Well, they're *each* 90 degrees out of phase, so they're in complete
antiphase (180') WRT each other. The cap's eneryg is stored in an
electric field; the inductor's is stored in a magnetic field and when
one's at a maximum, the other's at a minimum and vice versa.
I think we are talking about energy here, and it is true that the
time functions of the two energies are sinusoids, 180 out of phase,
but the reason is slightly more complicated, Steve. The current in L
and C are each 90 degrees out of phase with the reference (voltage),
in opposite directions (so to speak), so the two currents are indeed
180 out. But one might expect that since the energy in C is a
function of voltage and the energy in L is a function of current, that
the energies might be 90 degrees out of phase, since the voltage
across the C is only 90 degrees out phase with the current in the L.
The detail Rich is missing is that if you plot the energy in L and
C separately, you will see that the energy vs. time plot is a *double*
frequency function, compared to the voltage or current. This is
because the energy involves the *square* of the voltage or current
(for C or L), which is always positive regardless of whether the
voltage (or current) is in the positive or negative direction.
Remember your
trigonometry, specifically the formula: SIN^2(x) = (1 -
COS(2x))/2 When you square a sinusoid, you get a double frequency
sinusoid plus a constant (the constant is the *average* energy). When
you look at the squares of two sinusoids that are 90 deg out of phase,
you get a couple of double frequency sinusoids that are *180* out of
phase with each other. When you add these two double frequency
sinusoids (plus their constant terms), the sinusoidal portions cancel
and the contants add to give a constant equal to the total energy in L
and C.
