1. Lecture 04: AC SERIES/ PARALLEL CIRCUITS, VOLTAGE/ CURRENT DIVIDER

2. OBJECTIVES 1.Compute the total circuit impedance for series RLC circuits. 2.Explain the effects of frequency changes on RLC circuit response. 3.Determine circuit voltages and currents in series RLC circuits. 4.Compute voltage drops across components in an RLC circuit using the voltage divider formula.

3. Example #1: Parallel Circuits

4. (a) Find total impedance The circuit given is already in freq domain:The circuit given is already in freq domain:

5. Circuit simplification

7. (b) Draw Impedance Triangle ZTZTZTZT XCXCXCXC R ZTZTZTZT   j - j R

8. (c) Find is, i C, i RL

9. (d) Using Current Divider

10. Example #2: Find i and v c

11. Elements in Frequency domain =4 rad/s Time domain Freq domain

12. Circuit in Freq Domain

13. (a) The current, i The current in series circuit,The current in series circuit, The total impedance is;The total impedance is;

15. (b) The capacitor voltage, V C

16. Example #3: Find i X (time domain) Solution:

17. Example #4: Find Z 1 and Z 2 Solution:

18. Example #5: Find i(t)

19. Different waveform of V S  V S1 and V S2 are different:  When analyzing ac circuit, it is expedient to express both signals as either Sine or Cosine.

20. Change the waveform of V S1 Using identity:Using identity:

21. Changing Cosine to Sine:

22. Example #6: (a) Find i(t)

23. Different waveform of V S  V S1 and V S2 are different:  When analyzing ac circuit, it is expedient to express both signals as either Sine or Cosine.

24. Change the waveform of V S1 Using identity:Using identity:

25. Redraw the circuit

26. Elements in Frequency domain  =4 rad/s  =4 rad/s Time domain Freq domain

27. Find The Current

28. Solution:

29. (b) Find the v c (t), v L (t)

30. (c) Find the i c (t), i L (t)

31. (d) Sketch the waveform for v c (t), v L (t), i c (t), i L (t) (e) Explain the phase relationship between V and I for capacitor and inductor.

32. Example #7: Find Z T, I T, V C2, P Z2Z2

33. Find the total impedance:Find the total impedance: Then, the total current is:Then, the total current is: Solution

34. Solution P = VI cos (  T ) = (10V)(461  A) cos(-42.4 o ) = 3.40 mW

35. Ex: Find Z T, I L3, P Z3Z3 Z2Z2

36. Z 2, Z 3, Z T, and I T

37. I R3, I L3, P P = EI cos (  T ) = (10V)(1.01 mA) cos(31.4 o ) = 8.62 mW

38. TOOLS Note from the previous examples, all of our tools from DC work:Note from the previous examples, all of our tools from DC work: –Ohm’s Law –Voltage Divider –Current Divider –Kirchoff’s Current Law –Kirchoff’s Voltage Law They are the same – but we use COMPLEX NUMBERS.They are the same – but we use COMPLEX NUMBERS.