### rtd resistance ratios

How do you interpret a calibration report listing resistance ratio's and inverse differences?

The resistance ratio is the ratio of the resistance of the thermometer at some temperature (t) to the resistance of the thermometer at the ice point (t0).

Example:

If the resistance of a platinum resistance thermometer is 25.51548 ohms at the ice point, what is the temperature when its resistance is 26.53035

The Resistance ratio (RR) is expressed as: RR= RT / RO

The resistance ratio is found as follows: 26.53035 / 25.51548, RR= 1.03977467

The table indicates that this ratio corresponds to + 10°C.

The inverse difference column is provided as an aid to interpolation. The inverse difference listed in the table is the reciprocal of the difference between the resistance ratios at that temperature and the next lower temperature.

If the resistance ratio (RR) does not result in a whole number on the temperature scale, linear interpolation may be used to find the temperature using the following expression: t = t2 +[(RR - RR2) x ID] where:

t = the measurement temperature

t2 = the lower of the two temperatures in the table which bracket the resistance ratio computed

RR = the resistance ratio computed in the measurement

RR2 = the resistance ratio at t2

ID = the inverse difference for the temperature which has the resistance ratio which is just greater than RR

Example: The ice point resistance of a thermometer is 25.51548 ohms. The resistance of the thermometer at some temperature is measured as 25.84327 ohms. What is the temperature? The resistance ratio is found as follows:

RR=RT/R0

25.84327 / 25.51548

RR = 1.01284671

The chart indicates this ratio lies between 3°C and 4°C. The inverse difference for 4°C is 251.0493, and the resistance ratio for 3°C is 1.01191728.

Substituting these values into equation yields:

t = t2 +[(RR - RR2) x ID]

t = 3°C+ (1.01284671 - 1.01191728 ) x 251.0493

3°C + (.00092943) x 251.0493

3°C + .2333327 or: t = 3. 2333327C7 °C

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