Question

A temperature sensor having a range of 0-100°C has a worst case accuracy specification of $\pm 1.0\%$ of true value or $\pm 0.3\%$ 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. $\pm 0.105\%$
• B. $\pm 0.021\%$
• C. $\pm 1.05\%$
• D. $\pm 2.1\%$

Answer 1

The correct option is C $\pm 1.05\%$

In the given sensor, there are two sources of error, one expressed as % true value and other as % full scale.

$\text{Also sensitivity of transducer =}\frac{\text{output}}{\text{input}}$

$\Rightarrow \text{Sensitivity}=\frac{x}{T}$

where x is output of sensor at input temperature T.

Now, i.e., error in sensitivity,

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

$e_1=\frac{\frac{x}{24.75}-\frac{x}{25}}{\frac{x}{25}}\times 100=\pm 1.01\%$

$e_2=\frac{\frac{x}{74.25}-\frac{x}{75}}{\frac{x}{75}}\times 100=\pm 1.01$

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

error in input (in °C)

$=\pm \frac{100\times 0.3}{100}={0.3}^{\circ }C$

$e_3=\frac{\frac{x}{24.70}-\frac{x}{25}}{\frac{x}{25}}\times 100=\pm 1.21\%$

$e_4=\frac{\frac{x}{74.7}-\frac{x}{75}}{\frac{x}{75}}\times 100=\pm 0.4\%$

$So,e_{max}=max(e_1,e_2,e_3,e_4)$

$\Rightarrow e_{max}=\pm 1.21\%$

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,

$e_3^{{}^{\prime }}=\frac{\frac{x}{25.30}-\frac{x}{25}}{\frac{x}{25}}\times 100$

$=\pm 1.186\%<e_3$