Chapter 10 “ Average Power and RMS Values ”

1. Yangon Technological UniversityDepartment of Electronic Engineering & Information TechnologyVideo Conferencing on EcE 1011 ( EC + McE ) for A.G.T.I Yr Ipresented by Daw ThidaThanLecturerEC Dept. Y.T.U

2. EcE 1011 ( EC + McE ) Engineering Circuit ( 2nd Semester ) for A.G.T.I Yr. I • Chapter 10 • “ Average Power and RMS Values ”

3. Out lines of presentation • Five categories of power • Instantaneous power • Average power • Effective values of current and voltage • Apparent power and power factor • Complex power

4. Five categories of power : • (i) Instantaneous power ( W ) • (ii) Average power ( W ) • (iii) Apparent power ( VA ) • (iv) Complex power ( VA) • (v) Reactive power ( VAR )

5. (i) Instantaneous power • The product of the time-domain voltage and time-domain current associated with the element or network of interest. • The product of instantaneous voltage across the device and instantaneous current through it . • The passive sign convention is assumed. • Unit – W (Watt)

7. Periodic Function • f(t) = periodic function • T = period of periodic function ( s ) • Definition of periodic function mathematically is given by:

8. (ii) Average power or real power • if the instantaneous voltage across the device and instantaneous current through it are periodic waveforms ; then , average power of the device is given by

9. P= average power ( W ) T = period (s) p(t) = instantaneous power ( W ) If v(t) = Vm cos (t + ) (V) and i(t) = Im cos (t+) (A) ; then P = ½ Vm Im cos ( - ) (W) where p(t) = v(t) i(t)

10. For Resistor • PR = average power for resistor ( W )

11. For Inductor and Capacitor • PX = average power for Inductor and Capacitor • PX = 0 W

12. For Sources • P = average power for sources • P = ½ Vm Im cos ( - ) (W)

13. Effective values of current and voltage • For any resistor,

15. Veff = effective value of voltage ( Vrms ) • Ieff = effective value of current ( Arms ) • v(t) & i(t) are periodic functions • Similarly,

16. For Resistor • PR = average power for resistor ( W )

17. For Sources • P = average power for sources • P = Veff Ieff cos ( - ) (W)

18. (iii) Apparent power ( VA ) • Is the product of the effective values of the current and voltage of device • Apparent power = Veff Ieff • The ratio of the real power to the apparent power is called power factor ( PF ). • 0  PF  1

19. Power factor ( PF )

20. (iv) Complex power ( polar or exponential form ) • S = Veff Ieff e j() • The magnitude of S = apparent power • The angle of S = the PF angle • S = VI*

21. Complex power ( Rectangular form ) • S = P + jQ • Real part of S = P = average power ( W ) • Imaginary part of S = Q = reactive power • ( VAR) • P = Re[ S ] = Veff Ieff cos ( - ) (W) • Q = Im[ S ] = Veff Ieff sin ( - ) (W)

22. Thank you for your attention