Relationship between Resistance and Temperature

The electrical resistance of the material depends on its length, area, and resistivity by the following relationship.
Resistance = [Resistivity * Length] / Area 
Where
  • Resistivity = Ω-m
  • Area = m2
  • Length = m

Today you'll learn the relationship between resistance and temperature.
relationship between resistance and temperature

The resistivity (Ω-m) is the temperature dependent physical property of the material. A change in temperature impacts the resistivity of material which in turn alters the resistance.

Technically the rate of change of resistance is measured in terms of the temperature coefficient of the material. Greek symbol α represents temperature coefficient of the material.

The equation below is used to find the resistance of object at any temperature when the resistance at some specific temperature is known.
R2 = R[ 1 + α(T- T1)]
where
R= Conductors resistance at temperature T1
R= Conductors resistance at temperature T2
α1 = Temperature coefficient of the material
T= Reference temperature at which  α1 is specified
T= Conductor present temperature

The temperature coefficient of commonly used materials at 0, 20° C is given below:
Materials at 20 degree C at 0 degree C
Aluminum 0.00391 0.00424
Copper 0.00393 0.00427
Iron 0.0055 0.00618
Silver 0.0038 0.00412

Example: Copper wire has the resistance of 15 ohms at 20° C. Calculate the resistance at 80° C

Solution: R2 = R[ 1 + α(T- T1)]

R2 = 15 Ω [ 1 + 0.00393 (80 - 20)]

R2 = 15 Ω ( 1.2358 )

R2 = 18.53 Ω

Positive temperature coefficient vs Negative temperautre coefficient

The material whose temperature increases with increase in temperature is known as positive temperature coefficient. While material whose temperature decreases with increases in temperature is known as positive temperature coefficient.

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