In the single phase diode bridge rectifier shown in the figure, the load resistor is $$R = 50\,\Omega .$$ The source voltage is $$V=200$$ $$sin$$ $$\omega t,$$ where $$\omega = 2\pi \, \times \,50\,rad/sec.$$ The power dissipated in the load resistor $$R$$ is

The cut in voltage of both Zener diode $${D_z}$$ and diode $$D$$ shown in Figure is $$0.7$$ $$V,$$ while break down voltage of the zener is $$3.3$$ $$V$$ and reverse breakdown voltage of $$D$$ is $$50$$ $$V.$$ the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage ($${V_0}$$) are

Obtain a state variable representation of the system governed by the differential equation: $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} - 2y = u\left( t \right){e^{ - t}},\,\,\,$$ with the choice of state variables as $${x_1} = y,$$ $${x_2} = \left( {{{dy} \over {dt}} - y} \right){e^t}.$$ Aso find $${x_2}\left( t \right),$$ given that $$u(t)$$ is a unit step function and $${x_2}\left( 0 \right) = 0.$$

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = {{2\left( {s + \alpha } \right)} \over {s\left( {s + 2} \right)\left( {s + 10} \right)}}.$$ Sketch the root locus as $$\alpha $$ varies from $$0$$ to $$\infty $$. Find the angle and real axis intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any