Capacitor:
A capacitor is a passive electronic component that stores and releases electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material known as the dielectric. When a voltage is applied across the plates, an electric field is created, and the capacitor stores energy in this electric field.

Capacitance:
The capacitance of a capacitor is a measure of its ability to store electrical charge. It depends on the physical characteristics of the capacitor, such as the area of the plates, the distance between them, and the properties of the dielectric material.

Parallel Plate Capacitor:
A parallel plate capacitor is a simple type of capacitor with two parallel conductive plates separated by a dielectric material. The capacitance of a parallel plate capacitor is given by the equation:

C = ε₀A/d

Where:
- C is the capacitance of the capacitor
- ε₀ is the permittivity of free space (a constant value)
- A is the area of each plate
- d is the distance between the plates

Compound Dielectric:
A compound dielectric is a dielectric material that consists of multiple layers of different dielectric materials. Each layer may have different dielectric constants and thicknesses. The compound dielectric is used to enhance the overall dielectric strength and capacitance of the capacitor.

Expression of Capacitance:
To derive the expression of capacitance for a parallel plate capacitor with a compound dielectric, we consider a capacitor with N layers of dielectric materials.

Let:
- ε₁, ε₂, ..., εₙ be the dielectric constants of the N layers
- t₁, t₂, ..., tₙ be the thicknesses of the N layers
- A be the area of each plate
- d be the distance between the plates

The total capacitance C of the capacitor can be calculated by summing up the capacitances of each individual layer:

C = C₁ + C₂ + ... + Cₙ

where C₁, C₂, ..., Cₙ are the capacitances of each layer.

The capacitance of each layer can be calculated using the equation for a parallel plate capacitor:

Cᵢ = ε₀Aᵢ/(tᵢ * εᵢ)

where Aᵢ is the effective area of the i-th layer, and εᵢ is the dielectric constant of the i-th layer.

The effective area Aᵢ can be calculated as:

Aᵢ = A * (tᵢ / d)

Substituting the values of Aᵢ, εᵢ, and tᵢ into the equation for Cᵢ, we get:

Cᵢ = (ε₀A * εᵢ) / (d * tᵢ)

Therefore, the total capacitance C of the compound dielectric capacitor is:

C = (ε₀A * ε₁) / (d * t₁) + (ε₀A * ε₂) / (d * t₂) + ... + (ε₀A * εₙ) / (d * tₙ)

This expression gives the capacitance of a parallel plate capacitor with a compound dielectric consisting of N layers. It takes into account the dielectric constants and