The space between the two plates of a parallel plate capacitor is fully filled with a conducting slab. Then the capacitance of the capacitor is :

The capacitance $C$ of a parallel plate capacitor with plate area $A$ and separation $d$ is given by $C = \dfrac{\epsilon_0 A}{d}$.

When a conducting slab of thickness $t$ is inserted between the plates, the new capacitance is given by $C' = \dfrac{\epsilon_0 A}{d - t + \dfrac{t}{K}}$, where $K$ is the dielectric constant of the material.

For a conducting slab, the dielectric constant $K$ is infinite, i.e., $K \to \infty$.

Substituting $K \to \infty$ into the formula, the term $\dfrac{t}{K}$ becomes zero.

Since the slab fully fills the space between the plates, the thickness of the slab $t$ is equal to the separation $d$.

Therefore, $C' = \dfrac{\epsilon_0 A}{d - d + 0} = \dfrac{\epsilon_0 A}{0}$.

As the denominator approaches zero, the capacitance $C'$ approaches infinity.

Answer: Infinite