A field excitation of $$20A$$ in a certain alternator results in a armature current of $$400$$ $$A$$ in short circuit and a terminal voltage of $$2000$$ $$V$$ on open circuit. The magnitude of the internal voltage drop with in the machine at a load current of $$200$$ $$A.$$

Figure shows the extended view of a $$2$$ pole $$dc$$ machine with $$10$$ armature conductors. Normal brush positions are shown by $$A$$ and $$B,$$ placed at the inter polar axis. If the brushes are now shifted, in the direction of rotation to $$A'$$ and $$B'$$ as shown, the voltage waveform $${V_{A'B'}}$$ will resemble

The single phase, $$50$$ $$Hz$$ iron core transformer in the circuit has both the vertical arms of cross sectional area $$20\,\,c{m^2}$$ and both the horizontal arms of cross sectional area $$10\,\,c{m^2}$$. If the two windings shown were wound instead on opposite horizontal arms, the mutual inductances will

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?