Question

A resistor 'R' and $2\mu F$ capacitor in series is connected through a switch to $200V$ direct supply. Across the capacitor is a neon bulb that lights up at $120V$. Calculate the value of $R$ to make the bulb light up $5s$ 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 $q=q_0\left(1-e^{-t/RC}\right)$
or $V=\frac{q_0}{C}\left(1-e^{-t/RC}\right)$
$V=200\left(1-e^{-t/RC}\right)$
$120=200\left(1-e^{-t/RC}\right)$
$e^{-t/RC}=0.4$
$\frac{-t}{RC}=\ln (0.4)$
$\frac{t}{RC}=\ln \left(\frac{10}{4}\right)=2.303\times 0.4$
$R=\frac{5}{2\times 10^{-6}\times 2.303\times 0.4}$
$=2.7\times 10^6\Omega$