JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2024
- Hard
- MCQ
The resistance \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\) where \(\mathrm{V}=(200 \pm 5) \mathrm{V}\) and \(I=(20 \pm 0.2) A\), the percentage error in the measurement of \(R\) is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(3.5 \%\)
Step-by-step Solution
Detailed explanation
\(\mathrm{R}=\frac{\mathrm{V}}{1}\)
According to error analysis
\( \frac{\mathrm{dR}}{\mathrm{R}}=\frac{\mathrm{dV}}{\mathrm{V}}+\frac{\mathrm{dI}}{\mathrm{I}} \)
\( \frac{\mathrm{dR}}{\mathrm{R}}=\frac{5}{200}+\frac{0.2}{20} \)
\( \frac{\mathrm{dR}}{\mathrm{R}}=\frac{7}{200} \)
\( \% \text { error } \frac{\mathrm{dR}}{\mathrm{R}} \times 100=\frac{7}{200} \times 100=3.5 \%\)
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