The voltage at the input of an AC-DC rectifier is given by $$v(t) = 230\sqrt 2 \sin \omega t$$ where $$\omega = 2\pi \times 50$$ rad/s. The input current drawn by the rectifier is given by

$$i(t) = 10\sin \left( {\omega t - {\pi \over 3}} \right) + 4\sin \left( {3\omega t - {\pi \over 6}} \right) + 3\sin \left( {5\omega t - {\pi \over 3}} \right)$$

The input power factor, (rounded off to two decimal places), is _________ lag.

Consider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of 1000 V. The inverter output voltage v(t) shown below, is obtained when diagonal switches of the inverter are switched with 50% duty cycle. The inverter feeds a load with a sinusoidal current given by, $$i(t) = 10\sin \left( {\omega t - {\pi \over 3}} \right)A$$, where $$\omega = {{2\pi } \over T}$$. The active power, in watts, delivered to the load is __________. (round off to nearest integer).

For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is Idc = 15 A and is ripple free. The thyristors are fired with a delay angle of 45$$^\circ$$. The amplitude of the fundamental component of the source current, in amperes, is _________. (round off to two decimal places).

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).