A load is supplied by a $$230$$ $$V,$$ $$50$$ $$Hz$$ source. The active power $$P$$ and the reactive power $$Q$$ consumed by the load are such that $$1$$ $$kW$$ $$ \le P \le 2\,kW\,\,$$ and $$\,1\,\,kVAR \le 2\,\,kVAR.\,\,$$ A capacitor connected across the load for power factor correction generates $$1$$ $$kVAR$$ reactive power. The worst case power factor after power factor correction is

The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $$\,1.5\,\,\sin \delta ,\,\,$$ where $$\delta $$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to $$1$$ pu. If one of the transmission line circuits is removed, the maximum value of $$\delta ,$$ as the rotor swings is $$1.221$$ radian. If the expression for electrical power with one transmission line circuit removed is $$\,{P_{\max }}\,\sin \delta ,\,\,$$ the valueof $${P_{\max }}\,,$$ in pu is _________.

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero). (Give the answer up to one decimal place)

Let the signal $$$x\left(t\right)=\sum_{k=-\infty}^{+\infty}\left(-1\right)^k\delta\left(t-\frac k{2000}\right)$$$ be passed through an LTI system with frequency response $$H\left(\omega\right)$$, as given in the figure below The Fourier series representation of the output is given as