The figure above shows coil $$1$$ and $$2,$$ with dot markings as shown, having $$4000$$ and $$6000$$ turns respectively. Both the coils have a rated current of $$25$$ $$A.$$ Coil $$1$$ is excited with single phase, $$400$$ $$V,$$ $$50$$ $$Hz$$ supply.

The coils are to be connected to obtain a single-phase, $${{400} \over {1000}}\,\,V,$$ auto-transformer to drive a load of $$10$$ $$kVA.$$ Which of the options given should be exercised to realize the required auto-transformer?

The star-delta transformer shown above is excited on the star side with balanced, $$4$$-wire, $$3$$-phase, sinusoidal voltage supply of rated magnitude. The transformer is under no load condition.

With both $$S1$$ and $$S2$$ open, the core flux waveform will be

The star-delta transformer shown above is excited on the star side with balanced, $$4$$-wire, $$3$$-phase, sinusoidal voltage supply of rated magnitude. The transformer is under no load condition.

With $$S2$$ closed and $$S1$$ open, the current waveform in the delta winding will be

The circuit diagram shows a two-winding, lossless transformer with no leakage flux, excited from a current source, $$i(t)$$, whose waveform is also shown. The transformer has a magnetizing inductance of $$400/\pi \,\,mH.$$

If the waveform of $$i\left( t \right) = 10\sin \left( {100\pi t} \right)A,$$ the peak voltage across $$A$$ and $$B$$ with $$S$$ closed is