A single - phase voltage source inverter shown in figure is feeding power to load. The triggering pulses of the devices are also shown in the figure.

If the load current is sinusoidal and is zero at $$0,\,\,\pi ,2\pi ....,$$ the node voltage $${V_{AO}}$$ has the waveform

In a long transmission line with $$r, l, g$$ and $$𝑐$$ are the resistance, inductance, shunt conductance and capacitance per unit length respectively, the condition for distortionless transmission 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 ____________.