Equation $${e^x} - 1 = 0\,\,$$ is required to be solved using Newton's method with an initial guess $$\,\,{x_0} = - 1.\,\,$$ Then after one step of Newton's method estimate $${x_1}$$ of the solution will be given by

Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be

A three phase fully controlled bridge converter is feeding a load drawing a constant and ripple free load current of $$10$$ $$A$$ at a firing angle of $${30^ \circ }.$$ The approximate Total Harmonic Distortion $$(\% \,\,THD)$$ and $$r.m.s$$ value of fundamental component of the input current will respectively be

A single phase full bridge converter supplies a load drawing constant and ripple free load current. If the triggering angle is $${30^ \circ },$$ the input power factor will be