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A $100 \mathrm{~V}$ voltmeter of internal resistance $20 \mathrm{k} \Omega$ in series with a high resistance $R$ is connected to a $110 \mathrm{~V}$ line. The voltmeter reads $5 \mathrm{~V}$, the value of $R$ is
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The correct answer is:
$420 \mathrm{k} \Omega$
\(\begin{aligned}
& \mathrm{I}=\frac{110}{\mathrm{R}+20 \mathrm{k} \Omega} \\
& \text {Voltmeter reads } 5 \mathrm{~V}=\frac{(20 \mathrm{k} \Omega)(110)}{(\mathrm{R}+20 \mathrm{k} \Omega)} \\
& \mathrm{R}+20=4 \times 110=440 \\
& \mathrm{R}=440-20=420 \mathrm{k} \Omega \\
& R=420 \mathrm{k} \Omega
\end{aligned}\)
(C) is correct option.
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