Current and power with transformers

[Cocoleia]

Homework Statement

I am working on the following problem:

And ideal single phase transformer 240V/2880V is supplied with a 240V source via a resistance cable of 3ohm. If we connect a R=720ohm resistance to this, determine the primary current and the dissipated power in R.
(I'm sorry if some of the wording is wrong, I am translating the question into English ... )

Homework Equations

The Attempt at a Solution

I tried to find the current in 2 different ways, and came to 80A each time.
For the dissipated power, I am really not sure how to incorporate this 720ohm. I read in my notes that Power in = Power out, but I feel like this isn't the answer for this situation..

 

[CWatters]

Not sure I can follow your working. The voltage going into the transformer won't be 240V because some is lost across the 3R cable.

The way I would approach the problem is to "transform" the 720R load resistor to work out what the equivalent load would be on the primary side. Then use the potential divider method to work out the actual input voltage to the transformer.

Edit: If this is confusing start with a circuit diagram.

 

[Cocoleia]

Not sure I can follow your working. The voltage going into the transformer won't be 240V because some is lost across the 3R cable.

The way I would approach the problem is to "transform" the 720R load resistor to work out what the equivalent load would be on the primary side. Then use the potential divider method to work out the actual input voltage to the transformer.

Edit: If this is confusing start with a circuit diagram.

You mean transform it so everything is on the primary side ? Or how do I transform it ?

 

[Cocoleia]

Not sure I can follow your working. The voltage going into the transformer won't be 240V because some is lost across the 3R cable.

The way I would approach the problem is to "transform" the 720R load resistor to work out what the equivalent load would be on the primary side. Then use the potential divider method to work out the actual input voltage to the transformer.

Edit: If this is confusing start with a circuit diagram.

If I do this, I get an input voltage of 150V, which I then divide my 3ohm to get my current ?

 

[CWatters]

Yes I mean transform it so everything is on the primary side. An example...

Lets say you had a 2:1 step down transformer with a 10R on the secondary side. That 10R would be equivalent to a 40R on the primary side...

Proof...

The secondary current Is = Vs/Rs. If N is the winding ratio the primary current Ip would be Is/N = Vs/NRs.

The equivalent resistance Rp on the primary side = Vp/Ip = Vp/(Vs/NRs) = N²Rs

If N = 2 and Rs = 10 then Rp = 40.

 

[CWatters]

If I do this, I get an input voltage of 150V, which I then divide my 3ohm to get my current ?

Yes the input voltage to the transformer is 150V but it's not across the 3R. The voltage across the 3R is 240-150V.

 

[Cocoleia]

A

Yes the input voltage to the transformer is 150V but it's not across the 3R. The voltage across the 3R is 240-150V.

ah, I see.

would the power then be the secondary current multiplied by 720^2 ?

 

[CWatters]

Not 720 squared

You can use Is²*R or Vs²/R

 

[Cocoleia]

Not 720 squared

You can use Is²*R or Vs²/R

Perfect, thank you !