Question

Establish the formula for capacitance of a parallel plate capacitor
that has a partially dielectric medium between the plates and
partially air​

Answer 1

Answer:

A parallel plate capacitor with a dielectric between its plates has a capacitance given by C=κϵ0Ad C = κ ϵ 0 A d (parallel plate capacitor with dielectric).

Explanation:

I hope it helps you

Answer 2

Answer:

Concept:

The capacity of a partially filled parallel plate condenser with a dielectric medium- The distance between the plates is denoted by d, and there is a dielectric medium of thickness t and dielectric constant K between the plates.

Explanation:

If each plate is charged +q, the surface charge is

$\sigma=\frac{q}{A}$

Where A denotes the plate's surface area. If the distance between the plates is small in comparison to their area, the intensity of the electric field in the area between the plates will be high.

$E_{0}=\frac{\sigma}{\varepsilon_{0}}$

Electric field intensity within the dielectric medium

$\mathrm{E}=\frac{\sigma}{\mathrm{K} \varepsilon_{0}}$

The definition of potential difference is the potential difference between the plates.

V= Work done in moving a unit charge from one plate (negative) to another (positive) plate.

= Work done in moving a unit charge a distance (d−t) in air and distance t in a dielectric medium

$V=E_{0} \times(d-t)+E t$

On substituting the values of $\mathrm{E}_{\mathrm{o}}$ and $\mathrm{E}$

$\begin{aligned}&\mathrm{V}=\frac{\sigma}{\varepsilon_{\mathrm{o}}}(\mathrm{d}-\mathrm{t})+\frac{\sigma}{\mathrm{K} \varepsilon_{\mathrm{o}}} \mathrm{t} \\&\text { or } \mathrm{V}=\frac{\sigma}{\varepsilon_{\mathrm{o}}}\left[(\mathrm{d}-\mathrm{t})+\frac{\mathrm{t}}{\mathrm{K}}\right] \\&\text { or } \mathrm{V}=\frac{\mathrm{q}}{\mathrm{A} \varepsilon_{\mathrm{o}}}\left[(\mathrm{d}-\mathrm{t})+\frac{\mathrm{t}}{\mathrm{K}}\right]\end{aligned}$

Hence capacity of the condenser

$\begin{aligned}&C=\frac{q}{V} \\&C=\frac{\varepsilon_{0} A}{\left[(d-t)+\frac{t}{K}\right]}\end{aligned}$

This is our Capacitance equation.

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