This document discusses power (P) in an electrical circuit. It shows that power (P) equals the square root of 3 times voltage (V) times current (I) times the power factor (pf). The power factor accounts for the phase difference between the voltage and current. So power can be expressed as either the square root of 3 times voltage times current times power factor, or the square root of 3 times voltage times current times the cosine of the phase difference angle.

1. Text

2. P =V I pf
( pf = cos Φ)

3. PK = VP IP cos ΦK

4. PK + PL + Pm = 3 PK

5. 3 PK = 3 VP IP cos ΦK
or
3 PK = 3 VP IP pf

6. IL = IP and VL = √3 VP
and VP = VL/√3

7. (3 PK) = PK + PL + Pm

8. 3 PK = 3 VP IP pf
becomes P = 3
VL IL pf
√3
P = √3 VL IL pf
Expressed as:
P = √3V I pf
OR P = √3 VI cos Φ