Question

A variable w is related to three other variables $x,y,z$ as $w=xy/z$. The variables are measured with meters of accuracy $\pm 0.5$% reading, $\pm 1$% of full scale value and $\pm 1.5$% reading . The actual readings of the three meters are 80, 20 and 50 with 100 being the full scale value for all three. The maximum limiting error in the measurement of $w$ will be

• A. $\pm 0.5\%rdg$
• B. $\pm 5.5\%rdg$
• C. $\pm 6.7\%rdg$
• D. $\pm 7.0\%rdg$

Answer 1

The correct option is D $\pm 7.0\%rdg$

$\text{Variables are measured with accuracy}$

$x=\pm \text{0.5 \% of reading 80 [Limiting error]}$

$y=\pm \text{1 \% of full scale value [Guaranteed error]}$

$\text{Then Limiting error of y}$

$20\left[\frac{x}{100}\right]=\pm 1\%$

$x=5\%\text{[Limiting errors]}$

$z=\pm 1.5\%\text{reading so Limiting error}$

$w=\frac{xy}{z}$

$\text{Limiting error}$

$=\pm [0.5\%+5\%+1.5\%]$

$=\pm 7\%$