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Question

A temperature sensor having a range of 0-100°C has a worst case accuracy specification of ±1.0% of true value or ±0.3% of full scale, whichever is higher. The sensitivity of the sensor is experimentally obtained by taking its readings at true temperatures 25°C and 75°C. The maximum error in sensitivity, expressed as percentage of its ideal value is

A
±0.105%
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B
±0.021%
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C
±1.05%
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D
±2.1%
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Solution

The correct option is C ±1.05%
In the given sensor, there are two sources of error, one expressed as % true value and other as % full scale.

Also sensitivity of transducer =outputinput

Sensitivity=xT

where x is output of sensor at input temperature T.

Now, i.e., error in sensitivity,

(i) At 25°C/75°C due to ±1% of true value error in input only.

e1=x24.75x25x25×100=±1.01%

e2=x74.25x75x75×100=±1.01

(ii) At 25°C/75°C due to ±0.3% of full scale error in input only.

error in input (in °C)

=±100×0.3100=0.3C

e3=x24.70x25x25×100=±1.21%

e4=x74.7x75x75×100=±0.4%

So, emax=max(e1, e2, e3, e4)

emax=±1.21%

Note: While calculating maximum error, we have considered negative deviation. This is because error in above case will be more if negative deviation is taken.

For instance,

e3=x25.30x25x25×100

=±1.186% <e3

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