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Question:

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?

The potential difference between the plates decreases K times

The change in energy stored is 1/2CV²(1-1/K)

The energy stored in the capacitor decreases K times

The charge on the capacitor is not conserved

Solution:

Cf=KCi
Qi=CiV
Ui=1/2CiV²
Uf=1/2Qf²/Cf
After the capacitor is disconnected from the battery, charge on the capacitor cannot change.
∴Qf=Qi
∴Uf=1/2Qf²/Cf=1/2Ci²V²/KCi
ΔU=Uf-Ui=1/2Ci²V²/KCi-1/2CiV²=1/2CiV²(1/K-1)=-1/2CiV²(1-1/K)=-1/2CV²(1-1/K)
since Ci=C as given