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.

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 = R₁ [ 1 + α₁ (T₂ - T₁)]

where
R₁ = Conductors resistance at temperature T₁
R₂ = Conductors resistance at temperature T₂
α₁ = Temperature coefficient of the material
T₁ = Reference temperature at which  α₁ is specified
T₂ = 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 = R₁ [ 1 + α₁ (T₂ - 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.