Consider two buses connected by an impedance of $$\left( {0 + j5} \right)\Omega .$$ The bus $$1$$ voltage is $$100$$$$\angle {30^ \circ }\,\,\,V,$$ and bus $$2$$ voltage is $$100\angle {0^ \circ }\,\,\,V,$$ The real and reactive power supplied by bus $$1,$$ respectively, are

Consider a three-phase, $$50Hz,$$ $$11$$ $$kV$$ distribution system. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The self capacitance of the insulator is $$5$$ times the shunt capacitance between the link an the ground, as shown in the figure. The voltage across the two insulators are

Given f(t) and g(t)as shown below: g(t) can be expressed as

x(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown in the figure. The value of $$\int_{-\infty}^\infty\left|X\left(\omega\right)\right|^2d\omega$$ {where X($$\mathrm\omega$$) is the Fourier transform of x(t)} is