With $$K$$ as constant, the possible solution for the first order differential equation $${{dy} \over {dx}} = {e^{ - 3x}}$$ is

Solution, the variable $${x_1}$$ and $${x_2}$$ for the following equations is to be obtained by employing the Newton $$-$$ Raphson iteration method
equation (i) $$10\,{x_2}\,\sin \,{x_1} - 0.8 = 0$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$10\,x_2^2\, - 10\,{x_2}\cos \,{x_1} - 0.6 = 0$$
Assuming the initial values $${x_1} = 0.0$$ and $${x_2} = 1.0$$ the Jacobian matrix is

Circuit turn-off time of an $$SCR$$ is defined as the time

A solar energy installation utilize a three – phase bridge converter to feed energy into power system through a transformer of $$400V/400 V,$$ as shown below. The energy is collected in a bank of $$400$$ $$V$$ battery and is connected to converter through a large filter choke of resistance $$10\Omega $$.

The $$kVA$$ rating of the input transformer is