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 $${i_L}$$?

In fig, the ideal switch $$S$$ is switched on and off with a switching frequency $$f = 10 kHz.$$ The switching time period is $$\,T = {t_{ON}} + t{}_{off} = 100\,\,\mu s.$$ The circuit is operated in steady state at the boundary of continuous and discontinuous conduction, so that the inductor current i is as shown in Fig.P20. Find

(a) The on-time $${t_{ON}}$$ of the switch
(b) The value of the peak current $${{\rm I}_p}$$

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 $${V_{12}}$$:

Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is $$0.25$$ cm and the distance between their centers is $$1$$m. If this distance is doubled, then the inductance per unit length.