There are two generators in a power system. No-load frequencies of the generators are $$51.5$$ $$Hz$$ and $$51$$ $$Hz,$$ respectively, and both are having droop constant of $$1$$ $$Hz/MW.$$ Total load in the system is $$2.5$$ $$MW.$$ Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in $$Hz$$ in the steady state is ____________.

A synchronous generator is connected to an infinite bus with excitation voltage $${E_f} = 1.3\,pu.$$ The generator has a synchronous reactance of $$1.1$$ $$pu$$ and is delivering real power $$(P)$$ of $$0.6$$ $$pu$$ to the bus. Assume the infinite bus voltage to be $$1.0$$ $$pu.$$ Neglect stator resistance. The reactive power $$(Q)$$ in $$pu$$ supplied by the generator to the bus under this condition is ____________.

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates. If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio $$\varepsilon_1\;:\;\varepsilon_2$$ is

The magnitude of magnetic flux density ($$\overrightarrow B$$) at a point having normal distance d meters from an infinitely extended wire carrying current of I A is $$\frac{\mu_0I}{2\mathrm{πd}}$$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ₀ is permeability of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. Assuming right handed coordinate system, magnetic field intensity, $$\overrightarrow H$$ at coordinate (2,1,0) will be