Question

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 $5 s$ after the switch has been closed. $\left(\log _{10} 2.5=0.4\right)$

• A. $3.3 \times 10^{7} \Omega$
• B. $1.3 \times 10^{4} \Omega$
• C. $1.7 \times 10^{5} \Omega$
• D. $2.7 \times 10^{6} \Omega$

Answer 1

Answer: (D)

Charge on capacitor $q=q_{0}\left(1-e^{-t / R C}\right)$
or $V=\frac{q_{0}}{C}\left(1-e^{-t / R C}\right)$
$V=200\left(1-e^{-t / R C}\right)$
$120=200\left(1-e^{-t / R C}\right)$
$e^{-t / R C}=0.4$
$\frac{-t}{R C}=\ln (0.4)$
$ \frac{t}{R C} =\ln \left(\frac{10}{4}\right)=2.303 \times 0.4 $
$R =\frac{5}{2 \times 10^{-6} \times 2.303 \times 0.4} $
$=2.7 \times 10^{6} \Omega $