1. Physics for Scientists and Engineers II, Summer Semester 2009 Lecture 6: June 1 st 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 Step 1: Assume charge Q resides on each conductor Step 2: Calculate the potential difference  V between the two conductors. Step 3: Calculate the capacitance: Calculating Capacitance +Q-Q

3. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Spherical Conductor as a Capacitor +Q -Q (residing at infinity) means, it isn’t even there….

4. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Parallel Plates +Q-Q Area = A d

5. Physics for Scientists and Engineers II, Summer Semester 2009 Capacitors in Electric Circuits Circuits diagrams: Symbolic representation how electric elements (like batteries, capacitors, etc.) are wired together. Symbolic representation of circuit elements: Wires Wires that cross but are not connected: Wires that cross but are connected: Capacitor: Battery or Power Supply: + - Open switch: Closed switch: Could be connected or not connected depending on particular circuit diagram. In our book, it means wires are connected.

6. Physics for Scientists and Engineers II, Summer Semester 2009 Circuit Diagram of Capacitor Connected to a Battery + - C + - Points in a circuit diagram that are connected by a wire are at the same electric potential (“voltage”).  V C+ =V b+ and V C- =V b-   V C =  V b

7. Physics for Scientists and Engineers II, Summer Semester 2009 Two Capacitors Connected to a Battery “in Parallel” + - C2C2 + - C1C1 + - Q2Q2 Q1Q1 + - C eq + -

8. Physics for Scientists and Engineers II, Summer Semester 2009 Two Capacitors Connected to a Battery “in Series” + - C2C2 + - C1C1 + - Q2Q2 Q1Q1 No net charge on inner two plates + - C eq + -

9. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Replace Capacitor Network with a Single Capacitor + - C2C2 + - C1C1 + - C3C3 + - C4C4 + - C5C5 + - C6C6 + - + - C eq + -

10. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Replace Capacitor Network with a Single Capacitor + - C2C2 + - C1C1 + - C3C3 + - C4C4 + - C5C5 + - C6C6 + - CACA + - + - C2C2 + - C1C1 + - C6C6 + -

11. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Replace Capacitor Network with a Single Capacitor CACA + - + - C2C2 + - C1C1 + - C6C6 + - + - C2C2 + - CBCB + - C6C6 + -

12. Physics for Scientists and Engineers II, Summer Semester 2009 Example: Replace Capacitor Network with a Single Capacitor + - C2C2 + - CBCB + - C6C6 + - + - C eq + -

13. Physics for Scientists and Engineers II, Summer Semester 2009 Energy Stored in a Charged Capacitor Electric potential energy is stored in a capacitor because in a capacitor positive and negative charges separated. Imagine you have a positive and a negative charge together and you separate them.  You need to do work on the system to separate them from each other + - +- Charge being moved Electric field due to the other charge. Change in potential energy of the charge pair. Electric potential energy is stored in this system due to separated charges.

14. Physics for Scientists and Engineers II, Summer Semester 2009 Calculating the Energy Stored in a Charged Capacitor Assume a capacitor is charged such that it has charge q on it and thus has a voltage  V already across it. We now add a small amount of charge dq to the capacitor. The amount of work needed to do that is: ++++++++ -------- dq +q-q VV q dq

15. Physics for Scientists and Engineers II, Summer Semester 2009 Energy Stored in a Charged Capacitor The electric potential energy stored in a charged capacitor is

16. Physics for Scientists and Engineers II, Summer Semester 2009 Energy Stored in a Plate Capacitor Plate capacitor: