The electrical resistance of the material depends on its length, area, and resistivity by the following relationship.
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.
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.
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:
R2 = R1 [ 1 + α1 (T2 - T1)]
whereR1 = 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.