Physics - Error Question with Solution | TestHub

Equivalent resistance in parallel combination is given by
$\begin{array}{rl}& \frac{1}{R_{\text{eq }}}=\frac{1}{R_1}+\frac{1}{R_2}\\ & \Rightarrow R_{\text{eq }}=\frac{R_1{R}_2}{R_1+R_2}=\frac{10\times 15}{10+15}=6\end{array}$
Differentiating both sides, we get
$\begin{array}{rl}& \frac{\Delta R_{\text{eq }}}{{\mathrm{R}}_{\mathrm{eq}}^2}=\frac{\Delta {\mathrm{R}}_1}{{\mathrm{R}}_1^2}+\frac{\Delta {\mathrm{R}}_2}{{\mathrm{R}}_2^2}\\ & \Rightarrow \frac{\Delta {\mathrm{R}}_{\mathrm{eq}}}{{\mathrm{R}}_{\mathrm{eq}}}=\left(\frac{\Delta {\mathrm{R}}_1}{{\mathrm{R}}_1^2}+\frac{\Delta {\mathrm{R}}_2}{{\mathrm{R}}_2^2}\right){\mathrm{R}}_{\mathrm{eq}}\\ & =\left(\frac{0.5}{100}+\frac{0.5}{225}\right)\cdot 6=\left(\frac{6\times 0.5}{25}\right)\left(\frac{1}{4}+\frac{1}{9}\right)=\frac{13}{300}\\ & \frac{\Delta {\mathrm{R}}_{\mathrm{eq}}}{{\mathrm{R}}_{\mathrm{eq}}}\times 100=\frac{13}{3}=4.33\%\end{array}$