Question 33.The resistance is given by R=\frac{V}{I}. The measured values are
V=(200\pm5) V I=(20\pm0.2) A The percentage error in the measurement of resistance is :
(1) 3.5\%
(2) 7\%
(3) 3\%
(4) 5.5\%
Answer: (1)
Explanation:
The expression for resistance is R=\frac{V}{I}
According to error analysis for division,
\frac{dR}{R}=\frac{dV}{V}+\frac{dI}{I}Substitute the given values,
\frac{dR}{R}=\frac{5}{200}+\frac{0.2}{20} \frac{dR}{R}=\frac{5}{200}+\frac{2}{200} \frac{dR}{R}=\frac{7}{200}Percentage error in resistance is \frac{dR}{R}\times100
\text{Percentage error}=\frac{7}{200}\times100 \text{Percentage error}=3.5\%