If a thin metal foil of same area is placed between the two plates of a parallel plate capacitor of capacitance C, then new capacitance will be

Options

A. C
B. 2C
C. 3C
D. 4C

Explanation

To solve the problem of finding the new capacitance when a thin metal foil is placed between the plates of a parallel plate capacitor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Capacitance**:
- Capacitance (C) is defined as the ability of a capacitor to store charge per unit voltage. It is given by the formula:
\[ C = \frac{Q}{V} \]
where \(Q\) is the charge stored and \(V\) is the voltage across the plates.

2. **Capacitance of a Parallel Plate Capacitor**:
- The capacitance of a parallel plate capacitor without any dielectric material is given by:
\[ C = \frac{\varepsilon_0 A}{d} \]
where:
- \( \varepsilon_0 \) is the permittivity of free space,
- \( A \) is the area of the plates,
- \( d \) is the separation between the plates.

3. **Introducing the Metal Foil**:
- When a thin metal foil is placed between the plates, it effectively divides the capacitor into two capacitors in series. However, since the metal foil is conductive, it will not change the electric field between the plates.

4. **Effect on Electric Field**:
- The electric field between the plates of the capacitor is given by:
\[ E = \frac{V}{d} \]
- The introduction of the metal foil does not change the electric field because the metal foil will be at the same potential as the plates, thus not affecting the voltage across the capacitor.

5. **Capacitance Calculation**:
- Since the electric field remains unchanged and the distance between the plates effectively remains the same (the foil does not change the separation distance in terms of the capacitor's operation), the capacitance remains the same.
- Therefore, the new capacitance \(C'\) is:
\[ C' = C \]

### Conclusion:
The new capacitance after placing the thin metal foil between the plates of the parallel plate capacitor remains the same as the original capacitance \(C\).