We use a cute little latching relay that will pull in in 500 usec, using about 125 microjoules, just once. After it's pullec in, it will easily dump 50 watts, which is 50 joules per second. Measured over one second, its power gain is 400,000. Over one year, it's 1.3e13. There's no limit on the power gain if you're patient enough.
John
^ power
JF
On a sunny day (Fri, 14 Nov 2008 10:47:11 -0600) it happened John Fields wrote in :
No, for Wo infinite, Gp is also infinite.
You are attempting to define power gain as joules in and watts out, but joules are not a unit of power and thus cannot be used to define power gain. Joules are a unit of energy, watts are a unit of power. energy is a measure of power over time; one joule equals one watt for one second. Your latching relay has an arbitrarily large *energy* gain, but energy gain is not power gain.
Also, arbitrarily large is not the same as infinite. As you wait longer and longer the energy gain becomes larger and larger, but for it to be infinite you would have to wait an infinite amount of time. Your relay is not capable of keeping up that 50W output forever. It will, for example, stop working when all the protons in the atoms that it is made of decay. Thus the claim that "a latching relay has infinite gain" cannot be true.
Those who flame others for making technical errors in Usenet posts should take care to avoid making technical errors of their own.
...Jim Thompson
Work is energy, not power. *Energy* gain is expressed as the ratio of work out to work in. Not power gain.
Sure; the integral is unbounded. What's your rush?
John
That'd
It has some gate leakage current, so no, its power gain is finite. If the valve eventually fails for some reason, its power gain would be finite, too... depending on the failure mode.
The power gain of the valve, or a latching relay, is an integral with no upper bound. If you name any finite power gain, I can name an interval over which the gain is 10x as much. So there is no upper limit. As an engineer, "no upper limit" means "infinite" to me.
John
Am not. I am merely averaging the power gain over time.
Oh, thank you. We always appreciate your helpful lectures.
Joules are a unit of energy, watts are a unit of power.
Protons don't decay.
Those who lecture should do a little fact-checking first.
John
On a sunny day (Fri, 14 Nov 2008 11:53:27 -0600) it happened John Fields wrote in :
I absolutely agree. It is a theoretical game.
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That'd
It may not be infinite, but it can be arbitrarily large!
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That'd
water
Careful, mathematically the limit:
limit(x --> oo, x/k) --> oo for finite k.
The gain isn't infinite in that Win > 0, and Wout < infinity.
True, BUT, we being engineers, it's close enough.
Cheers, James Arthur
That'd
Hey, we could do (and do do) this with MOSFETs too--load up the gate, then leave it on.
James Arthur
I consider something that's unbounded to be infinite. What other definition of "infinite" makes sense?
John
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