I'm given this transmission line problem in which I have a 3-phase transformer and I'm also given its impedence. I usually solve these problems using only one phase. So what should the impedence value be in the equivalent single phase circuit I make? More specifically , if it is correct to say it this way, is the 'phase' impedence different from the 'line' impedence?
The impedance on the transformer's nameplate (Z%) is the positive-sequence impedance, Z1.
You don't need to modify this before putting it into your (positive-sequence) single-phase equivalent circuit, which you use for balanced three-phase calculations. There are no factors of √3 in the impedance value.
You may need to convert the impedance to the same basis as the rest of your calculations.
Example: if your calculations are per-unit on 100 MVA base, and your transformer impedance is 12% p.u. on 20 MVA, you would convert that to Z = 60% p.u. on 100 MVA.
If you are doing un-balanced three-phase calculations, you will need the negative-sequence impedance and the zero-sequence impedance, to put into your negative-sequence and zero-sequence equivalent circuits.