$(15$ points$)$ A weight$-$reducing process will be conducted to machine a titanium $($atomic weight $47\mathrm{.}9$ g $,$ density $0\mathrm{.}00452\frac{g}{m}{m}^3,$ and valency $3)$ workpiece with surface area of $2500m{m}^2$ using an ECM machine. This ECM machine provides a voltage of $20$ V and can afford current up to $1000$ A $.$ The electrolyte used in this machine has electrical conductivity of $20((S)m^{-1}).$

a$.$ What will be the minimum resistance of electrolyte that can be used with this ECM machine

b$.$ What is the smallest possible gap distance?

c$.$ How long does it take to reduce weight by $30$ g $?$

d$.$ Will titanium mechanical properties like modulus, hardness or ductility affect the electrochemical machiniability?