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.

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 =  0 A / d.  is 1 for a vacuum, and  1 for air. (You can also define  =  0 and write C =  A / d). Dielectrics

The dielectric is the thin insulating sheet in between the plates of a capacitor. dielectric Any reasons to use a dielectric in a capacitor?  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.  Makes your life as a physics student more complicated. Gives you a bigger kick when you discharge the capacitor through your tongue! A lot of interesting physics happens in the dielectric, but we’ll skip that section.

dielectric 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 Homework hint: what if the dielectric fills only half the space between the plates? C1C1 C2C2 Q2Q2 Q1Q1 CQ

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 exactly two capacitors are connected such that they have the same voltage across them, they are probably in parallel (but check the circuit diagram). 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, 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 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.