The space between two parallel conducting plate each having an area

S filled with an inhomogeneous ohmic medium whose conductivity varies

linearly from $\_1$ at one plate $($ y$=0)$ at the other plate $($y $=$ d$).$ A d$-$c

voltage V$0$ applied across the plates. Determine:

a$)$ the total resistance across the plates, and

b$)$ the surface charge density on the plates.