Question

The solution for the unknown resistance for a wheatstone bridge is

$R_x=\frac{R_2{R}_3}{R_1}$

where,
$R_1=100\pm 0.5\%$ $\Omega$, $R_2=1000\pm 0.5\%\Omega and$ $R_3=842\pm 0.5\%\Omega$

The range of the unknown resistance $R_x$ is

• A. $8293.7\Omega to8546.3\Omega$
• B. $8546.3\Omega to8672.6\Omega$
• C. $8167.4\Omega to8293.7\Omega$
• D. $8167.4\Omega to8546.3\Omega$

Answer 1

The correct option is A $8293.7\Omega to8546.3\Omega$

$\text{Unknown resistance,}$

$R_x=\frac{R_2{R}_3}{R_1}=\frac{1000\times 842}{100}=8420\Omega$

$\text{Relative limiting error of unknown resistance is}$

$\frac{\delta R_x}{R_x}=\pm (\frac{\delta R_2}{R_2}+\frac{\delta R_3}{R_3}+\frac{\delta R_1}{R_1})=\pm (0.5+0.5+0.5)=\pm 1.5\%$

$\text{Limiting error in ohm}$

$=8420\times \frac{1.5}{100}=\pm 126.3\Omega$

$\text{Guranteed values of resistance are between}$

$(8420-126.3)to(8420+126.3)$

$\left(8293.7\Omega \right)to\left(8546.3\Omega \right)$