Resistance reactance Impedance calculation

Discussion in 'Homework Help' started by hotrocks, Jun 29, 2010.

  1. hotrocks

    Thread Starter New Member

    Jun 29, 2010
    8
    0
    I am currently working my way through a book called Electrical Installation Calculations Advanced 7th edition and have reached the following question

    The current in a single phase circuit lags behind the voltage by 60 degrees. The power in the circuit is 3600w and the voltage is 240v. Calculate the value in ohms of the resistance ,the reactance and the impedance.

    I have calculated

    VA=3600 so 3600/240=I so I = 15amps. V=IR so 240/15 = Z Z = 16 ohms

    cosine phi of the angle 60 = 0.5

    0.5= R/Z which is 0.5 = R/16 or 0.5 * 16 = R R = 8 ohms

    Using Pythagoras Z squared = R squared + X squared or 256 – 64 = X squared X = 13.86 ohms

    The answers in the book are given as

    Resistance R = 4 ohm
    Reactance X = 6.928 ohm
    Impedance Z = 8 ohm

    Where am I going wrong.
    (all help much appreciated)
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    You missed a step. The correct order of equations is:
     S=V\angle0 \cdot I\angle{-60} = V\cdot I\cdot \cos{60}\Leftrightarrow\\<br />
I=\frac{S}{V\cdot\cos{60}}=30Amps<br />

    From now on you are good to go.
     
  3. hotrocks

    Thread Starter New Member

    Jun 29, 2010
    8
    0
    Thanks Geo

    Easy when you know how.
     
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