A $6-$pole, $500$ V dc generator has a flux $/$ pole of $50$ mWb$,$ produced a field current of $10$ A$.$ Each pole is wound with $600$ turns. The resistance of entire field is $50$ ohms. If the field is broken in $0\mathrm{.}02$ s$,$ calculate: $($i$)$ the inductance of the field coils; $($ii$)$ the induced emf, and $($iii$)$ the value of discharge resistance so that the induced emf should not exceed $1,000$ V$.$ b$)$ An iron ring wound with $500$ turns solenoid produces a flux density $0\mathrm{.}94$ tesla in the ring carrying a current of $2\mathrm{.}4$ A$.$ The mean length of iron path is $80$ cm $,$ and that of an air$-$gap is $1$ mm $.$ Determine $(\backslash ($ i $\backslash ))$ the relative permeability of iron. $($ii$)$ the coefficient of self inductance, and energy stored in the above arrangement, if the area of cross$-$section of ring is $20$ cm $2.$

$[10$ Marks$]$