In the figure shows on period of the output voltage of an inverter. $$\alpha $$ should be chosen such that $${60^0} < \alpha < {90^0}.$$ If $$rms$$ value of the fundamental component is $$50$$ $$V$$, then $$\alpha $$ in degree is _________.

Figure (i) shows the circuit diagram of a chopper. The switch $$S$$ in the circuit in figure (i) is switched such that the voltage $${V_D}$$ across the diagram as the wave shape as shown in figure (ii). The capacitance $$C$$ is large so that the voltage across it is constant. If switch $$S$$ and the diode are ideal, the peak to peak ripple (in A) in the inductor current is ________.

In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( { - {{150}^0}} \right)\,\,pu,\,\,$$ zero sequence current $$\,\,{{\rm I}_{c0}} = 3\angle {90^0}\,\,pu.\,\,\,$$ The magnitude of phase current $${{\rm I}_b}$$ in $$pu$ is

The over current relays for the line protection and loads connected at the buses are shown in the figure.

The relays are IDMT is natural having the characteristic
$${t_{op}} = {{0.14\, \times \,time\,\,multiplier\,\,setting} \over {{{(plug\,\,setting\,\,multiplier)}^{0.02}} - 1}}$$
The maximum and minimum fault current at bus $$B$$ are $$2000A$$ and $$500$$ $$A$$ respectively. Assuming the time multiplier setting and plug setting for relay $${R_B}$$ to be $$0.1$$ and $$5$$ $$A$$ respectively, the operating time of $${R_B}$$ (in seconds) is __________.