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]

Options

A. `14.86s`
B. `6.93s`
C. `7s`
D. `14s`

Answer

A

Explanation

Given `E_(C)=3V_(R)=3(V-V_(C))`
Here V is the applied potential
`thereforeV_(C)=(3)/(4)V` or `E(1-e^((-t)/(tc)))=(3)/(4)V`
`thereforee^((-t)/(tauc))=(1)/(4)` Here `tau_(c)=CR=10s`
substituting this value of `tau_(c)` in Eq (i) and solving for `t` we get `t=13.86because`