Thread: Brainteaser
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Old May 27th 06, 07:38 AM posted to rec.radio.amateur.antenna
K7ITM
 
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Default Brainteaser

In a previous posting, I noted that for the 100 ohm line driven by
200*sqrt(2) volts DC through 100 ohms, there are two load resistors
that dissipate 100 watts: 100*(3 +/- sqrt(8) ) ohms. Continuing the
observation about energy stored in electric versus energy stored in
magnetic fields, for the low resistance, the steady state load and line
voltage is low and the current is high; for the high resistance, the
steady state voltage is high and the current is low. In the first
case, 8.5786 joules is stored in the electric field and 291.42 in the
magnetic; in the second those are reversed and 291.42 are stored in the
electric and 8.5786 in the magnetic. The ratio of the two energies is
exactly the same as the ratio of the load resistances.

In our lossless line, if the excitation is AC and steady-state has been
reached, then the total energy stored per unit length varies as a
function of time and distance in a somewhat complex manner. The ratio
of electric to magnetic varies along the length of the line and as a
function of time, with extremes being in a ratio equal to the square of
the SWR, occuring of course at voltage and current maxima, spaced 1/4
wave apart, alternating down the line.

I'm not sure that those observations will be any use to anyone, but
maybe they are of academic interest. Who knows what I might come up
with after some Glenmorangie.

Cheers,
Tom