KCET · Physics · Mathematics in Physics
The resistance \( \mathrm{R}=\frac{V}{I} \) where \( \mathrm{V}=(100 \pm 5) \mathrm{V} \) and \( \mathrm{I}=(10 \pm 0.2) \mathrm{A} . \) The percentage error in \( \mathrm{R} \)
is
- A \( 5.2 \% \)
- B \( 4.8 \% \)
- C \(7 \%\)
- D \( 3 \% \)
Answer & Solution
Correct Answer
(C) \(7 \%\)
Step-by-step Solution
Detailed explanation
Resistance, \(R=\frac{V}{I}\)
Given \(V=(100 \pm 5) V ; I=(10 \pm 0.2) A\)
The percentage error in \(\mathrm{R}\) is
\(\begin{array}{l}\frac{\Delta R}{R} \times 100=\frac{\Delta V}{V} \times 100+\frac{\Delta I}{I} \times 100 \\=\frac{5}{100} \times 100+\frac{0.2}{10} \times 100 \\=5 \%+2 \%=7 \%\end{array}\)
Therefore, percentage error in \(R=7 \%\)
Given \(V=(100 \pm 5) V ; I=(10 \pm 0.2) A\)
The percentage error in \(\mathrm{R}\) is
\(\begin{array}{l}\frac{\Delta R}{R} \times 100=\frac{\Delta V}{V} \times 100+\frac{\Delta I}{I} \times 100 \\=\frac{5}{100} \times 100+\frac{0.2}{10} \times 100 \\=5 \%+2 \%=7 \%\end{array}\)
Therefore, percentage error in \(R=7 \%\)
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