On Fri, 16 May 2014, Uncle Peter wrote:

But I wonder if it would help reduce the meter reading?

No. The coil and the capacitor add up (ideally) to zero impedence, so it's
like you put a wire accoss the mains. It burns and/or the breaker/fuse
opens. For real components the coil & cap still cancel out and leave
basically the resistance of the coil, which for a ``large'' coil is
probably small, so again bad things happen.

But you have a basic fallacy anyway. At resonance the current is /in/
phase with the voltage, the capacitive and inductive reactance cancel out
so the circuit looks purely resistive.

If you like complex impedences (and adding a bit of series R &
using the EE jxj=-1 & w standing in for omega = 2 pi f)

XL=jwL
XC=1/jwC
Z=jwL+1/jwC+R

at resonance w=sqrt(1/LC)
Z=j( sqrt(1/LC)L-1/sqrt(1/LC)C )+R=j( sqrt(L/C)-sqrt(L/C) )+R=R
I=V/R

and

VL=(V/R)jwL = j(V/R)sqrt(L/C)
VC=(V/R)(1/jwC)=-j(V/R)sqrt(L/C)

The voltages on the cap & coil are 90 out of phase with the currrent and
180 out with each other so they add to zero but can be very large
depending on the choice of R, L & C (and clearly they as well as the
current get large as R gets small).

If you did have current 180 out of phase with voltage you would have to be
supplying power and the meter ``should'' run backwards (it may or may not,
depending on design) but the power company doesn't normally buy power at
the rate they sell it so they wouldn't like it.

Ron

aye means yes to a sailor
eye in a needle I can thread
i is the imaginary unit
but EEs use j instead