AC equations page.

Discussion in 'Feedback and Suggestions' started by DrMarten, Aug 11, 2008.

  1. DrMarten

    Thread Starter New Member

    Aug 11, 2008
    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 =


    approx 191 Volts A.C.


    Last edited: Aug 11, 2008
  2. Dave

    Retired Moderator

    Nov 17, 2003
    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. even though we have a comprehensive three-phase section (ref.

    The reference section may benefit from your suggested addition. Thanks.