Question

Two resistors $R_1$ and $R_2$ are connected in series. The value of resistance are
$R_1=100.0\pm 0.1\Omega ,R_2=50\pm 0.03\Omega$
If the error in $R_{1}or{R}_2$ has to be considered as standard deviation then the standard deviation in series equivalent resistance is

• A. $\pm 0.13\Omega$
• B. $\pm 0.10\Omega$
• C. $\pm 0.20\Omega$
• D. $\pm 0.15\Omega$

Answer 1

The correct option is B $\pm 0.10\Omega$

When the two resistances are connected in series, the resultant resistance is
$R=R_1+R_2$

$\frac{\partial R}{\partial R_1}=1and\frac{\partial R}{\partial R_2}=1$
Hence, standard deviation in series is resistance

${\sigma }_R=\sqrt{{\left(\frac{\partial R}{\partial R_1}\right)}^2{\sigma }_{R_1}^2+{\left(\frac{\partial R}{\partial R_2}\right)}^2{\sigma }_{R_2}^2}$

$=\pm \sqrt{1^2{\left(0.1\right)}^2+{\left(1\right)}^2{\left(0.03\right)}^2}=\pm 0.104\Omega$