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

Inserting a metal sheet between the plates of a parallel plate capacitor effectively decreases the separation distance. The capacitance of a parallel plate capacitor is defined by the formula:\[C = \frac{\varepsilon_0 A}{d}\]In this equation:
- \(C\) denotes capacitance,
- \(\varepsilon_0\) represents the permittivity of free space,
- \(A\) is the area of the plates,
- \(d\) signifies the distance between the plates.When a metal sheet is introduced, the effective distance \(d_{\text{eff}}\) between the plates diminishes. Consequently, the capacitance rises, as it is inversely proportional to the plate separation.The metal sheet enhances the effective area available for charge accumulation. This enables the plates to hold more charge at a given applied voltage, leading to an overall increase in capacitance.Therefore, the resultant capacitance exceeds the original value of \(C\).