In the circuit shown, the switch is shifted from position 1rightarrow 2 at t=0. The switch was initially in position I since a long time. The graph between charge on capacitor C and time 't' is

Options

A.
B.
C.
D.

Answer

B

Explanation

`V_(0)+2Sigma-2iR-q/C=V_(0)`
`1=Sigma/R-q/(2RC)`
also `i=(dq)/(dt)`
`:. underset(CSigma)overset(q)int (dq)/((Sigma/R-q/(2RC)))=underset0overset(t)intdt`
`ln(Sigma/R-q/(2RC))|_(CSigma)^(q)/((-1/(2RC)))=t`
`ln ((2SigmaC-q)/(SigmaC))=-t/(2RC)`
`q=2SigmaC-SigmaC_(e)^(-t//2RC)`
`q=SigmaC(2-e^(-t//2RC))`