The expression $$V = \int\limits_0^H {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,} $$ for the volume of a cone is equal to _________.

A single - phase bridge converter is used to charge a battery of $$200$$ $$V$$ having an internal resistance of $$2\,\,\Omega $$ as shown in figure. The $$SCRs$$ are triggered by a constant $$dc$$ signal. If $$SCR$$ $$2$$ gets open circuited, what will be the average charging current?

A single $$-$$ phase half wave uncontrolled converter circuit is shown in figure. A $$2$$ -winding transformer is used at the input for isolation. Assuming the load current to be constant and $${V_{in}} = {V_m}$$ $$\,\sin \omega t,$$ the current waveform through diode $${D_2}$$ will be

A voltage commutation circuit is shown in figure. If the turn off time of the $$SCR$$$$s$$ is $$50$$ $$\mu \sec $$ and as safety margin of $$2$$ is considered, what will be the approximate minimum value of capacitor required for proper commutation?