The plates of a parallel capacitor are charged up to 100 V. If 2 mm thick plate is inserted be

step 1 Hi student welcome to the solution of problem number 1617. Here we have a parallel plate capacit

The plates of a parallel capacitor are charged up to 100 V....

The plates of a parallel capacitor are charged up to $100 \mathrm{~V}$. If $2 \mathrm{~mm}$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6 \mathrm{~mm}$ the dielectric constant of the plate is (A) 5 (B) 4 (C) $1.25$ (D) $2.5$

Key Concepts

Composite Capacitor Systems

When a dielectric of finite thickness is introduced between capacitor plates, the configuration typically becomes a composite system made up of regions with different dielectric properties. This composite system is modeled by considering the dielectric section and any remaining gaps as separate capacitors connected in series or parallel. Analyzing such systems requires understanding how each region contributes to the total voltage and capacitance, ensuring that the conditions, such as maintaining a fixed potential difference, are satisfied.

Effect of Dielectrics on Capacitance

When a dielectric slab is inserted into a capacitor, the overall capacitance increases because the dielectric reduces the electric field and promotes charge storage. However, if the introduction of the dielectric alters the physical configuration — such as creating gaps or changing separation distances — the effective capacitance must be analyzed by modeling the capacitor as a composite system, often treated as capacitors in series or parallel.

Parallel Plate Capacitor

A parallel plate capacitor consists of two conductive plates separated by an insulating material (or vacuum). Its capacitance is determined by the plate area, the distance between them, and the permittivity of the medium between the plates. This basic configuration forms the foundation for understanding capacitor behavior and its modifications when additional materials are introduced.

Dielectric Materials

Dielectric materials are insulators that, when placed in an electric field, become polarized. This polarization reduces the effective electric field within the material, resulting in an increased capacitance. The effectiveness of a dielectric is quantified by its dielectric constant (or relative permittivity), which is the ratio of the capacitance with the dielectric present to the capacitance without it.

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