Two identical capacitors `1` and `2` are connected in series to a batery as shown in figure. Capacitor `2` contains a dielectric slab of dieletric constant `k` as shown. `Q_(1)` and `Q_(2)` are the charges stored in the capacitors. Now the dielectirc slab us removed and the corresponding charges are `Q'_(1)` and `Q'_(2)`. Then

Options

A. `(Q'_(1))/(Q_(1))=(k+1)/k`
B. `(Q'_(2))/(Q_(2))=(k+1)/2`
C. `(Q'_(2))/(Q_(2))=(k+1)/(2k)`
D. `(Q'_(1))/(Q_(1))=k/2`

Answer

C

Explanation

`Q_(2)=Q_(1)=(KC)/(K+1) ErArr Q_(2)^(2)=Q_(1)^(2)=C/2E rArr (Q_(2)^(1))/(Q_(2))=(K+1)/(2K)`