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In an electrical circuit, the voltage is measured as $V=(200 \pm 4)$ volt and the current is measured as $I=(20 \pm 0.2) \mathrm{A}$. The value of the resistance is:
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The correct answer is:
$(10 \pm 0.3) \Omega$
$R=\frac{V}{l}=\frac{200}{20}=10 \Omega$
$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta l}{l}=\frac{4}{200}+\frac{0.2}{20}=\frac{4+2}{200}=\frac{6}{200}$
$\Rightarrow \Delta R=\frac{6}{200} \times R=\frac{6}{20}=\frac{3}{10}=0.3 \Omega$
$\therefore$ Resistance $=R \pm \Delta R=(10 \pm 0.3) \Omega$
$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta l}{l}=\frac{4}{200}+\frac{0.2}{20}=\frac{4+2}{200}=\frac{6}{200}$
$\Rightarrow \Delta R=\frac{6}{200} \times R=\frac{6}{20}=\frac{3}{10}=0.3 \Omega$
$\therefore$ Resistance $=R \pm \Delta R=(10 \pm 0.3) \Omega$
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