Q96 / 120 · VITEEE 2014 · Physics

A resistor of $6 \mathrm{k} \Omega$ with tolerance $10 \%$ and another resistance of $4 \mathrm{k} \Omega$ with tolerance $10 \%$ are connected in series. The tolerance of the combination is about

  • A
    $5 \%$
  • Correct answer
    B
    $10 \%$
  • C
    $12 \%$
  • D
    $15 \%$

Solution

In series combination equivalent resistance, $\begin{array}{l} \mathrm{R}=\mathrm{R}_{1}+\mathrm{R}_{2} \\ =6+4=10 \mathrm{k} \Omega \end{array}$ Error in combination, $\begin{array}{l} \Delta \mathrm{R}=\Delta \mathrm{R}_{1}+\Delta \mathrm{R}_{2} \\ =\frac{10}{100} \times 6+\frac{10}{100} \times 4 \\ =0.6+0.4=1 \\ \frac{\Delta \mathrm{R}}{\mathrm{R}}=\frac{1}{10}=10 \% \end{array}$

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

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