Question

When the voltage and current in a conductor are measured as $(100\pm 4)V$ and $(5\pm 0.2)A$, then the percentage of error in the calculation of resistance is:

• A. $8\%$
• B. $4\%$
• C. $20\%$
• D. $10\%$
• E. $6\%$

Answer 1

Answer: (A)

$8\%$

Given : $V\pm \Delta V=(100\pm 4)V$
And $I\pm \Delta I=(5\pm 0.2)A$
$\Rightarrow \frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}=\frac{4}{100}+\frac{0.2}{5}=0.08$
$\Rightarrow \left(\frac{\Delta R}{R}\right)\%=0.08\times 100=8\%$.