Auto-transformer is used in transmission and distribution

Keeping in view the requirement of parallel operation, which of the $$3$$-phase connections given below are possible?

If v, w, q stand for voltage, energy and charge, then v can be expressed

The energy stored in the magnetic field of solenoid $$30$$ $$cm$$ long and $$3$$ $$cm$$ diameter wound with $$1000$$ turns of wire carrying a current of $$10$$ $$A$$ is