Question 96: Units , Dimensions and Error Analysis

Question

The resistance $$R=\frac{V}{I}$$ where $$\mathrm{V}=(200 \pm 5) \mathrm{V}$$ and $$I=(20 \pm 0.2) \mathrm{A}$$, the percentage error in the measurement of $$\mathrm{R}$$ is :

Accepted Answer

$$\mathrm{R}=\frac{\mathrm{V}}{1}$$
According to error analysis
$$\begin{aligned}
& \frac{\mathrm{dR}}{\mathrm{R}}=\frac{\mathrm{dV}}{\mathrm{V}}+\frac{\mathrm{dI}}{\mathrm{I}} \
& \frac{\mathrm{dR}}{\mathrm{R}}=\frac{5}{200}+\frac{0.2}{20} \
& \frac{\mathrm{dR}}{\mathrm{R}}=\frac{7}{200} \
& \% 	ext { error } \frac{\mathrm{dR}}{\mathrm{R}} 	imes 100=\frac{7}{200} 	imes 100=3.5 \%
\end{aligned}$$

Answer

5.5%

Answer

3%

Answer

7%

Answer

3.5%

Units , Dimensions and Error Analysis

The resistance $R=\frac{V}{I} where \mathrm{V}=(200 \pm 5) \mathrm{V} and I=(20 \pm 0.2) \mathrm{A}, the percentage error in the measurement of \mathrm{R}$ is :

Choose the correct answer: