Q163 / 180 · KCET 2018 · 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
    \( 4.8 \% \)
  • Correct answer
    C
    $7 \%$
  • D
    \( 3 \% \)

Solution

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 $R=7 \%$

Hence, the correct answer is option: 'C'.

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