Electrical circuits lecture notes b. Tech

Concept of power factor, real, reactive and complex power: 
Complex Power is defined as the product of Voltage phasor and conjugate of current phasor 
If S is the complex power then, 
S = V . I
*
V is the phasor representation of voltage and I* is the conjugate of current phasor.
So if V is the reference phasor then V can be written as |V| 
∠
0. 
(Usually one phasor is taken reference which makes zero degrees with real axis. It eliminates 
the necessity of introducing a non zero phase angle for voltage) 
Let current lags voltage by an angle φ, so I = | I | 
∠
-φ 
(current phasor makes -φ degrees with real axis) 
I
*
= | I | 
∠
φ 
So, 
S = |V| | I | 
∠
(0+φ) = |V| | I | 
∠
φ 
(For multiplication of phasors we have considered polar form to facilitate calculation) 
Writing the above formula for S in rectangular form we get 
S = |V| | I | cos φ + j |V| | I | sin φ
The real part of complex power S is |V| | I | cos φ which is the real power or average 
power and the imaginary part |V| | I | sin φ is the reactive power.
So, S = P + j Q 
Where P = |V| | I | cos φ and Q = |V| | I | sin φ 
P is measured in watt and Q is measured in VoltAmp-Reactive or VAR. In power systems 
instead of these smaller units larger units like Megawatt, MVAR and MVA is used. 

---

The ratio of real power and apparent power is the power factor
power factor = Cos φ = |P| / |S| 
= |P| / √(P 
2
+Q 
2
) 

---

ELECTRICAL CIRCUITS 
UNIT-IV 
NETWORK THEOREMS 
 

Thevenin’s Theorem

Norton’s Theorem

Maximum Power Transfer Theorem
