**Locus Diagram of Parallel RLC Circuit:**

**(a) Variable X _{L }–** Locus plots are drawn for parallel branches containing RLC elements in a similar way as for series circuits. Here we have more than one current locus. Consider the Locus Diagram of Parallel RLC Circuit shown in Fig. 8.25(a). The quantities that may be varied are X

_{L}, X

_{C}, R

_{L }and R

_{C}for a given voltage and frequency.

Let us consider the variation of X_{L} from zero to ∞. Let OV shown in Fig. 8.25(b), be the voltage vector, taken as reference. A current, I_{C}, will flow in the condenser branch whose parameters are held constant and leads V by an angle θ_{C} = tan^{-1} (X_{C}/R_{C}), when X_{L} = 0, the current I_{L}, through the inductive branch is maximum and is given by V/R_{L }and it is in phase with the applied voltage.

When X_{L} is increased from zero, the current through the inductive branch I_{L} decreases and lags V by θ_{L} = tan^{-1} X_{L}/R_{L} as shown in Fig. 8.25(b). For any value of I_{L}, the I_{L}R_{L} drop and I_{L}X_{L} drop must add at right angles to give the applied voltage. These drops are shown as OA and AV respectively. The locus of I_{L} is a semicircle, and the locus of I_{L}R_{L} drop is also a semicircle. When X_{L} = 0, i.e. I_{L} is maximum, I_{L} coincides with the diameter of its semicircle and I_{L}R_{L} drop also coincides with the diameter of its semi-circle as shown in the figure; both these semicircles are shown with dotted circles as OI_{L}B and OAV respectively.

Since the total current is I_{C} + I_{L}. For example, a particular value of I_{C} and I_{L} the total current is represented by OC on the total current semicircle. As X_{L} is varied, the locus of the resultant current is therefore, the circle I_{C} CB as shown with thick line in the Fig. 8.25(b).

**(b) Variable X _{C }**– A similar procedure can be adopted as outlined above to draw the locus plots of I

_{1}and I when X

_{C }is varying while R

_{L}, R

_{C}, X

_{L}, V and f are held constant. The curves are shown in Fig. 8.25(c).

OV presents the voltage vector, OB is the maximum current through RC branch when X_{L} = 0; OI_{L} is the current through the R_{L} branch lagging OV by an angle θ_{L} = tan^{-1} C_{L}/R_{L}.

As X_{C} is increased from zero, the current through the capacitive branch I_{C} decreases and leads V by θ_{C} = tan^{-1} X_{C}/R_{C}. For a particular I_{C}, the resultant current I = I_{L} + I_{C} and is given by OC. The dotted semicircle OI_{C}B is the locus of the I_{C}, thick circle I_{L}CB is the locus of the resultant current.

**(c)Variable R _{L }–** The locus of current for the variation of R

_{L}in Fig. 8.26(a) is shown in Fig. 8.26(b). OV represents the reference voltage, OI

_{L}B represents the locus of I

_{L}and I

_{C}CB represents the resultant current locus. Maximum I

_{L }= V/X

_{L }is represented by OB.

**(d)Variable R _{C }–** The locus of currents for the variation of R

_{C}in Fig. 8.27(a) is plotted in Fig. 8.27(b) where OV is the source voltage and semicircle OAB represents the locus of I

_{C}. The resultant current locus is given by BCI

_{L}.