25 | 7 x 10^{-8} | ||
Bismuth | 115 x 10^{-8} | ||
Brass - 58% Cu | 5.9 x 10^{-8} | 1.5 x 10^{-3} | |
Brass - 63% Cu | 7.1 x 10^{-8} | 1.5 x 10^{-3} | |
Cadmium | 7.4 x 10^{-8} | ||
Caesium (0 ^{o}C) | 18.8 x 10^{-8} | ||
Calcium (0 ^{o}C) | 3.11 x 10^{-8} | ||
Carbon (graphite) ^{ 1) } | 3 - 60 x 10 ^{ -5 } | -4.8 x 10^{-4} | |
Cast iron | 100 x 10^{-8} | ||
Cerium (0 ^{o}C) | 73 x 10^{-8} | ||
Chromel (alloy of chromium and aluminum) | 0.58 x 10^{-3} | ||
Chromium | 13 x 10^{-8} | ||
Cobalt | 9 x 10^{-8} | ||
Constantan | 49 x 10^{-8} | 3 x 10 ^{ -5 } | 0.20 x 10^{7} |
Copper | 1.724 x 10^{-8} | 3.93 x 10^{-3} | 5.95 x 10^{7} |
Cupronickel 55-45 (constantan) | 43 x 10^{-8} | ||
Dysprosium (0 ^{o}C) | 89 x 10^{-8} | ||
Erbium (0 ^{o}C) | 81 x 10^{-8} | ||
Eureka | 0.1 x 10^{-3} | ||
Europium (0 ^{o}C) | 89 x 10^{-8} | ||
Gadolium | 126 x 10^{-8} | ||
Gallium (1.1K) | 13.6 x 10^{-8} | ||
Germanium ^{ 1) } | 1 - 500 x 10^{-3} | -50 x 10^{-3} | |
Glass | 1 - 10000 x 10^{9} | 10^{-12} | |
Gold | 2.24 x 10^{-8} | ||
Graphite | 800 x 10^{-8} | -2.0 x 10^{-4} | |
Hafnium (0.35K) | 30.4 x 10^{-8} | ||
Hastelloy C | 125 x 10^{-8} | ||
Holmium (0 ^{o}C) | 90 x 10^{-8} | ||
Indium (3.35K) | 8 x 10^{-8} | ||
Inconel | 103 x 10^{-8} | ||
Iridium | 5.3 x 10^{-8} | ||
Iron | 9.71 x 10^{-8} | 6.41 x 10^{-3} | 1.03 x 10^{7} |
Lanthanum (4.71K) | 54 x 10^{-8} | ||
Lead | 20.6 x 10^{-8} | 0.45 x 10^{7} | |
Lithium | 9.28 x 10^{-8} | ||
Lutetium | 54 x 10^{-8} | ||
Magnesium | 4.45 x 10^{-8} | ||
Magnesium alloy AZ31B | 9 x 10^{-8} | ||
Manganese | 185 x 10^{-8} | 1.0 x 10 ^{ -5 } | |
Mercury | 98.4 x 10^{-8} | 8.9 x 10^{-3} | 0.10 x 10^{7} |
Mica (Glimmer) | 1 x 10 ^{ 13 } | ||
Mild steel | 15 x 10^{-8} | 6.6 x 10^{-3} | |
Molybdenum | 5.2 x 10^{-8} | ||
Monel | 58 x 10^{-8} | ||
Neodymium | 61 x 10^{-8} | ||
Nichrome (alloy of nickel and chromium) | 100 - 150 x 10^{-8} | 0.40 x 10^{-3} | |
Nickel | 6.85 x 10^{-8} | 6.41 x 10^{-3} | |
Nickeline | 50 x 10^{-8} | 2.3 x 10^{-4} | |
Niobium (Columbium) | 13 x 10^{-8} | ||
Osmium | 9 x 10^{-8} | ||
Palladium | 10.5 x 10^{-8} | ||
Phosphorus | 1 x 10 ^{ 12 } | ||
Platinum | 10.5 x 10^{-8} | 3.93 x 10^{-3} | 0.943 x 10^{7} |
Plutonium | 141.4 x 10^{-8} | ||
Polonium | 40 x 10^{-8} | ||
Potassium | 7.01 x 10^{-8} | ||
Praseodymium | 65 x 10^{-8} | ||
Promethium | 50 x 10^{-8} | ||
Protactinium (1.4K) | 17.7 x 10^{-8} | ||
Quartz (fused) | 7.5 x 10 ^{ 17 } | ||
Rhenium (1.7K) | 17.2 x 10^{-8} | ||
Rhodium | 4.6 x 10^{-8} | ||
Rubber - hard | 1 - 100 x 10^{13 } | ||
Rubidium | 11.5 x 10^{-8} | ||
