Explanation:

Briefly explain the principle of a capacitor.Derive an expression for the capacitance of a parallel plate conductor ,whose plates are separated by a dielectric medium

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Answer:

Explanation:

A capacitor is a two-terminal electrical component that stores electric charge. Imagine it like a bucket for electrons. The more charge you put in, the higher the voltage across the capacitor, similar to how filling a bucket with water raises the water level.

Here's the basic principle:

1. Two conducting plates: A capacitor typically consists of two parallel metal plates separated by a non-conducting material called a dielectric (e.g., air, ceramic, plastic).
2. Charge separation: When you connect the capacitor to a voltage source, positive charges (protons) are attracted to one plate, while negative charges (electrons) are drawn to the other.
3. Electric field: This separation of charges creates an electric field between the plates, opposing the further flow of charges.
4. Stored energy: The capacitor stores the electrical potential energy due to the separated charges.

The capacitance of a capacitor tells us how much charge it can store for a given voltage. It's like the bucket's capacity – a larger bucket can hold more water for the same water level (voltage).

The capacitance (C) is directly proportional to the stored charge (Q) and inversely proportional to the voltage (V) across the plates:

C = Q / V

This equation tells us that:

A capacitor with higher capacitance can store more charge for the same voltage.

For a fixed capacitance, storing more charge increases the voltage across the plates.

let's derive the expression for the capacitance of a parallel plate capacitor with a dielectric medium:

Electric field between plates: The electric field (E) inside the capacitor is related to the voltage (V) and the distance (d) between the plates by:

E = V / d

Dielectric constant: The dielectric material affects the electric field. Its permittivity (ε) is related to the free space permittivity (ε₀) by a factor called the dielectric constant (k):

ε = kε₀

Electric field due to polarization: The dielectric material gets slightly polarized in the presence of the electric field, contributing to the total electric field:

E = V / (kd)

Charge on each plate: The electric field relates to the surface charge density (σ) on each plate by:

σ = εE

Total charge: The total charge (Q) on each plate is the product of its surface charge density and area (A):

Q = σA

Substituting: Combining the equations, we get:

C = Q / V = (εA) / (kd) = (kAε₀A) / d

Therefore, the capacitance of a parallel plate capacitor with a dielectric medium depends on the:

Area (A) of the plates

Dielectric constant (k) of the material

Free space permittivity (ε₀)

Distance (d) between the plates

By changing these parameters, we can create capacitors that have the capacitance we want. This formula shows us how to do that.