A resistor '$R$' and $2\ μF$ capacitor in series is connected through a switch to $200\ V$ direct supply. Across the capacitor is a neon bulb that lights up at $120\ V$. Calculate the value of $R$ to make the bulb light up $5\ s$ after the switch has been closed. $(log_{10} 2.5 = 0.4)$.
AIEEE 2011, Medium
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We have, $\mathrm{V}=\mathrm{V}_{0}\left(1-\mathrm{e}^{-t / \mathrm{RC}}\right)$
$\Rightarrow 120=200\left(1-e^{-t / R C}\right)$
$\Rightarrow t=R C \operatorname{in}(2.5)$
$\Rightarrow \quad R=2.71 \times 10^{6} \,\Omega$
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