Ruthenium (0.49K) | 11.5 x 10^{-8} | ||
Samarium | 91.4 x 10^{-8} | ||
Scandium | 50.5 x 10^{-8} | ||
Selenium | 12.0 x 10^{-8} | ||
Silicon ^{ 1) } | 0.1-60 | -70 x 10^{-3} | |
Silver | 1.59 x 10^{-8} | 3.82 x 10^{-3} | 6.29 x 10^{7} |
Sodium | 4.2 x 10^{-8} | ||
Soil, typical ground | 10^{-2} - 10^{-4} | ||
Solder | 15 x 10^{-8} | ||
Stainless steel | 10^{6} | ||
Strontium | 12.3 x 10^{-8} | ||
Sulfur | 1 x 10 ^{ 17 } | ||
Tantalum | 12.4 x 10^{-8} | ||
Terbium | 113 x 10^{-8} | ||
Thallium (2.37K) | 15 x 10^{-8} | ||
Thorium | 18 x 10^{-8} | ||
Thulium | 67 x 10^{-8} | ||
Tin | 11.0 x 10^{-8} | 4.2 x 10^{-3} | |
Titanium | 43 x 10^{-8} | ||
Tungsten | 5.65 x 10^{-8} | 4.5 x 10^{-3} | 1.79 x 10^{7} |
Uranium | 30 x 10^{-8} | ||
Vanadium | 25 x 10^{-8} | ||
Water, distilled | 10^{-4} | ||
Water, fresh | 10^{-2} | ||
Water, salt | 4 | ||
Ytterbium | 27.7 x 10^{-8} | ||
Yttrium | 55 x 10^{-8} | ||
Zinc | 5.92 x 10^{-8} | 3.7 x 10^{-3} | |
Zirconium (0.55K) | 38.8 x 10^{-8} |
^{ 1) } Note! - the resistivity depends strongly on the presence of impurities in the material.
^{ 2 } ^{ ) } Note! - the resistivity depends strongly on the temperature of the material. The table above is based on 20 ^{o}C reference.
Convert between Electrical Resistivity Units
- 1 Ω m = 0.001 kΩ m = 10^{2} Ω cm = 39.37 Ω inch = 3.28 Ω foot
Electrical Resistance in a Wire
The electrical resistance of a wire is greater for a longer wire and less for a wire of larger cross sectional area. The resistance depend on the material of which it is made and can be expressed as:
R = ρ L / A (1)
where
R = resistance (ohm, Ω )
ρ = resistivity coefficient (ohm m, Ω m)
L = length of wire (m)
A = cross sectional area of wire (m^{2})
The factor in the resistance which takes into account the nature of the material is the resistivity. Since it is temperature dependent, it can be used to calculate the resistance of a wire of given geometry at different temperatures.
The inverse of resistivity is called conductivity and can be expressed as:
σ = 1 / ρ (2)
where
σ = conductivity (1 / Ω m)
Example - Resistance in an Aluminum Wire
Resistance of an aluminum cable with length 10 m and cross sectional area of 3 mm^{2} can be calculated as
R = (2.65 10^{-8} Ω m) (10 m) / ((3 mm^{2}) (10^{-6} m^{2}/mm^{2}))
= 0.09 Ω
Resistance
The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it:
R = U / I (3)
where
R = resistance (ohm)
U = voltage (V)
I = current (A)
Ohm's Law
If the resistance is constant over a considerable range of voltage, then Ohm's law,
I = U / R (4)
can be used to predict the behavior of the material.
