Q. A resistor $'R'$ and $2\mu F$ 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 $5s$ after the switch has been closed. $(\log_{10}{2.5 = 0.4})$
A) $1.3 \times 10^{4}\Omega$
B) $1.7 \times 10^{5}\Omega$
C) $2.7 \times 10^{6}\Omega$
D) $3.3 \times 10^{7}\Omega$
Explanation
(c) $V = V_{0}(1 - e^{- t/\tau})$
$120 = 200(1 - e^{- t/RC})$
[image:1_image289.emf]
$\Rightarrow 1 - e^{- t/RC} = \frac{3}{5}$
$e^{- t/RC} = \frac{2}{5}$
$\Rightarrow \frac{t}{RC} = \ln\left( \frac{5}{2} \right)$
$\frac{t}{RC} = 2.303\log_{10}{(2.5)}$
$\Rightarrow R = \frac{5}{2 \times 10^{- 6} \times 2.303 \times 0.4} \Rightarrow R = 2.7 \times 10^{6}\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.