Stephen-I-am said:
Slightly off topic, but something I was wondering about.
How do you get less loss in the same transmission line with higher
voltage? Wouldn't the loss scale as the square of the voltage?
Please set me straight.
P = I*V
and I = V/R <==> V = IR
So
P = I^2*R
or
P = V^2/R
So the second power dissipation equation is reduced by a factor of R while
the first is multiplied by it. This helps you with the idea if you want to
send X volts or X amps along the line with some fixed R. Always choose X
volts because you will be wasted less power. i.e.
P1 = X^2*R
P2 = X^2/R
Then P1 = R^2*P2
i.e., you will be wasting R^2 times the amount of power by choosing to send
X amps instead of X volts. for R > 1 this is huge.
e.g.,
Say you want to transfer power of 100Watts. You can do this by choosing any
I and V such that I*V = 100. Or I = 100/V.
choosing a real large number for V, say, 1000, gives I = 100/1000 = 1/10 A
and the power we are trying to send is 100W(obviously, because this is what
we started with). Or we could choose I = 1000A while V = 1/10V.
Now, we have a dissipation in the line so what is our actual power at the
other end, say, of a 10Ohm line?
100W - 1/10A*10 = 99W
VS
100W - 1000A*10 = -99900W
i.e., in the first case of using 1000V we only lost 1W and in the second
case we lost all of our power.
Why does this happen though? You have to look into why ohms law exists. It
has to do with how electrons flow in wire. As electrons flow they are
bumping into atoms of the wire.
An analogy is like a freeway. If you just have a few cars going really fast
then its usually not a problem... but what happens if you have a lot of cars
going slow? Current is like the number of cars and voltage is there speed.
(and just note that they are inversely proportional) If you want a lot of
cars then they all must go slow and going slow makes people mad(power
dissipation). If you just allow a few fast cars then no one is mad. The
total power behind the cars is like momentum. If you have 10 cars going 1
MPH or 1 car going 10 MPG then you still have the same momentum. But we
loose a little momentum from people getting off the freeway from being
pissed because its to slow... i.e., electrons hitting atoms and loosing
energy to that atom creating heat.
The idea is simple though. Sending one electron through a wire at a high
speed is much less likely to collide with an atom. Sending a large amount of
electrons through a wire, even at a very slow speed will have many more
collisions. The reason has to do with the interaction between the electrons
themselfs too. Its kinda like a whole crowd of people trying to walk over a
man hole but avoid falling in. Its much harder to do the more people you
have. If you walking towards it and you think you can jump over it but get
bumped in the process you might fall in.
