A parallel-plate capacitor is attached to a battery. A metal sheet...

When a metal sheet of thickness $t$ is introduced between the plates of a parallel-plate capacitor, the new capacitance is given by $C' = \dfrac{\epsilon_0 A}{d - t}$.

Since the thickness of the metal sheet is negligible ($t \approx 0$), the capacitance remains unchanged ($C' = C$).

As the capacitor remains connected to the battery, the potential difference $V$ across the plates is constant. Because both $C$ and $V$ are unchanged, the charge on the capacitor $Q = CV$ also remains constant. Thus, the battery does not provide any additional charge.

The metal sheet is placed in the uniform electric field of the capacitor. To maintain a net zero electric field inside the conducting metal sheet, free electrons redistribute. This electrostatic induction causes equal and opposite charges to appear on the two faces of the metal sheet.