Re: A Question About A Simple LRC circuit

["John S. Denker" <jsd@MONMOUTH.COM>]

At 05:29 AM 3/6/01 -0500, Robert B Zannelli asked :

> what is the mechanical analog
> to an electrical circuit. I would think just from intuition that a spring
> would serve in a similar manner to a capacitor while mass inertia would be
> the equivalent to inductance.

Actually... You can do it either way!

        ** Scheme 1 **                  ** Scheme 2 **
        mass ~ inductor                 mass ~ capacitor
        spring ~ capacitor              spring ~ inductor
        position ~ charge               position ~ flux
        momentum ~ flux                 momentum ~ charge
        dashpot ~ series resistance     dashpot ~ parallel conductance


Note that I said flux and charge, not current and voltage.  This was not an
accident.  Flux and charge are dynamically conjugate, like position and
momentum.  They obey the Heisenberg equation
        delta Q delta Phi > hbar/2
whereas voltage and current don't even have the right units for this.

>  Resistance would correlate to the dissipation
> of energy by friction.

Yeah, but be careful, it's 1/resistance in scheme 2.

==============================================================

The fainthearted should stop reading now......

a) It turns out that you can do the same thing in plain old mechanics!  You
can make exact correspondences that turn the momentum variable into the
position variable and vice versa.

b) In fact there are all sorts of weird things you can choose as your
"coordinate".  Once you know the coordinate, the Lagrangian will tell you
what the dynamically-conjugate momentum is.