1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 18: July 6 th 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Energy loss in the circuit

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Energy loss in the circuit

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Example from book: Chapter 32, Problem 18

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Use Kirchhoff’s Rules 1 2

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Solving the system of equations

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Solving the system of equations

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Solving the system of equations

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Solving the system of equations

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Solving the system of equations For long times t:

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 AC (“alternating current”) Sources

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Resistors in AC Circuits

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Resistors in AC Circuits Applied voltage and resulting current reach their peaks at the same time  They are “in phase”.

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Phasor Diagram In phasor diagram: Vectors rotate counterclockwise with frequency . The projection of the rotating vectors onto the vertical axis yields the instantaneous values of voltage and current.

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Average current, rms current, average power

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Measuring AC voltage and AC current with volt/current meters.

17. Physics for Scientists and Engineers II, Summer Semester 2009 17 Inductors in an AC Circuits

18. Physics for Scientists and Engineers II, Summer Semester 2009 18 Inductors in an AC Circuits For sinusoidal voltages: The phase of the current through the inductor lags behind the voltage across the inductor by 90 degrees (one quarter cycle in time).

19. Physics for Scientists and Engineers II, Summer Semester 2009 19 Inductors in an AC Circuits

20. Physics for Scientists and Engineers II, Summer Semester 2009 20 Capacitors in an AC Circuits

21. Physics for Scientists and Engineers II, Summer Semester 2009 21 Capacitors in an AC Circuits For sinusoidal voltages: The phase of the current to the capacitor leads the voltage across the capacitor by 90 degrees (one quarter cycle in time).

22. Physics for Scientists and Engineers II, Summer Semester 2009 22 Capacitors in an AC Circuits