A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $$kVAR)$$ of the delta connected (capacitive) reactive power bank necessary to bring the $$pf$$ to unity is

A balanced delta connected load of $$\left( {8 + j6} \right)$$ $$\Omega $$ per phase is connected to a $$400V,$$ $$50Hz,$$ $$3-$$ phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors, the required $$kV$$ $$AR$$ of the bank is

A set of $$3$$ equal resistors, each of value $${R_X},$$ connected in star across $$RYB$$ of given Fig. consumes the same power as the unbalanced delta-connected load shown. The value of $${R_X}$$ is _____________ $$\Omega .$$

Using Thevenin equivalent circuit, determine the $$rms$$ value of the voltage across the $$100$$ $$ohm$$ resistor after the switch is closed in the $$3$$ $$-$$ phase circuit shown in Figure.