rig. $(1)$

A single$-$phase to single$-$phase cycloconverter is shown in Fig. $(1)$ supplying and inductive

load comprising of a resistance of $5$ and an inductance of $40mH$ from a $230V,50Hz$

single$-$phase supply. It is required to provide an output frequency which is $\frac{1}{3}$ of the input

frequency. If the converters are operated in the Circulating Current Free mode $($the two

bridges are acting alternately only one bridge carries load current at any given time; there is

no current circulating between the two bridges, the temporarily idle converter must be

blocked$),$ such that $0$ and firing delay angle ${}_p=120.$ Neglecting the harmonic

content of the load voltage, the $A\frac{C}{A}C$ converter is an ideal converter. Determine:

$($a$)$ ms value of the output voltage;

$($b$)$ rms value of the load current;

$(10$ marks$)$

$($c$)$ input VA power rating;

$(10$ marks$)$

$($d$)$ input power factor;

$(10$ marks$)$

$($e$)$ Fundamental Component $a_l,$

$b_1$

$(10$ marks$)$

and $c_l$

$(5$ marks$)$

of the load voltage waveform

$($f$)$ average value of the load voltage;

and then

$($g$)$ sketch approximately to scale, the waveforms of $v_s(t),v_{\text{a}\text{n}\text{g}}(t),$ and $v_0(t)$;