Show via the construction of a suitable Gaussian surface, that the capacitance of a spherical capacitor consisting of two concentric shells of radii $$a$$ and $$b$$ is given by $$C = 4\pi {\varepsilon _0}{{ab} \over {\left( {b - a} \right)}}$$ where $${\varepsilon _0}$$ is the free space permittivity.

A thyristorised three phase fully controlled converter feeds a $$dc$$ load that draws a constant current. Then the input $$ac$$ line current to the converter has

Triangular $$PWM$$ control, when applied to a $$BJT$$ based three phase voltage source inverter, introduces.

A step down chopper operates from a $$dc$$ voltage source $${V_s}$$ feeds a $$dc$$ motor armature with a back $$e.m.f$$ $$\,\,{E_b}.$$ From oscilloscope traces, it is found that the current increases for time $${t_r}$$ falls to zero over time $${t_f},$$ and remains zero for time $${t_0}$$ in every chopping cycle, then the average $$dc$$ voltage across the freewheeling diode is