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 __________.

For the system shown below, S_D1 and S_D2 are complex power demands at bus $$1$$ and bus $$2$$ respectively. If $$\left| {{V_2}} \right| = 1$$ pu, the VAR rating of the capacitor (Q_G2) connected at bus $$2$$ is

A lossy capacitor $${C_x}$$, rated for operation at $$5$$ $$kV,$$ $$50$$ $$Hz$$ is represented by an equivalent circuit with an ideal capacitor $${C_p}$$ in parallel with a resistor $${R_p}$$. The value $${C_p}$$ is found to be $$0.102$$ $$\mu F$$ and the value of $${R_p}$$ $$=$$ $$1.25$$ $$M\Omega .$$ Then the power loss and $$tan\delta $$ of the lossy capacitor operating at the rated voltage, respectively, are

Consider a three-core, three phase, $$50$$ $$Hz$$, $$11$$ $$kV$$ cable whose conductors are denoted as $$R, Y$$ and $$B$$ in the figure. The inter-phase capacitance $$\left( {{C_1}} \right)$$ between each pair of conductors is $$0.2$$ $$\mu F$$ and the capacitance between each line conductor and the sheath is $$0.4$$ $$\mu F$$ . The per-phase charging current is