A parallel-plate capacitor of capacitance C is connected to an ideal battery with emf V. The capacitor is filled with a low-conductivity material that has a dielectric constant 1 and the resistivity that varies as ρ = ρ0[1 + (2x/d)], where x is the distance from the bottom plate, and d is the plate separation, as shown in the diagram below. Find the current through the capacitor and the energy stored in it.

Let the area of the capacitor plates be A. Since the resistivity (ρ) is position dependent, the resistance of a thin slice of the medium parallel to the plates is
dR=ρAdx
The resistance between the plates is then
R=0dρ0(1+2xd)Adx=ρ0A(x+x...
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