Resistance of rod is calculated by measuring its length with help of meter scale of least count $1\ mm$ . Its radius is measured with help of screw gauge having $50$ division on circular scale and pitch is of $1\ mm$ . Resistivity of material is exact. Length of the wire is found to be $20\ cm$ and diameter of wire is $4\ mm$ . Find the percentage error in calculation of resistance ............... $\%$
Medium
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$\mathrm{R}=\frac{\rho \ell}{\mathrm{A}}$
$\frac{1 \Delta \mathrm{R}}{\mathrm{R}}=\frac{1 \Delta \ell}{\ell}+\frac{2 \Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \rho}{\rho}$
Maximum error is least count of an instrument
$\therefore \quad 1.5 \%$
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