Supply to one terminal of a $$\triangle$$ - Y connected three-phase core type transformer which is on no-load, fails. Assuming magnetic circuit symmetry, voltages on the secondary side will be:

A synchronous motor on load draws a current at a leading power factor angle $$\phi$$. If the internal power factor angle – which is the phase angle between the excitation e.m.f. and the current in the time phasor diagram is $$\psi$$, then the air gap excitation m.m.f lags the armature m.m.f by

A monochromatic plane electromagnetic wave travels in vacuum in the position $$x$$ direction ($$x, y, z$$ system of coordinates). The electric and magnetic fields can be expressed as

The Laplace transform of $$f(t)$$ is $$F(s).$$ Given $$F\left( s \right) = {\omega \over {{s^2} + {\omega ^2}}},$$ the final value of $$f(t)$$ is __________.