I have a simple question. The way the power company delivers power from the

power plant to the homes is using stepped-up transformers and high voltage

lines. The reason is that they want to minimize the power loss which is

P=I * I * R. But P can also be equal to P=V*I. If you increase the

voltage, why don't you have the same power loss which equals to P=I*I*R=V*I?

---

Because for the same line resistance, if V increases, I will go

down.

Say the power company was sending 120V through one mile of of #0 AWG

into a 1000 watt load. Then the circuit would look like this:

+-------+ <--8.333A-->

| 120AC|-----[0.519R]---<<--+

| | |

| | [14R4]

| | |

| 120AC|-----[0.519R]---<<--+

+-------+ <--8.333A-->

Since the power company is putting out 120VRMS and the lines look

like 0.519 ohm each, the total circuit resistance is:

Rt = 0.516R + 14R4 + 0.516R = 15.432R

and the current in the circuit is:

E 120V

It = --- = -------- ~ 7.78 amperes.

R 15.43R

And the power lost in each the lines would be:

P = I²R = 7.78A² * 0.519R ~ 31.4 watts.

For both lines, that would come to ~ 63 watts.

Now, assuming that the power company has a 1:10 step-up transformer

at the plant and a 10:1 step-down transformer at the load, the

circuit will look like this:

+-----+ +--------+ <--0.833A--> +--------+

|120AC|--|120 1200|----[0.519R]----|1200 120|---<<--+

| | | | | | |

| | | | | | [14R4]

| | | | | | |

|120AC|--|120 1200|---[0.519R]-----|1200 120|---<<--+

+-----+ +--------+- <--0.833A--> +--------+

Assuming for a moment that the transformers are lossless, the

current into our 1000 watt load, to a first approximation, will be:

E 120V

I = --- = ------ ~ 8.33 amperes.

R 14R4

Since the transformers are transforming power, if we increase the

voltage out of the secondary to ten times that across the primary,

then the current which the secondary can supply will be one tenth of

that flowing in the primary. In this case, for a 1000 watt load,

0.833A.

Now, since the line resistance hasn't changed, the power which the

lines will dissipate in moving 1000 watts over ten miles of cable