-Combinations of Capacitors -Energy Stored in a Charged Capacitor

1. -Combinations of Capacitors-Energy Stored in a Charged Capacitor AP Physics C Mrs. Coyle

2. Circuit Symbols used in Circuit Diagrams Resistor

3. The potential difference across the capacitors is the same. • The flow of charges ceases when the voltage across the capacitors equals that of the battery. • The total charge of the capacitors in series is the sum of the individual charges. Capacitors in Parallel

4. Equivalent Capacitance for Capacitors in Parallel • Ceq is greater than any of the individual capacitors C. • It is as if the areas of the capacitors were combined.

5. Capacitors in Series • Electrons are transferred from the left plate of C1 to the right plate of C2 through the battery • An equal amount of negative charge is removed from the left plate of C2, leaving it with an excess positive charge • All of the right plates gain charges of –Q and all the left plates have charges of +Q

6. Equivalent Capacitance for Capacitors in Series The equivalent capacitance of a series combination is always less than any individual capacitor in the combination.

7. Ex: Find the equivalent capacitance, the charge and the voltage across in one of the 2μF capacitors. 6 V Ans: 8 μF, 6 μC

8. Ex 26.4: Find the Equivalent Capacitance Answer: 6mF

9. Work to Charge a Capacitor • The work needed to transfer a charge, q, from one plate to the other through the battery is: • The total work required to charge the capacitor from q=0 to Q is:

10. Energy Stored in a Capacitor • The work done in charging the capacitor is stored as electric potential energy U: • This applies to a capacitor of any geometry. • The energy stored increases as the charge increases and as the potential difference increases. • At a certain maximum voltage, corona discharge occurs between the plates.

11. Energy and Energy density for a Parallel Plate Capacitor • Energy density (energy per unit volume)