How to Convert Resistance to Temperature

Resistance is the electrical property of a material that opposes the flow of electricity through it. This degree of resistance to electricity is defined by another property of the material called Resistivity.

The resistivity of a material is defined as the resistance to current flow between the opposite faces of a unit cube of the material (ohm per unit length). Hence the resistance R of a component is expressed by:

R = ρL/A

Where:
R = Resistance of the component in Ohms
L = Length of the component
A = Cross sectional Area of the component
ρ = Resistivity of the material

To use the above formula, L and A must be in compatible units

The resistivity, ρ, and resistance, R, are temperature dependant, usually having a positive temperature coefficient (resistance increases as temperature increases), except for some metal oxides and semiconductors which have a negative temperature coefficient. The metal oxides are used for making thermistors. The variation of resistance with temperature is given by:

R(T2) = R(T1)[1 + αΔT] 

Where:
R(T2) = Resistance at temperature T2
R(T1) = Resistance at temperature T1
α         = Temperature coefficient of resistance
ΔT      = (T2 – T1), Temperature difference between T1 and T2

The principle of temperature change with resistance is what is utilized in Resistance Temperature Detectors, RTDs to sense and measure temperature in many industrial applications. RTD resistance versus temperature tables are used to determine the resistance of an RTD at any given temperature. See How to Convert RTD Resistance to Temperature.

Next we take a look at how to convert resistance to temperature:

Problem 1:
What is the resistance of a platinum resistor at 250°C, if its resistance
at 20°C is 1000 Ω? Take α = 0.00385 per degree C

Solution:
R(T1) = 1000Ω , T1 = 20 degree C, T2 = 250 degree C and α  for platinum = 0.00385
Hence R(T2) = 1000[1+ (250 – 20)*0.00385] = 1,885.5Ω 

Problem 2:
A tungsten filament has a resistance of 1998 Ω at 20°C. What will its resistance
be at 263°C? Take α for tungsten = 0.0045.

Solution:
R(T1) = 1998Ω , T1 = 20 degree C, T2 = 263 degree C and α  for tungsten = 0.0045
Hence R(T2) = 1998[1+ (263 – 20)*0.0045] = 4,182.813Ω

Problem 3:
What is the coefficient of resistance per degree Celsius of a material, if the resistance is 2246Ω at 63°F and 3074Ω at 405°F?

Solution:
Recall that:
R(T2) = R(T1)[1 + αT] 

This we can re-arrange to give:
 α = [R (T2)/R (T1) – 1]/ΔT 

Now, R(T2) = 3074Ω, R(T1) = 2246Ω, T2 = 405 degree F, T1 = 63 degree F
ΔT = 405 – 63 = 342 degree F
But degree C =  (F - 32)*5/9

Therefore 342 degree F = [(342 – 32)*5]/9 = 172.222 degree C
α = [(3074/2246) – 1]/172.222 = 0.00214 per degree C