Heating Effect of Current wrt Transformers

Question

I just learnt that we use step up transformers to reduce heating losses in overhead wires. I was given some values.

Say, the power plant is a 1 million watt rated plant. The voltage is $400V$ at the plant, so the Current must be $2500A$.

$R = V/I$

R = 400/2500 = 0.16 ohms

Now, using a step up transformer, voltage is $33000 V$. Current must be $30.3 A$. New resistance is coming as $1090 ohms$

Q1) How has resistance changed when the length of the wire is the same and current decreased. $R = ρL/A$

Q2) Say heat produced $H = I^2Rt$, first case it is $2500^2 *.16 = 1,000,000J$ and with $V^2/R$ we also get 1 million J, but in second case, we also get 1 mil joules. $H = 33000^2/1090 = 1,000,000$ and $H = 30.3^2*1090 = 1,000,000 Joules$

something is wrong in my concepts or calculations, it might be a very dumb question, but i am not able to understand this stuff.

Thank you for any replies!!

Answer 1

There is a flaw in your initial reasoning, as follows.

When you calculate the resistance in the case of the generator source (400V, 2500A) the "resistance" you get is the source impedance of the generator itself and for the transmission line case it is the lumped impedance of the transmission line.

Your calculations require knowledge of the load impedance at the far end of the transmission line, not the characteristic impedance of either the generator or the transmission line.