In the following network, the voltage magnitudes at all buses are equal to $$1$$ p.u., the voltage phase angles are very small, and the line resistance are negligible. All the line reactances are equal to $$j1\Omega .$$

If the base impedance and the line-to-line base voltage are $$100\Omega $$ and $$\,100kV,\,\,$$ respectively, then the real power in MW delivered by the generator connected at the slack bus is

For a periodic signal the $$v\left(t\right)=30\sin100t\;+\;10\cos300t\;+\;6\sin\left(500t\;+\;\frac{\mathrm\pi}4\right)$$ fundamental frequency in radians/s is

The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output is

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is