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 _______.

Two parallel connected, three-phase, $$50Hz,$$ $$11kV,$$ star-connected synchronous machines $$A$$ and $$B,$$ are operating as synchronous condensers. They together supply $$50$$ $$MVAR$$ to a $$11$$ $$kV$$ grid. Current supplied by both the machines are equal. Synchronous reactances of machine $$A$$ and machine $$B$$ are $$1\,\,\Omega $$ and $$3\,\,\Omega ,$$ respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine $$A$$ to that of machine $$B$$ is ____________. (Give the answer up to two decimal places).

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?

A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will