Mathematics In Physics Question 3
Question 3 - 2024 (29 Jan Shift 1)
The resistance $R=\frac{V}{I}$ where $V=(200 \pm 5) V$ and $I=(20 \pm 0.2) A$, the percentage error in the measurement of $R$ is :
(1) $3.5 \%$
(2) $7 \%$
(3) $3 \%$
(4) $5.5 \%$
Show Answer
Answer: (1)
Solution:
$R=\frac{V}{l}$
According to error analysis
$$ \begin{aligned} & \frac{dR}{R}=\frac{dV}{V}+\frac{dI}{I} \\ & \frac{dR}{R}=\frac{5}{200}+\frac{0.2}{20} \\ & \frac{dR}{R}=\frac{7}{200} \end{aligned} $$
$%$ error $\frac{dR}{R} \times 100=\frac{7}{200} \times 100=3.5 \%$
