Q152 / 180 · COMEDK 2020 · Physics
If voltage $V=(200 \pm 8) \mathrm{V}$ and current $I=(20 \pm 05) \mathrm{A}$, then the percentage error in resistance $R$ is
- A$5.2 \%$
- B$25 \%$
- C$3 \%$
- Correct answerD$6.5 \%$
Solution
Voltage, $V=\langle 200 \pm 8) \mathrm{V}$
Current, $I=(20 \pm 05) \mathrm{A}$
$\therefore$ Fesistance, $R=\frac{V}{I}=\frac{200}{20}=10 \Omega$
Taking maximum error condition,
$$
\begin{aligned}
\frac{\Delta R}{R} &=\frac{\Delta V}{V}+\frac{\Delta l}{l}=\frac{8}{200}+\frac{05}{20}=\frac{13}{200} \\
\Rightarrow \quad \frac{\Delta R}{R} \times 100 &=\frac{13}{200} \times 100 \\
&=\frac{13}{2} \angle=6.5 \%
\end{aligned}
$$
Hence, the correct answer is option: 'D'.