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.
$$1.7 \times {10^5}\Omega $$
B.
$$2.7 \times {10^6}\Omega $$
C.
$$3.3 \times {10^7}\Omega $$
D.
$$1.3 \times {10^4}\Omega $$
Answer :
$$2.7 \times {10^6}\Omega $$
Solution :
$$\eqalign{
& {\text{We have, }}V = {V_0}\left( {1 - {e^{\frac{{ - t}}{{RC}}}}} \right) \cr
& \Rightarrow 120 = 200\left( {1 - {e^{\frac{{ - t}}{{RC}}}}} \right) \cr
& \Rightarrow t = RC{\text{ in }}\left( {2.5} \right) \cr
& \Rightarrow R = 2.71 \times {10^6}\Omega \cr} $$