Question

The resistance $R=V/I$, where $V=(100\pm 5)V$ and $I=(10\pm 0.2)A$. Find the percentage error in R.

• A. 17%
• B. 7%
• C. 5%
• D. 11%

Answer 1

The correct option is B 7%

$\begin{array}{c}V=100\pm 151\text{v}\\ I=10\pm 0.2A\\ \text{ohm's law:}\\ V=IR\\ \text{taking}\log \\ \log V=\log I+\log R\end{array}$

$\begin{array}{c}\text{differentiating}\\ \frac{dV}{V}=\frac{dI}{I}+\frac{dR}{R}\\ \frac{dR}{R}=\frac{dV}{V}-\frac{dI}{I}\\ \because \text{error always added}\\ \frac{dR}{R}=\frac{dV}{V}+\frac{dI}{I}\\ \frac{dR}{R}=\frac{5}{100}+\frac{0.2}{10}\\ \frac{dR}{R}=\frac{7}{100}\end{array}$

$\begin{array}{cc}\%\text{error in}R& =\frac{7}{100}\times \mathrm{100}\%\\ & =7\%\end{array}$