1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 10: June 12 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 RC Circuits RC Circuits: Circuits containing Resistors and Capacitors. In such circuits, the current(s) may not be constant. + -

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Charging the Capacitor Apply Kirchoof’s loop rule: + - +-

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Solving the Differential Equation

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Getting the current t q(t) t I(t)

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 The time constant  of the RC circuit

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Measuring the time constant t V c (t) t I(t)

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Discharging the Capacitor Apply Kirchhof’s loop rule: + - +-

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Solve….

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Discharging the Capacitor…the way Serway does it Apply Kirchhof’s loop rule: + - +-

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Solve….

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Example: Problem 31 in the book 10V 1.00  4.00  8.00  2.00  1)For long time: What is V c ? 2)For long time: What is Q c ? 3)If battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth of it’s initial voltage? 1.00  F 1) For long times, the current I c =0 (no more charging or discharging). 10V IcIc a b

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Example: Getting Voltage over Capacitor 10V 1.00  4.00  8.00  2.00  ab

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Example: Discharging without Battery 1.00  4.00  8.00  2.00  1.00  F 6.00  9.00  1.00  F 3.60  1.00  F

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Magnetic Fields

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Magnetic Fields and Forces N S