# RLC CIRCUIT parallel

Cuthbert Nyack
The magnitude of the admittance of the circuit is given by:-
Y = Ö{1/R2 + (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 Ir (orange curve), Ic, (red curve) Is (green curve) and Il (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 Ir, Ic and Il represented in phasor form. The The sum of Ic and Il and the parallelogram showing the resultant of Il - Ic and Ir 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.