Three phase system questions
Three similar impedances are connected in star across 2000 V, 50 Hz three phase supply. Power absorbed is 300 kW. Current taken is 100 A lagging. Find the values of circuit parameters in each phase.
  
  
  I calculated : V_ph = 2000 / √3 = 1154.7V and the impedence to be: Z = Vph / 100 = 1.154 ohms.


Double-check that last bit.


  The power factor is: 2000 /3 &times; Vph &times; Iph which comes out to be 0.28.


That's not the correct way to calculate PF. You need to calculate the per-phase power (kW) and per-phase apparent-power (kVA) and go from there.


  My question is how can I calculate the power for each impedence. As far as I know ,I only know equation for total power.


As shown above.




  
    A three phase 400 V motor has an output of 20 HP with efficiency of 90% and at a power factor of 0.8. Determine the reading on each of the two wattmeters connected to measure the input. Also find the line current.
  
  
  So input Power is 90% of 20 that is 18 watts. 


Alarm bell 1: You reckon you can supply it with 18 W and get 20 W out!

Alarm bell 2: You think that 20 HP = 20 W. (It doesn't so you need to look that up.)


  So I presume W1 + W2 = 18 watts.
  
  My book gives the formula: tan(θ) = √3(w2 - w1 / w2 + w1) or tan(θ) = -√3(w2 - w1 / w2 + w1) where w1 and w2 are wattmeter readings in the wattmeter. My question is how do i identify which equation to use.


It depends on the relative polarity of the two meters. Since it's a motor you know the load is inductive and can base your result on that.



From the comments:


  Why can't we use: P = 3 x V_ph x I_ph x p.f.?


You can but you wrote "The power factor is:2000/3XVphXIph" or \$ PF = \frac V {3V_{ph}I_{ph}} \$. It should be \$ PF = \frac P {3V_{ph}I_{ph}} \$ where \$ V_{ph} is the phase to star-point voltage (not phase to phase).

Yes, you can calculate from the total power.


  Also I didn't get how u concluded that the load is inductive.


It's a motor.