# RLC CIRCUIT parallel

Cuthbert Nyack

The magnitude of the admittance of the circuit is given by:-

Y = Ö{1/R^{2} + (wC - 1/wL)
^{2} }

The phase of the admittance of the circuit is given by:-

Ðq = atan
{(wC - 1/wL)
R}

At resonance the admittance goes to a minimum and the impedance to
a maximum. This is the opposite of the series case.

For parallel resonance the driving parameter is a current and
the response is a voltage.
The magnitudes and phases of I_{r} (orange curve),
I_{c}, (red curve) I_{s} (green curve) and
I_{l} (blue curve) are shown by the sinusoidal
waves in the applet above. The
variation of the magnitudes and phases as a function of frequency
and Q can be demonstrated by the applet. A frequency of 1
corresponds to the resonant frequency. For the series case the Q is given by
Q = wL/R while for the parallel case Q =
R/(wL).

The above applet shows the magnitudes and phases of I_{r},
I_{c} and I_{l} represented in phasor form. The
The sum of I_{c} and I_{l} and the parallelogram
showing the resultant of I_{l} - I_{c} and
I_{r} are shown by the purple lines. Note that at low
frequencies most of the current flows through the inductor
while at higher frequencies most of the current flows through
the capacitor.

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COPYRIGHT © 1996 Cuthbert A. Nyack.