A three-phase cable is supplying $$800$$ kW and $$600$$ kVAr to an inductive load. It is intended to supply an additional resistive load of $$100$$ kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is $$3.3$$ kV, $$50$$ Hz, the capacitance per phase of the bank expressed in microfarads, is ________.

A composite conductor consists of three conductors of radius $$R$$ each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is ______.

For a $$400$$ $$km$$ long transmission line, the series impedance is $$(0.0 + j0.5)$$ $$\Omega /km$$ and the shunt admittance is $$(0.0 + j5.0)$$ $$\mu \,mho/km.$$ The magnitude of the series impedance (in $$\Omega $$) of the equivalent $$\pi $$ circuit of the transmission line is __________.

The complex power consumed by a constant-voltage load is given by $$\left( {{P_1} + {J_{q1}}} \right).\,\,$$ Where, $$\,1\,\,kW \le \,\,{P_1} \le \,\,\,1.5\,\,kW\,\,\,$$ and $$\,\,0.5\,KVAR \le \,\,\,{Q_1} \le 1kVAR.\,\,\,$$ A compensating shunt capacitor is chosen such that $$\,\left| Q \right| \le 0.25\,\,KVAR,\,\,$$ where $$Q$$ is the net reactive power consumed by the capacitor-load combination. The reactive power (in kVAR) supplied by the capacitor is ____________.