Standing-Wave Current vs Traveling-Wave Current
Roger wrote:
By my using the words 'power' "storage factor", you got my point, hence
the reaction.
Before dismissing the concept of "storing power", consider that when
discussing a transmission line, it could be a useful description.
As you know, power is energy delivered over a time period.
No, it's the rate of energy delivery or movement, which is not quite the
same thing.
It always
carries a time dimension having beginning and end. Power(watt)
=v*i/(unit time) = 1 joule/second.
Sorry, you've got this wrong. One watt is indeed one joule/second, but
P(t) = v(t) * i(t), period. Energy is the integral of P(t) dt. Power is
the time derivative of energy, or dE(t)/dt where E is the energy.
You could as reasonably say that energy always "carries a time
dimension". After all, one joule = 1 watt-second.
In the example you give of charging a capacitor, the time dimension is
lost, so you are correct that only energy is conserved. Power is lost.
Sorry, I don't understand that.
With a transmission line, we have an entirely different case. Here
power is conserved because the time information is maintained. Power is
stored on the line during the period it resides on the line. For
example, we excite the line at one end and some time period later find
that power is delivered to some destination. During the time period
that the power was on the line, the information that defines the energy
distribution over time has been preserved.
Ok, let's test this. Please tell me exactly how many watts are stored on
the line of the second analysis (where the perfect source is in series
with a 150 ohm resistor). Next, tell me how many watts will come out of
the line if we quickly disconnect the perfect source and source
resistance and replace it with:
A: A 50 ohm resistor, or
B: A 150 ohm resistor
If power is stored, we implicitly store energy. Energy is v*i measured
in joules without a time factor.
No, Energy is not v*i. Power is v*i. Energy is the time integral of v*i.
Power is not stored; energy is.
Obviously we store energy on a
transmission line when we store power.
I guess it would be obvious if you believe you can store power. But
before going further, please demonstrate what you mean by calculating
how many watts of power are stored on the example line. I showed exactly
how many joules of energy were stored, you can show how many watts of power.
So if in the future, I use the term "power storage", please take it to
mean that energy distributed over time is under consideration.
I'm afraid I'm not very good at translating what people mean when they
say something else. Why not call energy storage "energy storage", power
"power", and energy "energy"? Then I and hopefully other readers will
know what you mean. The MKSA unit of power is the watt, and of energy,
the joule. The two are no more the same than speed and distance, or
charge and current.
I hope
the term might be useful to you as well.
No, I have enough trouble communicating when I take great care with my
terminology. The last thing I need is to be saying something which means
something else -- or means nothing at all. When I mean energy storage,
I'll say "energy storage", thank you.
Roy Lewallen, W7EL
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