1. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 1 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 43 Prob 5.80 Solution Dual-Source Complex-Power Balance

2. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 2 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices BackGround EE (§5.5)  Consider Sinusoidal Sources of the form  Alternatively  Recall for a Sinusoid  Complex Power Where –S ≡ Complex Power in V∙A –P ≡ Real Power in Watts –Q ≡ ReActive Power in VAR

3. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 3 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices BackGround EE (§5.5)  Each Passive Component (R, C, L, V src, I src ) Generates it’s own Complex Power in an operating Circuit  Furthermore Complex Power is Conserved, just a real power was conserved in purely resistive Circuits; i.e.:  Equating Real & Imag Parts

4. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 4 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices R, C, L vs. P&Q  Note that the passive sign Convention Applies to Complex Power a well Positive Pwr → ABSORBED or DISSIPATED Negative Pwr → SUPPLIED or GENERATED  RESISTORS can only DISSIPATE Real Power per Text Eqns (5.69) & (5.71) I Rrms ≡ Current thru R V Rrms ≡ Voltage across R

5. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 5 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices R, C, L vs. P&Q  INDUCTORS create POSITIVE ReActive (imaginary) Power per Text Eqns (5.70) & (5.72) Where –I Lrms ≡ Current thru L – V Lrms ≡ Voltage across L –X L ≡ Inductive ReActance, ωL

6. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 6 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices R, C, L vs. P&Q  CAPACITORS create NEGATIVE ReActive (imaginary) Power per Text Eqns (5.70) & (5.72) Where –I Crms ≡ Current thru C – V Crms ≡ Voltage across C –X C ≡ Capacitive ReActance, −1/(ωC)

7. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 7 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices S by ShortHand Calc  Alternatively Calculate S for any Component using the COMPLEX CONJUGATE of the CURRENT Thru the device  Recall Conjugation for Imaginary of Phasor Values

8. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 8 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices S by ShortHand Calc  If  Then  Also For Sources the Apparent Power:

9. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 9 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices Apparent Power  Apparent Power Calculations are usually used with SOURCES, but the concept also applies to Impedance Loads  Given an Impedance with Current I Z, and Voltage-Drop V Z then

10. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 10 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices Problem 5.80  Given Circuit  Find The Power Condition for each element, the Quantity, Nature, and if the element is Absorbing/Supplying Power  Note that this is SINGLE LOOP Circuit which thus has ONE Current

11. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 11 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

12. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 12 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

13. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 13 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

14. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 14 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

15. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 15 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices Confirm: ∑P avg = 0  Note that the Average Powers Add to ZERO as they must by conservation of Energy

16. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 16 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices Check ReActive Power

17. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 17 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

18. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 18 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices

19. BMayer@ChabotCollege.edu ENGR-43_Prob_5-80_Dual-Src_Complex-Pwr_Solution_.pptx 19 Bruce Mayer, PE Engineering 43: Electrical Circuits & Devices