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.

Resistivity Coefficient (ohm m) (default value for copper)

Cross sectional area of the conductor (mm ² ) - AWG Wire Gauge

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 = 10 ^-2 Ω cm = 2.54 10 ^-2 Ω inch = 3.048 10 ^-1 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.

ρ - resistivity coefficient (10 ^-8 ohm m ² /m)

α - temperature coefficient (10 ^-3 1/ ^o C)

dt - change in temperature ( ^o C)

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.

R _s - resistance (10 ³ (ohm)

α - temperature coefficient (10 ^-3 1/ ^o C)

dt - change in temperature ( ^o C)

Temperature Correction Factors for Conductor Resistance

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

Temperature ^oC
K
^oF

Length m
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naut miles

Area m²
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Volume m³
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us gal

Weight kg_f
N
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Velocity m/s
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Pressure Pa
bar
mm H₂O
kg/cm²
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inches H₂O

Flow m³/s
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US gpm
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