Resistivity vs. Temperature
Change in resistivity vs. temperature can be calculated as
dρ = ρ α dt (5)
where
dρ = change in resistivity (ohm m^{2}/m)
α = temperature coefficient (1/ ^{o}C)
dt = change in temperature (^{o}C)
Example - Change in Resistivity
Aluminum with resistivity 2.65 x 10^{-8} ohm m^{2}/m is heated from 20 ^{o}C to 100 ^{o}C . The temperature coefficient for aluminum is 3.8 x 10^{-3} 1/ ^{o}C . The change in resistivity can be calculated as
dρ = (2.65 10^{-8} ohm m^{2}/m) (3.8 10^{-3} 1/ ^{o}C) ((100 ^{o}C) - (20 ^{o}C))
= 0.8 10 ^{-8} ohm m^{2}/m
The final resistivity can be calculated as
ρ = (2.65 10^{-8} ohm m^{2}/m) + (0.8 10^{-8} ohm m^{2}/m)
= 3.45 10 ^{-8} ohm m^{2}/m
Resistivity Coefficient vs. Temperature Calculator
This caculator can be used to calculate resistivity in a conductor material vs. temperature.
Resistance and Temperature
For most materials the electrical resistance increases with temperature. Change in resistance can be expressed as
dR / R _{ s } = α dT (6)
where
dR = change in resistance (ohm)
R _{ s } = standard resistance according reference tables (ohm)
α = temperature coefficient of resistance ( ^{o}C^{-1} )
dT = change in temperature from reference temperature ( ^{o}C, K)
(5) can be modified to:
dR = α dT R _{ s }(6b)
The "temperature coefficient of resistance" - α - of a material is the increase in the resistance of a 1 Ω resistor of that material when the temperature is increased 1 ^{o}C .
Example - Resistance of a Copper Wire in Hot Weather
A copper wire with resistance 0.5 kΩ at normal operating temperature 20 ^{o}C is in hot sunny weather heated to 80 ^{o}C . The temperature coefficient for copper is 4.29 x 10^{-3} (1/ ^{o}C) and the change in resistance can be calculated as
dR = ( 4.29 x 10^{-3} 1/ ^{o}C) ((80 ^{o}C) - (20 ^{o}C) ) (0.5 kΩ)
= 0.13 (kΩ)
The resulting resistance for the copper wire in hot weather will be
R = (0.5 kΩ) + (0.13 kΩ)
= 0.63 (kΩ)
= 630 (Ω)
Example - Resistance of a Carbon Resistor when Temperature is changed
A carbon resistor with resistance 1 kΩ at temperature 20 ^{o}C is heated to 120 ^{o}C . The temperature coefficient for carbon is negative -4.8 x 10^{-4} (1/ ^{o}C) - the resistance is reduced with increasing temperature.
The change in resistance can be calculated as
dR = ( -4.8 x 10^{-4} 1/ ^{o}C) ((120 ^{o}C) - (20 ^{o}C) ) (1 kΩ)
= - 0.048 (kΩ)
The resulting resistance for the resistor will be
R = (1 kΩ) - (0.048 kΩ)
= 0.952 (kΩ)
= 952 (Ω)
Resistance vs. Temperature Calculator
This caculator can be used to calculate resistance in a conductor vs. temperature.
Temperature Correction Factors for Conductor Resistance
Temperature of Conductor (°C) | Factor to Convert to 20°C | Reciprocal to Convert from 20°C |
---|---|---|
5 | 1.064 | 0.940 |
6 | 1.059 | 0.944 |
7 | 1.055 | 0.948 |
8 | 1.050 | 0.952 |
9 | 1.046 | 0.956 |
10 | 1.042 | 0.960 |
11 | 1.037 | 0.964 |
12 | 1.033 | 0.968 |
13 | 1.029 | 0.972 |
14 | 1.025 | 0.976 |
15 | 1.020 | 0.980 |
16 | 1.016 | 0.984 |
17 | 1.012 | 0.988 |
18 | 1.008 | 0.992 |
19 | 1.004 | 0.996 |
20 | 1.000 | 1.000 |
21 | 0.996 | 1.004 |
22 | 0.992 | 1.008 |
23 | 0.988 | 1.012 |
24 | 0.984 | 1.016 |
25 | 0.980 | 1.020 |
26 | 0.977 | 1.024 |
27 | 0.973 | 1.028 |
28 | 0.969 | 1.032 |
29 | 0.965 | 1.036 |
30 | 0.962 | 1.040 |
31 | 0.958 | 1.044 |
32 | 0.954 | 1.048 |
33 | 0.951 | 1.052 |
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