A `4 muF` capacitor, a resistance of `2.5 M Omega` is 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)/Re^(t/(RC))`
`therefore` Potential difference across R is
`V_R-iR=V_0e^(t/(RC))`
`therefore` Potential difference across .C. is `V_c=V_0-V_R`
`-V_0-V_0e^(t/(RC))=V_0(1-e^(t/(RC)))`
but given `V_c=3V_R` we get
`1-e^(-t//RC)=3e^(-t//RC) or 4e^(-t//RC)`
`e^((-t)/(RC))=4rArr t/(RC)=ln 4 rArr t=2RC ln 2`
`t=2.5 xx10^6xx4xx10^(-6)xx2xx0.693`
or t=13.86 sec