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. 13.80s
B. 6.93s
C. 7s
D. 14s

Answer

A

Explanation

Given `V_c=3V_R=3(V-V_c)` Here V is the applied potential
`therefore V_c=3/4V or V(1-e^(-t//tau_0))=3/4V therefore e^(-t//tau_0)=1/4`…….(i)
Here `tau_c=CR=10s`
Subsituting this value of `tau_c` in Eq(i) and solving for t, we get
`therefore t=13.86s therefore` Correct answer is (A)