In the chopper circuit shown in fig the input $$dc$$ voltage has a constant value $${{V_s}}$$. the output voltage $${{V_0}}$$ is assumed ripple free. The switch $$S$$ is operated with a switching time period $$T$$ and a duty ratio $$D.$$ What is the value of $$D$$ at the boundary of continuous and discontinuous conduction of the inductor current $${i_L}$$?

Fig. $$(a)$$ shows an inverter circuit with a $$dc$$ source voltage $${V_{s}}$$. The semiconductor switches of the inverter are operated in such a manner that the pole voltages $${V_{10}}$$ and $${V_{20}}$$ are as shown in fig.
Fig. $$(b).$$ What is the rms value of the pole-to-pole voltage $${V_{12}}$$:

A step down chopper is operated in the continuous conduction mode in steady state with a constant duty ratio $$D.$$ If $${V_0}$$ is the magnitude of the $$dc$$ output voltage and if $${V_s}$$ is the magnitude of the $$dc$$ input voltage, the ratio $${{{V_0}} \over {{V_s}}}$$ is given by

A six pulse thyristor rectifier bridge is connected to a balanced $$50Hz$$ three phase $$ac$$ source. Assuming that the $$dc$$ output current of the rectifier is constant, the lowest frequency harmonic component in the $$ac$$ source line current is