A three-phase slip-ring induction motor, provided with a commutator winding, is shown in the figure. The motor rotates in clockwise direction when the rotor windings are closed. If the rotor winding is open circuited and the system is made to run at rotational speed f_r with the help of prime-mover in anti-clockwise direction, then the frequency of voltage across slip rings is f₁ and frequency of voltage across commutator brushes is f₂. The values of f₁ and f₂ respectively are

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

All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are