Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

1. Engineering 43 Prob 5.80SolutionDual-SourceComplex-PowerBalance Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. 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. BackGround EE (§5.5) • Each Passive Component (R, C, L, Vsrc, Isrc) 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. 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) • IRrms ≡ Current thru R • VRrms ≡ Voltage across R

5. R, C, L vs. P&Q • INDUCTORS create POSITIVEReActive (imaginary) Power per Text Eqns (5.70) & (5.72) • Where • ILrms ≡ Current thru L • VLrms ≡ Voltage across L • XL ≡ Inductive ReActance, ωL

6. R, C, L vs. P&Q • CAPACITORS create NEGATIVEReActive (imaginary) Power per Text Eqns (5.70) & (5.72) • Where • ICrms ≡ Current thru C • VCrms ≡ Voltage across C • XC ≡ Capacitive ReActance, −1/(ωC)

7. 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. S by ShortHand Calc • If • Then • Also For Sources the Apparent Power:

9. Apparent Power • Apparent Power Calculations are usually used with SOURCES, but the concept also applies to Impedance Loads • Given an Impedance with Current IZ, and Voltage-Drop VZ then

10. 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

15. Confirm: ∑Pavg = 0 • Note that the Average Powers Add to ZERO as they must by conservation of Energy

16. Check ReActive Power