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# In an experiment to determine the Resistance of a coil it is found the volit meter values is $30.3\;V$ and ammeter reading is $0.020\;A$ least count of voltmeter is $0.1\;V$ and Least count of ammeter is $1\;mA$. The value of R is

$(a)\;1.50 \pm 0.08\;k \Omega \\(b)\;1.50 \pm 0.8\;k \Omega\\(c)\;1.50 \pm 0.008\;k \Omega\\(d)\;1.50 \pm 0.080\;k \Omega$

$V=30.0$
$I=0.020\;A$
$R=\large\frac{V}{I}=\frac{30}{0.020}$
$\quad= 1.50\;R \Omega$
Error $=R=\large\frac{V}{I}$
$\large\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$
$\Delta R=R \bigg(\large\frac{\Delta V}{V} +\frac{\Delta I}{I} \bigg)$
$\qquad= 1.50 \times 10^3 \bigg (\large\frac{0.1}{30.0}+\frac{0.001}{0.020} \bigg)$
$\qquad= 0.080\;k \Omega$
Hence d is the correct answer.