# Input power with PF, impedance on transmission line and transformer

I've just had and exam (Renewable Energy) and we had a problem that I'm not sure if is correct. The answers should be simple as we haven't studied tranmission lines at all.

Okay, here we go.
We have an AC signal, tranmission line with impedance and transformer at the end.
At the beginning of transmission line we have a signal with(max values):
V=240kV
I=400A
PF=0.85

First question was to calculate apparent power etc. what was straightforward, but the second question was:
There was voltage drop of 1kV on the transmission line.
The impedance of transmission line 0.1+0.1j per km.

So Vin=240kV sin(alpha)
Phase angle was arccos(0.85)=32 degrees
Iin=400A cos (alpha + 32)

How can we calculate what was length of the line?
Won't this initial phase shift somehow make it more complex?
Also, do transmission line do have inductance or they just have characteristic impedance?

Maybe I'm overthinking it and the answer should be just
V=IR -> 1000V=400A*(0.1*l) and therefore l = 1000/(400*0.1)=25km
Or maybe, as sqare root of (0.1^2+0.1^2) = 0.14
V=IR -> 1000V=400A*(0.14*l) and therefore l = 1000/(400*0.14)=17.85km

After calculating this we were asked what is be impedance on the secondary side of transformer with turn ratio = 16 (i.e. secondary voltage = 15kV).

• The transmission line here is a power transmission line and is modeled as a lumped element with 0.1+0.1j per km. It is not a signal transmission line with characteristic impedance and finite propagation delay. – rioraxe May 6 '16 at 22:31