1. Example 1
Load 1
Load 2
20 kVA
230 Vrms R
20 mH
pf 0.8 lagging
50 Hz
If the combined power factor of the load 1 and load 2 is 0.75 lagging, determine the value of R.

2. Things You Should know:
Power-Impedance Relationships
Reactive power of L, QL, is positive
Reactive power of C, QC, is negative
Pre-requisite:
Basic Trigonometry
Complex number

3. Solution: Load 1: Load 2: P2 Q2 S2 q2 P1 Q1 S1 q1 Total Load: ST
QT=Q1+Q2 qT
PT=P1+P2
Note: The power triangles were drawn not to scale

4. P1 Q1 S1 q1  

5. P2 Q2 S2 q2 

6. PT QT ST qT  

7. PT QT ST qT  

8. Exercise 1
Load 1
pf 0.8 lagging
20 kVA C
5 W
Load 2
230 Vrms
50 Hz
If the combined power factor of the load 1 and load 2 is 0.95 lagging, determine the value of C.

9. If V1 = 2000 V rms, determine:
Example 2:
4 kW
pf 0.9
lagging
6 kVAR
pf 0.5
leading Vs Is
0.1 W
0.3 W
0.2 W + - V1
Load 1
Load 2
If V1 = 2000 V rms, determine:
(i) Vs and Is
(ii) Complex power for all circuit elements (exclusive of the source)
(iii) Complex power supplied by the source.

10. If I1 = 4545 A rms, determine:
Exercise 2:
4 kW
pf 0.9
lagging
6 kVAR
pf 0.5
leading Vs Is
0.1 W
0.3 W
0.2 W
Load 1
Load 2 I1
If I1 = 4545 A rms, determine:
(i) Vs and Is
(ii) Complex power for all circuit elements (exclusive of the source)
(iii) Complex power supplied by the source.