Q. A resistor $R$ and $2\mu F$ capacitor in series is connected through a switch to 200 V direct supplies. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of $R$ to make the bulk light up 5 s alter the switch has been closed $\left( \log_{10}{2.5 = 0.4} \right)$
A) ${1.7 \times 10}^{5}\ \Omega$
B) ${2.7 \times 10}^{6}\ \Omega$
C) ${3.3 \times 10}^{7}\ \Omega$
D) ${1.3 \times 10}^{4}\ \Omega$
Explanation
(a) Neon bulb is filled with gas, so the resistance is infinite; hence no current flows through it.
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Now, $\ \ \ \ V_{c} = E(1 - e^{- t/RC})\ $
$\Rightarrow \ \ \ \ \ \ \ 120 = 200(1 - e^{- t/RC})\ $
$\Rightarrow e^{- t/RC} = \frac{2}{5}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ t = RC\ln{2.5}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ R = \frac{t}{C\ln{2.5}} = \frac{5}{2.303 \times 2 \times 10^{6}\log{2.5}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2.7 \times 10^{6}\ \Omega\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.