The radius ( r), length (l) and resistance (R) of a metal wire wa… - Vidyadip

MCQ

The radius ( $\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as

$\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}$

$\mathrm{R}=(100 \pm 10) \mathrm{ohm}$

$l=(15 \pm 0.2) \mathrm{cm}$

The percentage error in resistivity of the material of the wire is :

A
$25.6 \%$
✓
$39.9 \%$
C
$37.3 \%$
D
$35.6 \%$

✓

Answer

Correct option: B.

$39.9 \%$

b
$\rho={R} \frac{\rho}{\ell}$

$\frac{\Delta \rho}{\rho}=\frac{\Delta \mathrm{R}}{\mathrm{R}}+2 \frac{\Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \ell}{\ell}$

$=\frac{10}{100}+2 \times \frac{0.05}{0.35}+\frac{0.2}{15}$

$=\frac{1}{10}+\frac{2}{7}+\frac{1}{75}$

$\frac{\Delta \rho}{\rho}=39.9 \%$

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