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A potential difference $V=100 \pm 5 \mathrm{~V}$, when applied across a resistance, gives a current $I=10 \pm 0.2 \mathrm{~A}$. What is the percentage error in $R$ ?
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The correct answer is:
$7 \%$
Potential difference is $V=100 \pm 5 \mathrm{~V}$
Current is $I=10 \pm 0.2 \mathrm{~A}$.
Percentage error in voltage is obtained as
$\frac{\Delta V}{V}=\frac{5}{100} \times 100 \%=5 \%$
Percentage error in current is obtained as
$\frac{\Delta I}{I}=\frac{0.2}{10} \times 100 \%=2 \%$
Using, $R=\frac{V}{I}$, the percentage error in resistance is calculated as $R=5 \%+2 \%=7 \%$.
Current is $I=10 \pm 0.2 \mathrm{~A}$.
Percentage error in voltage is obtained as
$\frac{\Delta V}{V}=\frac{5}{100} \times 100 \%=5 \%$
Percentage error in current is obtained as
$\frac{\Delta I}{I}=\frac{0.2}{10} \times 100 \%=2 \%$
Using, $R=\frac{V}{I}$, the percentage error in resistance is calculated as $R=5 \%+2 \%=7 \%$.
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