The triggering circuit of a thyristor is shown in figure. The thyristor requires a gate current of $$10$$ $$mA,$$ for guaranteed turn-on. The value of $$R$$ required for the thyristor to turn on reliably under all conditions of $${V_b}$$ variation is

The circuit in figure shows a $$3$$ $$-$$ phase half $$-$$ wave rectifier. The source is a symmetrical, $$3$$ $$-$$ phase four $$-$$ wire system. The line-to-line voltage of the source is $$100 V.$$ The supply frequency is $$400$$ $$Hz.$$ The ripple frequency at the output is

The generalized circuit constants of a $$3$$-phase, $$220$$ $$kV$$ rated voltage, medium length transmission line are $$A = D = 0.936 + j\,0.016 = 0.936\angle {0.98^ \circ }$$
$$B = 33.5 + j138 = 142.0\angle {76.4^ \circ }\,\Omega $$
$$\,C = \left( { - 5.18 + j914} \right) \times \,{10^{ - 6}}\,\Omega $$
If the load at the receiving end is $$50$$ MW at $$220$$ $$kV$$ with a power factor of 0.9 lagging, then magnitude of line to line sending end voltage should be

The phase sequence of the $$3$$-phase system shown in figure is