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 α_{o}), 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, R_{o}, at 0 °C.

where,

** **R_{0} = resistance of rtd at 0 °C (ohm), and

R_{100} = resistance of rtd at 100 °C (ohm),

Note: Here we are discussing about RTD PT100 only.

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

where: R_{t} = resistance of rtd at temperature t (ohm),

R_{o} = resistance of rtd at 0 °C (ohm), and

α_{o }= 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 resistance of the RTD at 50 °C

From Equation – 2 :

R_{50} = R_{o}(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)

Rt =1 + 0.00391t = 1.1 ⇒ 0.00391t = 0.1 ⇒ t = 25.58 °C.

**Also Read : RTD Working Principle**

## 5 comments

Dear sir,

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

Thank you Anand. updated the answer.

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

I think there is another easy method to convert ohms to temperature

To convert temperature to ohms..

If u knows then write please

subtract the ohms you get from 138.5 and the answer you get divide by 38.5 then multiply by 100. eg. 110ohms from 138.5 ohms you get 28.5 ohms. divide that by 38.5 equals 0.714 multiply by 100 equals 71.2 deg.