physicsTo understand that the charge stored by capacitors represents energy; to be able to calculate the stored energy and its changes under different circumstances.
An air-filled parallel-plate capacitor has plate area $A$ and plate separation $d$. The capacitor is connected to a battery that creates a constant voltage $V$.
**Part A**
Find the energy $U_0$ stored in the capacitor.
Express your answer in terms of $A$, $d$, $V$, and $ϵ_0$.
**Part B**
The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches **3d**.
Find the new energy $U_1$ of the capacitor after this process.
Express your answer in terms of $A$, $d$, $V$, and $ϵ_0$.
**Part C**
The capacitor is now reconnected to the battery, and the plate separation is restored to $d$. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled.
Find the energy $U_2$ of the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is $K$.
Express your answer in terms of $A$, $d$, $V$, $K$, and $ϵ_0$.