An air-cored parallel plate capacitor having a capacitance C is charged by connecting it to a battery. Now, it is disconnected from the battery and a dielectric slab of dielectric constant K is inserted between its plates so as to completely fill the space between the plates. Compare `:`
(I) Initial and final capacitance
(ii) Initial and final charge.
(iii) Initial and final potential difference.
(iv) Initial an final electric field between the plates.
(v) Initial and final energy stored in the capacitor.

Explanation

(i) Initial capacitance = C
Final capacitance = KC ( after inserting dielectric )
`implies (C_(1))/(C_(i))= K`
(ii) Charge on isolated capacitor remains same therefore `(Q_(t))/(Q_(i))` =1
(iii) As `Q= CVimplies V = (Q)/(C ) implies (V_(t))/(V_(t))= (C_(i))/(C_(t))= (1)/(K)`
(iv) `E=(V)/(d) implies (E_(1))/(E_(i))=(V_(t))/(V_(i))=(1)/(K)`
`U= (Q^(2))/(2C) implies (U_(r))/(U_(t))=(C_(i))/(C_(r))=(1)/(K)`