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.
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