Electrical Engineering ⇒ Topic : Susceptance-frequency curve

Susceptance-frequency curve. Fig. (a) shows the graph between susceptance (inductive and capacitive) of the two parallel branches and the supply frequency

It is clear that inductive susceptance B_L is inversely proportional to the frequency f. Hence BL -fgraph is a rectangular hyperbola as shown in Fig.(a). Note that graph lies in the fourth quadrant because B_L is considered negative

It is clear that capacitive susceptance B_c is directly proportional to the frequency f Hence B_c  -f graph is a straight line passing through the origin as shown in Fig.(a). Note that graph lies in the first quadrant because B_c is considered positive. The net circuit susceptance is the difference of the two susceptances and is represented by the dotted hyperbola (not rectangular). At point A in Fig. (a), the supply frequency f = f_r and the circuit susceptance is zero. Therefore, parallel resonance occurs. Under this condition :

                                                     figure (a)

(1) the circuit admittance is minimum (i.e. circuit impedance is maximum) and is equal to the conductance G of the circuit.

(2) the circuit current is minimum.

(3) the circuit current is in phase with the supply voltage i.e. circuit pf. is unity.

At supply frequency f > f_r, the capacitive susceptance of the circuit becomes greater than the inductive susceptance of the circuit. Consequently, the circuit is effectively capacitive and the circuit current leads the supply voltage. On the other hand, at f < f_r, inductive susceptance predominates and the circuit becomes effectively inductive. Therefore, the circuit current lags behind the supply voltage. Fig. (a) also shows the Y - f or I - f graph. (I = V Y ) so that I ∝ Y) as well as G - f graph.

Note that conductance G of the circuit is independent of the supply frequency f