The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0)=1$$ and $${{{\left. {\,\,\,\,{{dx} \over {dt}}} \right|}_{t = 0}} = 1,\,\,}$$ is

Figure shows four electronic switches $$(i), (ii), (iii)$$ and $$(iv).$$ Which of the switches can block voltages of either polarity (applied between terminals $$‘a’$$ and $$‘b’$$) when the active device is in the OFF state?

The figure shows the circuit diagram of a rectifier. The load consists of a resistance $$10\,\Omega $$ and an inductance $$0.05$$ $$H$$ connected in series. Assuming ideal thyristor and ideal diode, the thyristor firing angle (in degree) needed to obtain an average load voltage of $$70$$ $$V$$ is _______________.

Figure (i) shows the circuit diagram of a chopper. The switch $$S$$ in the circuit in figure (i) is switched such that the voltage $${V_D}$$ across the diagram as the wave shape as shown in figure (ii). The capacitance $$C$$ is large so that the voltage across it is constant. If switch $$S$$ and the diode are ideal, the peak to peak ripple (in A) in the inductor current is ________.