If a parallel plate capacitor is fully filled with a conducting slab and is connected to a battery then how does current flows in the circuit? As the electric field between the capacitor plates is zero then how does charge flows? Does the capacitance of the capacitor infinite? Now consider an isolated capacitor which is charged and then we introduce a conducting slab then the whole charge on the capacitor should flow from one plate to the other and the capacitance should be zero but in all textbooks, it is said that introducing a conducting slab will increase capacitance
Introduction of a conducting slab will not increase the capacitance, as you introduce a conductor that doesn't shorts the plates then the system will act like two capacitors in series, and hence my capacitance will decrease. Two capacitors will be formed between (first plate and conductor ) and (conductor and second plate). This way capacitance decreases .
When conductor's length fits in the capacitor it'll short circuit it and hence now it'll behave like a simple conductor and capacitance will decrease.
Hope that helps:) , Thanks