A 3-phase grid-connected voltage source converter with DC link voltage of 1000 V is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the rid phase current is 10 A and the 3-phase complex power supplied by the converter is given by ($$-$$4000 $$-$$ j3000) VA, then the modulation index used in sinusoidal PWM is _________. (round off to two decimal places).

The steady state current flowing through the inductor of a DC-DC buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the converter is 1 V, then the value of the output capacitor, in $$\mu$$F, is _________. (round off to nearest integer).

The most commonly used relay, for the protection of an alternator against loss of excitation, is

The geometric mean radius of a conductor, having four equal strands with each strand of radius r, as shown in the figure below, is