## Capacitor with a Dielectric

4.4 Capacitor with a Dielectric

### Learning Objectives

By the end of this section, you will be able to:

- Describe the effects a dielectric in a capacitor has on capacitance and other properties
- Calculate the capacitance of a capacitor containing a dielectric

### Energy Density and Dielectrics

**Practice!**

*Example problem: Work through this problem on your own. Afterward, you can watch my video solution to check your results.*

A dielectric-filled parallel-plate capacitor has plate area A = 20.0 cm^{2}, plate separation d = 9.00 mm, and dielectric constant 𝛋 = 4.00. The capacitor is connected to a battery that creates a constant voltage V = 7.50 V.

(a) Find the energy U_{1} of the dielectric-filled capacitor. Express you answer in pJ, with 3 sig figs.

(b) The dielectric plate is now slowly pulled out of the capacitor, which remains connected to the battery. Find the energy U_{2} of the capacitor at the moment when the capacitor is half-filled with the dielectric. Express you answer in pJ, with 3 sig figs.

(c) The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U_{3}. Express you answer in pJ, with 3 sig figs.

(d) In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work W is done by the external agent acting on the dielectric? Express you answer in pJ, with 3 sig figs.