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?

Concept:

When a dielectric material is inserted into a capacitor, it affects the capacitance, stored energy, and potential difference across the plates.

1. New capacitance with dielectric: C' = K * C

2. Energy stored in a capacitor: U = (1/2) * (Q^2 / C) = (1/2) * C * V^2

3. Potential difference: V' = V / K

Calculation:

Initially, the energy stored in the capacitor:

⇒ U₁ = (1/2) * C * V²

After inserting the dielectric slab:

⇒ New capacitance C' = K * C

⇒ New energy stored in the capacitor: U₂ = (1/2) * (Q² / C') = (1/2) * ((C * V)² / (K * C)) = (1/2) * C * V² / K = U₁ / K

Change in energy stored:

⇒ ΔU = U₂ - U₁ = (1/2) * C * V² * (1/K - 1)

Charge on the capacitor remains the same as it was disconnected from the cell:

⇒ Q = C * V

Potential difference between the plates decreases K times:

⇒ V' = V / K

Hence, option 3 is incorrect as the charge on the capacitor is conserved.