Question

Given potential difference, $V=(8\pm 0.5)V$ and current, $I=(2\pm 0.2)A$. The value of resistance $R$ in $\Omega$ is

• A. $4\pm 8\%$
• B. $4\pm 10\%$
• C. $4\pm 16.25\%$
• D. $4\pm 6.25\%$

Answer 1

The correct option is C $4\pm 16.25\%$

Find true (mean)value of resistance.

As we know,
Resitance is given by,
$R=\frac{V}{I}=\frac{8}{2}=4\Omega$

Find the % error in resistance

$\frac{\Delta R}{R}\times 100=\frac{\Delta V}{V}\times 100+\frac{\Delta I}{I}\times 100$
Put the value in above equation,
$\frac{\Delta R}{R}\times 100=\frac{0.5}{8}\times 100+\frac{0.2}{2}\times 100$
$\frac{\Delta R}{R}\%=16.25\%$

Express the error in resistance

$=4\pm 16.25\%$