A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30 Ω per phase. The load angle is $$30^\circ$$. The power delivered to the motor in kW is _______.

A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): $$Z_m=\left(12.50\;+\;j15.75\right)\;\Omega$$ (main winding), $$Z_a=\left(24.50\;+\;j12.75\right)\;\Omega$$(auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in µF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.

The magnitude of magnetic flux density (B) in micro Teslas ( µT ) at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I = 1A), and placed in vacuum as shown in the figure is __________.

Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?