Capacitance of a parallel plate capacitor becomes (4 / 3)...

Capacitance of a parallel plate capacitor becomes $(4 / 3)$ times its original value if a dielectric slab of thickness $t=d / 2$ is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is
(A) 8
(B) 4
(C) 6
(D) 2

Key Concepts

Effect of Partial Dielectric Insertion

Partial insertion of a dielectric material in a capacitor creates a system with multiple regions — some with the dielectric and some without. This configuration requires breaking down the capacitor into regions that are analyzed separately (often as series combinations), leading to an effective capacitance that reflects the contributions of both the dielectric and the air gaps.

Parallel Plate Capacitors

A parallel plate capacitor consists of two conductive plates separated by an insulating medium. Its capacitance is determined by the area of the plates, the distance between them, and the permittivity of the material in the gap, providing a simple model for understanding energy storage in electric fields.

Dielectric Materials

Dielectric materials are insulators that can be inserted between the plates of a capacitor to increase its capacitance. They work by reducing the effective electric field and permitting additional energy storage, with their effectiveness quantified by the dielectric constant, which is the ratio of the permittivity of the dielectric to the permittivity of free space.

Series Combination of Capacitors

When a capacitor comprises different layers or regions that have distinct properties (such as varying dielectric constants or separations), it can be modeled as a set of capacitors connected in series. The overall capacitance is then computed by taking the reciprocal of the sum of the reciprocals of the individual capacitances.

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