Question

The resistance of a wire is given by $R=\frac{V}{I}$, where
$V=(100\pm 5)V$ and $I=(10\pm 0.2)A$. What is the total percentage error in $R$ ?

Answer 1

Given;
$V=(100\pm 5)V$
$I=(10\pm 0.2)A$
As we know
$R=\frac{V}{I}$
Therefore, percententage error in $R$ is given by,

$\frac{\Delta R}{R}\times 100=\frac{\Delta V}{V}\times 100+\frac{\Delta I}{I}\times 100$

by putting the gives values, we get,

$\frac{\Delta R}{R}\times 100=\frac{5}{100}\times 100+\frac{0.2}{10}\times 100$

$\frac{\Delta R}{R}\%=5\%+2\%$

$\frac{\Delta R}{R}\%=7\%$

Final answer : $7\%$