Some Questions about Polyphase Circuits

[xcvxcvvc]

I'm reading over my chapter and I encountered practice problem 12.6 below. I had some questions about this problem:

1.)how can the problem define the loads as balanced if the loads don't have the same power drawn.

3.) for a.) i thought total power meant total average power(real power). So I multiplied the given powers by the PF and added them. I got 21.55 KW instead of 22.6KW

work shown: 6 * 1 + 10 * .96 + 7 * .85 = 21.55KW

3.) The chapter says I cannot analyze the circuit on a per-phase basis if the neutral line has a resistance, but it never shows an example of doing one of those problems. Do I just run a mesh or nodal analysis?

12.6:
Three balanced Y-connected loads are installed on a balanced three-phase four-wire system. Load 1 draws a total power of 6kW at unity PF, load 2 requires 10kVA at PF = .96 lagging, and load 3 needs 7 kW at .85 lagging. If the phase voltage at the loads is 135 V, if each line has a resistance of .1 ohm, and if the neutral has a resistance of 1 ohm, find (a) the total power drawn by the loads; (B) the combined PF of the loads; (c) the total power lost in the four lines; (d) the phase voltage at the source; (e) the power factor at which the source is operating.

edit: the homework problems in the chapter are easier than this monster, so it's ok if I can't solve it. I just wanted to take some steps toward understanding it. What's worse is the practice problems rarely have diagrams drawn like with this one, which really puts my knowledge of terminology to the test.

 

[Kruum]

3.) The chapter says I cannot analyze the circuit on a per-phase basis if the neutral line has a resistance, but it never shows an example of doing one of those problems. Do I just run a mesh or nodal analysis?

Are you sure you didn't misread? If the loads are balanced (like they are in this case) the current in the neutral wire is 0, so the impedance in the neutral wire shouldn't affect anything. And that's the whole point of 3-phase systems - half the loss in transfer lines.

 

[xcvxcvvc]

Are you sure you didn't misread? If the loads are balanced (like they are in this case) the current in the neutral wire is 0, so the impedance in the neutral wire shouldn't affect anything. And that's the whole point of 3-phase systems - half the loss in transfer lines.

well yeah, it has to be an unbalanced load with either no neutral wire or a neutral wire resistance. But how is that example problem balanced?

 

[Kruum]

But how is that example problem balanced?

Nevermind that, I didn't read the question with thought...