Question

A metal sheet is inserted between the plates of a parallel plate capacitor of capacitance C. If the sheet partly occupies the space between the plates, the capacitance:

• A. remains C
• B. becomes greater than C
• C. becomes less than C
• D. becomes zero

Hint:

Inserting a dielectric material, such as a metal sheet, between the plates of a parallel plate capacitor decreases the effective distance between the plates and increases the capacitance. This happens because the metal sheet alters the electric field between the plates, leading to more charge storage capability.

Answer 1

The Correct Option is B

When a metal sheet is inserted between the plates of a parallel plate capacitor, it effectively reduces the distance between the plates. The capacitance of a parallel plate capacitor is given by: \[ C = \frac{\varepsilon_0 A}{d} \] Where:
- \(C\) is the capacitance,
- \(\varepsilon_0\) is the permittivity of free space,
- \(A\) is the area of the plates,
- \(d\) is the distance between the plates. By inserting a metal sheet between the plates, the effective distance \(d_{\text{eff}}\) between the plates is reduced. As a result, the capacitance increases because the capacitance is inversely proportional to the distance between the plates. The presence of the metal sheet increases the effective area for charge storage, and it also allows the plates to store more charge for the same applied voltage, leading to an increase in the overall capacitance. Thus, the capacitance becomes greater than \(C\).