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 phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by $${V_0} = {{{V_m}} \over {2\pi }}\left( {3 + \cos \alpha } \right)$$, where $${V_m} = 80\pi $$ volts and $$\alpha $$ is the firing angle. If the power delivered to the lossless battery is 1600 W, $$\alpha $$ in degree is________ (up to 2 decimal places).

The figure below shows an uncontrolled diode bridge rectifier supplied form a $$220$$ Z$$V,$$ $$50$$ $$Hz,$$ $$1$$-phase $$ac$$ source. The load draws a constant $${{\rm I}_0}$$ $$=14A.$$ The conduction angle of the diode $${D_1}$$ in degrees (rounded off to two decimal places) is ______________.

A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All devices are ideal. It is used to charge a battery at 400 V with power of 5 kW from a source V_s = 220 V (rms), 50 Hz sinusoidal AC mains at unity p.f. If its AC side interfacing inductor is 5 mH and the switches are operated at 20 kHz, then the phase shift (δ) between AC mains voltage (V_s) and fundamental AC rms VSC voltage (V_C1), in degree, is _________.