1. The problem statement, all variables and given/known data The space between the plates of a parallel plate capacitor is completely filled with a conducting slab.What is the capacitance of the system ? 2. Relevant equations 3. The attempt at a solution The capacitance of a capacitor when a dielectric medium is placed between the plates is given by : C=εoA/(d-t+t/K) Where, εo is permittivity of free space, A is the area of a plate , d is the distance between the plates , t is thickness of the dielectric medium, K is dielectric constant of the medium. Now if the conductor completely occupies the space, then K=∞ and t=d Hence we get, C=∞ . Now look at the same situation in terms of the definition of capacitance i.e Q=CV . The capacitance is the ability of the plates to hold charge. But here if we connect the plates of the capacitor to the terminals of the battery , the current flows through the conducting slab ,across the plates .No charge will be accumulated on the plates . The potential difference across the plates is zero. What should we put as Q in Q=CV ? If we put zero ,as is the case, then we have C = 0/0 ,which is undefined . What is the correct way of looking at the problem ?