A resistor 'R' and `2(mu)F` capacitor in series is connected through a switch to 200 V direct supply. A cross 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. (`log_(10) 2.5 = 0.4`)

Options

A. `1.7xx10^(5)Omega`
B. `2.7xx10^(6)Omega`
C. `3.3xx10^(7)Omega`
D. `1.3xx10^(4)Omega`

Answer

B

Explanation

Neon bulb filled with gas, so its resistance in infinite, hence no current flows through, it
Now, `V=E(1-e^(-t//RC))`
`implies 120=200(1-e^(-t//RC))implies e^(-t//RC)=(2)/(5)`
`implies t=RC ln2.5 implies R=(t)/(Cln2.5)`
`=(t)/(2.303Clog2.5)=2.7xx10^(6)Omega`