The normal - $$\pi $$ circuit of a transmission line is shown in the figure.

Impedance $$Z = 100\angle {80^ \circ }$$ and reactance $$\,X = 3300\Omega .$$ The magnitude of the characteristic impedance of the transmission line, in $$\Omega ,$$ is ________. (Give the answer up to one decimal place.)

A 3-phase 50 Hz generator supplies power of 3 MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25 $$\Omega $$ and 3.925 $$\Omega $$ respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

Consider an overhead transmission line with $$3$$-phase, $$50$$ $$Hz$$ balanced system with conductors located at the vertices of an equilateral triangle of length $$\,{D_{ab}} = {D_{bc}} = {D_{ca}} = 1\,\,\,$$ m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is $$0.01$$ $$m$$. Neglect the effect of ground, the magnitude of positive sequence reactance in $$\,\Omega $$/$$km$$ (rounded off to three decimal places) is ________________.

A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.