Re: looking for reference

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

 > Original poster: "Jim Lux by way of Terry Fritz <teslalist-at-qwest-dot-net>" 
<jimlux-at-earthlink-dot-net>
 >
 > Fairly straightforward to figure it out, qualitatively (sans books)..

I agree that  it's easy to reach the result with sinusoidal steady state
analysis using phasors. But this form of calculation is a trick often
not properly understood.
It's also easy to consider what happens in the time domain, also with
sinusoidal signals. The operations are very similar:
Assume a series connection of a voltage source v(t), a capacitor C,
and an inductor L.
The current in the three elements is the same. Assume it as:
i(t)=I sin(w t)
The voltage over the capacitor is the integral of i(t) divided by C
(there is a constant term too, but in steady state it eventually
disappears):
vc(t)=-(1/(w C))I cos(w t)
The voltage over the inductor is the derivative of the current
multiplied
by L:
vl(t)=w L I cos(w t)
So, the voltage over the series circuit LC is:
vlc(t)=I(w L-1/(w C))cos (w t)
Or, if vlc(t) is a cosinusoid V sin(w t), the current is a sinusoid
with amplitude I=V/(w L-1/(w C)).
Replace I in the equations for vc(t) and vl(t) to get the voltage
amplitudes. Note that 1/(L C) is the resonance frequency in rads/s:
vc(t)=-V/(L C)/(w^2-1/(L C))cos (w t)
vl(t)=V w^2/(w^2-1/(L C))cos (w t)
The phase difference between input (V) and output is zero or 180
degrees,
depending on where is the output and if the frequency is below or above
the resonance.

Antonio Carlos M. de Queiroz