# RLC CIRCUIT parallel.

Cuthbert Nyack  Schematic circuits of the parallel RLC combination are shown above. The first circuit (Circuit 1) is the ideal case which is easier to analyse, while the second (Circuit 2) may be more realistic. 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.
The applet below illustrates several properties of the parallel combination. Applet function can be changed by changing Fn. Numerical values of some of the variables plotted can be seen by varying wL.
Fn = 0 shows the step response of curcuit 1. eg (2.5, 0.1, na, na, na, 375, na, 0, 1.0, 5.0)
Fn = 1 shows the frequency response of curcuit 1. eg (1.0, 0.1, na, na, na, 375, na, 1, na, 3.0)
Fn = 2 shows the sinusoidal response of curcuit 1. eg (2.0, 0.1, 2.2, na, na, 375, na, 2, 2.0, 3.0)
Fn = 3 shows phasors for curcuit 1. eg (2.0, 0.1, 1.8, na, na, 375, na, 3, na, 3.0)
Fn = 4 shows impedances of curcuit 1. eg (1.0, 0.3, na, na, na, 375, na, 4, 2.0, 3.0)
Fn = 5 shows the step response of curcuit 2. eg (2.5, 0.05, na, na, na, 375, na, 5, 3.0, 3.0)
Fn = 6 shows the frequency response of curcuit 2. eg (1.0, 0.4, na, na, na, 375, na, 6, 3.0, 5.0)
Fn = 7 shows the sinusoidal response of curcuit 2. eg (2.5, 0.03, na, na, na, 375, na, 7, 2.0, 2.0)
Fn = 8 shows phasors for curcuit 2. eg (2.5, 0.2, 2.5, na, na, 375, 5.0, 8, na, na)
Fn = 9 shows impedances of curcuit 2. eg (1.0, 0.25, na, na, na, 375, na, 9, 2.0, 8.0)

When applet is enabled its appearance is illustrated by the gif image below. 