Question

A parallel plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates. If the sheet remains parallel to the plates of the capacitor then which one of the following statements is correct:

• A. The battery will supply more charge
• B. The capacitance will increase
• C. The potential difference between the plates will increase
• D. Equal and opposite charges will appear on the faces of the metal plate.

Answer 1

The correct option is D Equal and opposite charges will appear on the faces of the metal plate.

If the area of the plates is $A$ and the initial separation between them is $d$ then the capacitance will be$$C=\frac{{\epsilon }_{0}A}{d}$$As we know that capacitance of parallel plate capacitor with partially filled dielectric slab of thickness $t$ and dielectric constant $K$ is given by$$C^{\prime }=\frac{{\epsilon }_{0}A}{d-t+\frac{t}{K}}$$As, the thickness of metal sheet is negligible .i.e $t\approx 0$. So,

$C^{\prime }=\frac{{\epsilon }_{0}A}{d}=C$

Hence, option (b) is incorrect.

As we know that, charge $Q$ supplied by the battery will be $Q=CV$. Here, potential difference $V$ applied by the battery and the capacitance of the capacitor are constant so, the charge supplied by the battery also be constant.
Thus, option (a) is also incorrect.

Since, the plates are connected to the battery , the potential difference across the plates will remain constant.
Hence, option (c) is also incorrect.

So, what will happen is that the equal and opposite charges will appear on the two faces of the metal plates and everything else will remain unchanged.

Hence, option (d) is the correct answer.