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