1. Energy Storage in Capacitors.
Today’s agenda:
Energy Storage in Capacitors.
You must be able to calculate the energy stored in a capacitor, and apply the energy storage equations to situations where capacitor configurations are altered.
Dielectrics.
You must understand why dielectrics are used, and be able include dielectric constants in capacitor calculations.

2. Dielectrics
If an insulating sheet (“dielectric”) is placed between the plates of a capacitor, the capacitance increases by a factor , which depends on the material in the sheet.  is the dielectric constant of the material.
dielectric
In general, C = 0A / d.  is 1 for a vacuum, and  1 for air. (You can also define  = 0 and write C =  A / d).

3. Any reasons to use a dielectric in a capacitor?
The dielectric is the thin insulating sheet in between the plates of a capacitor.
dielectric
A lot of interesting physics happens in the dielectric, but we’ll skip that section.
Any reasons to use a dielectric in a capacitor?
Makes your life as a physics student more complicated.
Lets you apply higher voltages (so more charge).
Lets you place the plates closer together (make d smaller).
Increases the value of C because >1.
Gives you a bigger kick when you discharge the capacitor through your tongue!
Gives you a bigger kick when you discharge the capacitor through your tongue!
Gives you a bigger kick when you discharge the capacitor through your tongue!

4. Homework hint: what if the dielectric fills only half the space between the plates?
This is equivalent to two capacitors in parallel. Each of the two has half the plate area. The two share the total charge, and have the same potential difference Q1 C1 Q C Q2 C2

5. Some things for you to ponder…
If you charge a capacitor and then remove the battery and manipulate the capacitor, Q must stay the same but C, V, and U may change. (What about E?)
If you charge a capacitor and then remove the battery and manipulate the capacitor, Q must stay the same but C, V, and U may change. (What about E?)
If you charge a capacitor, keep the battery connected, and manipulate the capacitor, V must stay the same but C, Q, and U may change. (What about E?)
If you charge a capacitor, keep the battery connected, and manipulate the capacitor, V must stay the same but C, Q, and U may change. (What about E?)
If exactly two capacitors are connected such that they have the same voltage across them, they are probably in parallel (but check the circuit diagram).
If exactly two capacitors are connected such that they have the same voltage across them, they are probably in parallel (but check the circuit diagram).

6. If you charge two capacitors, then remove the battery and reconnect the capacitors with oppositely-charged plates connected together…
draw a circuit diagram before and after, and use conservation of charge to determine the total charge on each plate before and after.
If you charge two capacitors, then remove the battery and reconnect the capacitors with oppositely-charged plates connected together…
draw a circuit diagram before and after, and use conservation of charge to determine the total charge on each plate before and after.