A parallel plate air capacitor of capacitance `C` is connected to a cell of `emF V` and then disconnected from it. A dielectric slab of dielectric constant `K`, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect ?

Options

A. The energy stored in the capacitor decreases `K` times
B. The chance in energy stored is `1/2 CV^(2)(1/K-1)`
C. The change on the capacitor is not conserved
D. The potential difference between the plates decreases `K` times

Answer

C

Explanation

`U_(a)=(Q^(2))/(2C), U_(b)=(Q^(2))/(2KC), (U_(b))/(U_(a)),(1) is O.K.`
`DeltaU=U_(b)-U_(a)=(Q^(2))/(2C)(1/K-1)=((CV)^(2))/(2C)(1/K-1)`
`=1/2 CV^(2)(1/K-1), (2) is O.K.`
`Q_(a)=Q_(b)=Q, (3)` is wrong
`Q=CV_(a)=KCV_(b) implies V_(b)=(V_(a))/L=V/K, (4) is O.K.`