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

Answer

B

Explanation

`q = CV rArr V = q//C`
Due to dielectric insertion, new capacitance
`C_(2) = CK`
Initial energy stored in capacitor, `U_(1) = (q^(2))/(2C)`
Final energy stored in capacitor, `U_(2) = (q^(2))/(2KC)`
Change in energy stored,
`Delta U = U_(2) - U_(1)`
`Delta U = (q^(2))/(2C)((1)/(K) - 1) = (1)/(2)CV^(2)((1)/(K)-1)`
New potential difference between plates
`V. = (q)/(CK) = (V)/(K)`