`4muF` capacitor and a resistance 2.5M `Omega` are in series with 12V battery, Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor.
[Given In ( 2 ) = 0.693]

Explanation

a) Charging current `i=(V_(0))/(R)e^(-(t)/(RC))`
`:.` Potential difference across R is `V_(R) =iR=V_(0)e^(-(t)/(RC))`
`:.` Potential difference across .C. is `V_(C) =V_(0) - V_(R) = V_(0)-V_(0)e^(-(t)/(RC))= V_(0)(1-e^(-(t)/(RC)))` but given `V_(C) = 3V_(R)`, we get `1-e^(-t//RC)` or `1=4e^(-t//RC)` `e^((t)/(RC))=4 implies (t)/(RC)=ln4 implies t= 2RC ln2`
`t = 2.5 xx 10^(6)xx 4 xx 10^(-6)xx2 xx 0.693` or t = 13.86 sec