JEE Main 2023 — Mathematics in Physics Question with Solution

For a parallel combination the equivalent resistance is 

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2} ...\left(i\right)$

A general expression for error can be written as $x\pm ∆x$

Differentiating equation (i)

$\frac{dR}{R^2}=\frac{d{R}_1}{R_1^2}+\frac{d{R}_2}{R_2^2} ...\left(ii\right)$

The equivalent resistance with $R_1=10 \mathrm{\Omega } \& {\mathrm{R}}_2=15 \mathrm{\Omega }$ is

$\frac{1}{R}=\frac{1}{10}+\frac{1}{15}$

$\Rightarrow R=\frac{150}{25}=6\Omega$

Substituting the above value in equation (ii)

$dR=36\left(\frac{0.5}{100}+\frac{0.5}{15\times 15}\right)=0.26$

$\Rightarrow R=6\pm 0.26$

Hence, the percentage error is 

$\frac{dR}{R}\times 100=\frac{0.26}{6}\times 100$$=4.33\%$