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A 4 muF capacitor, a resistance of 2.5 M...

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]

A

13.86 s

B

6.93 s

C

7 s

D

14 s

Text Solution

Verified by Experts

The correct Answer is:
A
`C=4muF, R=2.5MOmega`
`V=12V`
`V_(C)=V_(0)(1-e^(-t//RC)),i=(V_(0))/(R)e^(-t//RC)`
`V_(R)=V_(0)e^(-t//RC)`
`V_(R)=V_(0)e^(-t//RC)`
`implies 4V_(0)e^(-t//RC)=V_(0)impliese^(-t//RC)=(1)/(4)`
`implies (t)/(RC)=2l n2impliest=2.5xx10^(6)xx4xx10^(-6)xx2xx0.693`
`=13.86` Sec.
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