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

Learn to compute circuit impedance, analyze RLC circuit response to frequency changes, and determine voltages using voltage divider formula. Explore parallel circuits and current division. Practice frequency domain analysis and waveform transformations.

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

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

  2. OBJECTIVES • Compute the total circuit impedance for series RLC circuits. • Explain the effects of frequency changes on RLC circuit response. • Determine circuit voltages and currents in series RLC circuits. • 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:

  5. Circuit simplification

  6. (b) Draw Impedance Triangle R R j q q XC ZT ZT - j

  7. (c) Find is, iC, iRL

  8. (d) Using Current Divider

  9. Example #2: Find i and vc

  10. Elements in Frequency domain • =4 rad/s

  11. Circuit in Freq Domain

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

  13. (b) The capacitor voltage, VC

  14. Example #3: Find iX(time domain) Solution:

  15. Example #4: Find Z1 and Z2 Solution:

  16. Example #5: Find i(t)

  17. Different waveform of VS • VS1 andVS2 are different: • When analyzing ac circuit, it is expedient to express both signals as either Sine or Cosine.

  18. Change the waveform of VS1 • Using identity:

  19. Changing Cosine to Sine:

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

  21. Different waveform of VS • VS1 andVS2 are different: • When analyzing ac circuit, it is expedient to express both signals as either Sine or Cosine.

  22. Change the waveform of VS1 • Using identity:

  23. Redraw the circuit

  24. Elements in Frequency domain • =4 rad/s

  25. Find The Current

  26. Solution:

  27. (b) Find the vc(t), vL(t)

  28. (c) Find the ic(t), iL(t)

  29. (d) Sketch the waveform for vc(t), vL(t), ic(t), iL(t) (e) Explain the phase relationship between V and I for capacitor and inductor.

  30. Z2 Example #7: Find ZT, IT, VC2, P

  31. Solution • Find the total impedance: • Then, the total current is:

  32. Solution P = VI cos (qT) = (10V)(461 mA) cos(-42.4o) = 3.40 mW

  33. Z3 Z2 Ex: Find ZT, IL3, P

  34. Z2, Z3, ZT, and IT

  35. IR3, IL3, P P = EI cos (qT) = (10V)(1.01 mA) cos(31.4o) = 8.62 mW

  36. TOOLS • 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.

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