time constant in resonant circuit

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Original poster: "Alfred Erpel" <alfred-at-erpel-dot-com> 


Hello All,

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                    switch
                        \
          .-----------.  \------------.
          |                           |
          |                           |
          |                           o
          |  +                        o
         ---                          o
         --- DC power supply          o .00024318 H
          |  -                        o
          |                           o
          |                           |
          |                           |
          .-----------\/\/\/\---------.

                   .0001 ohms

                    figure A



For purposes of discussion it is assumed that no resistance exists except as
specified.
In the circuit above, when the switch is closed, it will take 5 time
constants of L/R before the inductor is conducting at essentially 100%.

L/R = 1 time constant
1 time constant  = .00024318 H / .0001 ohms = .243 seconds
5 time constants = 1.215 seconds

************************************************************


                    switch
                        \
          .-----------.  \------------.
          |                           |
          |                           |
          |                           o
          |                           o
         ---                          o
         --- .00166666 µF             o .00024318 H
          |                           o
          |                           o
          |                           |
          |                           |
          .-----------\/\/\/\---------.

                    .0001 ohms

                     figure B



In this circuit let's assume no resistance except as specified and a fully
charged capacitor just before the switch closes.  When the switch closes the
circuit will ring at its resonant frequency of 250,000 hz.

resonant frequency = 1 / 2 * pi * sqrt[L * C]
resonant frequency =~ 250,000 hz

The quarter cycle time (the first 90 degrees) is ( 1 / 250,000 ) second / 4,
so the quarter cycle time is .000001 seconds

If the inductor in figure B above was subject to charging at the same rate
as the identical inductor in figure A there couldn't be resonance since the
time constant of .243 seconds is orders of magnitude away from .000001
seconds.  It appears that the time constant does not come into play in a
resonant circuit.  Is this what is happening?  Could someone please explain
this?  Thank you.

Regards,

Al Erpel