Transformer Losses Clarification for NCEES #524

[wfg42438]

In the sample NCEES question below we are given the losses at 0% and 50% kVA

I realize the 0% losses represent the no load losses which are constant

Now the 50% loading value includes both the partial copper and the no load losses so subtracting the no load losses makes sense

The part i dont follow is why the 50% core loss is multiplied by 4

Can someone please shed some light on why thats the case i would think we would double the copper loss instead of multiplying by 4?

 

[main197]

Copper loss at full load is Pfl= (I_fl)^2*R

At 50% load, I_50= 0.5* I_fl

This gives P50= (I_50)^2*R= (0.5*I_fl)^2*R= 0.25 *(I_fl)^2*R= 0.25*Pfl

So, P50= 0.25*Pfl. And Pfl= P50/0.25= 4*P50

 

[wfg42438]

Thank you this makes complete sense now!