Question

Study the given table for resistance values of a platinum thermometer measured at a range of temperatures. Calculate the sensitivity of the measurement of the instrument.

Resistance (Ω)	Temperature (°C)
200	100
205	150
210	200
215	250

1. 0.1 Ω/°C
2. 0.9 Ω/°C
3. 0.5 Ω/°C
4. 1.0 Ω/°C

Answer 1

Correct Answer - Option 1 : 0.1 Ω/°C

Concept:

Sensitivity or Figure of merit:

Sensitivity is the measure that indicates the relation between change in output readings for change in input quantity for an instrument.

Sensitivity (s) = (change in output)/(change in input) = tanθ 

• For an instrument, we always prefer s = 1, so that the change in output is directly proportional to the change in input.
• If s<1 or s>1, the instrument indicates the non-linear reading.
• So, sensitivity plays a crucial role in designing the type of scale at the time of designing.
• In order to reduce the loading effect or error, high sensitive instruments are preferred.

Calculation:

Let's assume output as resistance and input as temperature, so that for change in temperature there will be some change in resistance.

Resistance (Ω)	Temperature (°C)
200	100
205	150
210	200
215	250

From the above table, we can observe that

For every 50°C temperature (input) change,  there is a 5 Ω change in resistance(output).

Then, the sensitivity is given by

S = (5 / 50) = .1 Ω/°C