A $$20$$-pole alternator is having $$180$$ identical stator slots with $$6$$ conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is $${V_1}.$$ If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is $${V_ 2}.$$ Assuming full pitch, single-layer winding, the ratio $${V_1}/{V_2}$$ 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