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Formulas Temperature Measurement

Calculate Temperature Coefficient of RTD’s

RTD’s are based on the principle that the resistance of a metal increases with temperature. The temperature coefficient of resistance (TCR) for resistance temperature detectors (denoted by RTD temperature coefficient

), is normally defined as the average resistance change per °C over the range 0 °C to 100 °C, divided by the resistance of the RTD, Ro, at 0 °C.

temperature coefficient of RTD

where,

 R0 = resistance of rtd at 0 °C (ohm), and

R100 = resistance of rtd at 100 °C (ohm),

Note: Here we are discussing about RTD PT100 only.
RTD Graph

 As a first approximation, the relationship between resistance and temperature, may then be expressed as (see Figure 2):

RTD Formula to Calculate Resistance

where: Rt = resistance of rtd at temperature t (ohm),

Ro = resistance of rtd at 0 °C (ohm), and

RTD temperature coefficient = temperature coefficient of resistance (TCR) at 0 °C (per °C)

Example

A platinum RTD PT100 measures 100 Ω at 0 °C and 139.1 Ω at 100 °C.

  • calculate the resistance of the RTD at 50 °C.
  • Calculate the TCR for platinum.
  • calculate the temperature when the resistance is 110 Ω.

Calculate the Temperature Coefficient of RTD PT100

From Equation – 1 :

Calculate the Temperature Coefficient of RTD PT100

Calculate the resistance of the RTD at 50 °C

From Equation – 2 :

R50 = Ro(1 + αt) = 100(1 + 0.00391×50) = 119.55Ω

Calculate the temperature when the resistance is 110 ohms

From Equation – 2:

Rt = Ro(1 + αt) ⇒ 110 = 100(1 + 0.00391t)
=1 + 0.00391t = 1.1 ⇒ 0.00391t = 0.1 ⇒ t = 25.58 °C.

Also Read : Resistance Temperature Detectors Working Principle

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4 comments

Anand April 24, 2016 at 4:27 pm

Dear sir,
last question u made a mistake that calculate the temperature for the resistance at 110 ohm but u mentioned 100 *c

Reply
S Bharadwaj Reddy April 24, 2016 at 6:38 pm

Thank you Anand. updated the answer.

Reply
victory February 11, 2018 at 8:10 pm

please sir help me in this calculation,
the resistance Rt of a platinum wire at temperature Tdegree measured on the glass scale is given by Rt=Ro(1 + at +bt) where a=3.800*10^MINUS3 and b=5.6*10^minus7 .What temperature will the platinum thermometer indicate when the temperature of the gas scale is
200degree

Reply
mobin June 12, 2016 at 7:56 pm

I think there is another easy method to convert ohms to temperature
To convert temperature to ohms..
If u knows then write please

Reply

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