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