▁surface ▁S ▁en clos ing ▁the ▁volume ▁ ▁consist ▁of ▁a ▁part ▁ ▁covered ▁by ▁n ▁electro des ▁and ▁an ▁un cover ed ▁part ▁. ▁ ▁According ▁to ▁the ▁above ▁definitions ▁and ▁boundary ▁conditions , ▁and ▁to ▁the ▁super position ▁theorem , ▁the ▁second ▁equation ▁can ▁be ▁split ▁into ▁the ▁contributions ▁▁ ▁, ▁ ▁, ▁ ▁relative ▁to ▁the ▁carri ers ▁and ▁to ▁the ▁electro de ▁volt ages , ▁respectively , ▁ ▁being ▁the ▁total ▁number ▁of ▁carri ers ▁in ▁the ▁space , ▁inside ▁and ▁outside ▁, ▁at ▁time ▁t , ▁ ▁and ▁. ▁ ▁The ▁integr als ▁of ▁the ▁above ▁equations ▁account ▁for ▁the ▁disp lacement ▁current , ▁in ▁particular ▁across ▁. ▁ ▁Current ▁and ▁capac it ance ▁ ▁One ▁of ▁the ▁more ▁meaning ful ▁application ▁of ▁the ▁above ▁equations ▁is ▁to ▁compute ▁the ▁current ▁▁ ▁, ▁ ▁through ▁an ▁h th ▁electro de ▁of ▁interest ▁corresponding ▁to ▁the ▁surface ▁, ▁ ▁and ▁ ▁being ▁the ▁current ▁due ▁to ▁the ▁carri ers ▁and ▁to ▁the ▁electro de ▁volt ages , ▁to ▁be ▁computed ▁through ▁third ▁and ▁fourth ▁equations , ▁respectively . ▁ ▁Open ▁devices ▁ ▁Consider ▁as ▁a ▁first ▁example , ▁the ▁case ▁of ▁a ▁surface ▁S ▁that ▁is ▁not ▁completely ▁covered ▁by ▁electro des , ▁i . e ., ▁, ▁and ▁let ▁us ▁choose ▁Dir ich let ▁boundary ▁conditions ▁ ▁on ▁the ▁h th ▁electro de ▁of ▁interest ▁and ▁of ▁ ▁on ▁the ▁other ▁electro des ▁so ▁that , ▁from ▁the ▁above ▁equations ▁we ▁have ▁▁ ▁, ▁ ▁where ▁ ▁is