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 potential difference between the plates decreases K times
B. The energy stored in the capacitor decreases K times
C. The change in energy is `(1)/(2)C_(0)V^(2)(K-1)`
D. The change is energy is `(1)/(2)C_(0)V^(2)((1)/(K)-1)`

Answer

D

Explanation

`"Initial energy, "U_(i)=(1)/(2)C_(0)V^(2)`
`"Final energy, "U_(f)=(1)/(2)(KC_(0))((V)/(K))^(2)=(1)/(K)((1)/(2)C_(0)V^(2))`
`"Change in energy "=U_(f)-U_(i)=(1)/(2)C_(0)V^(2)((1)/(K)-1)`
Note that this change of energy is negative, i.e. there is a decrease of energy.