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)

 

You missed a step. The correct order of equations is:
\( S=V\angle0 \cdot I\angle{-60} = V\cdot I\cdot \cos{60}\Leftrightarrow\\
I=\frac{S}{V\cdot\cos{60}}=30Amps
\)

From now on you are good to go.

 

Thanks Geo

Easy when you know how.