# AC equations page.

#### DrMarten

Joined Aug 11, 2008
5
Hi ALL from an electrician in the U.K.,

Mentioned on the page for A.C. circuit equations under Volume V area.

Single phase power in Watts ( W ) should be

P = Vp Ip Cos$$\phi$$

Where P is power in watts, Vp is the phase voltage, Ip is the phase current and Cos$$\phi$$ is the power factor.

In other words P = Vp X Ip X Cos$$\phi$$

The power factor is the cosine of the angle phi or $$\phi$$ and this is the angle the phase current waveform lags or leads the voltage waveform.
Ideally the angle phi or $$\phi$$ should be close to zero
so that Cos $$\phi$$ = 1

I.E. Cos(0) = 1

3 phase power in Watts is

P = Square Root(3) VL IL Cos$$\phi$$

Where VL is the Line Voltage between any two phases,
IL is the Line Current and Cos$$\phi$$ is the power factor.

Additionally in all 3 phase systems the Line Voltage VL can be calculated by this

VL = Square Root(3) Vp

where the square root of 3 is approx 1.7320508075688772935274463415059
and Vp is the phase voltage.

In the U.K. and other countries

Vp = 240 Volts A.C. or 240VAC and VL = 415 Volts A.C. or 415VAC

Some countries use 220 Volts A.C.

In the USA the domestic Vp or phase voltage is 110Volts A.C. , or so I've heard. So that would make VL >>

110 X 1.7320508075688772935274463415059 =

190.52558883257650228801909756565

approx 191 Volts A.C.

Regards,

DrM.

Last edited:

#### Dave

Joined Nov 17, 2003
6,970
Hi DrMarten, welcome to AAC.

You are correct in your assessment. The single-phase equations are covered in that reference section, however as you note the three-phase equations are not. I assume this is because the Power Factor section of the e-book merely deals with the case of single phase (ref. http://www.allaboutcircuits.com/vol_2/chpt_11/index.html) even though we have a comprehensive three-phase section (ref. http://www.allaboutcircuits.com/vol_2/chpt_10/index.html)