Question

Define capacitance of a capacitor. Derive an expression for the capacitance of a
parallel plate capacitor filled with dielectric ( k ) between the plates.​

Answer 1

Answer:

Explanation:

The capacitance of a parallel plate capacitor is C=ϵ0Ad C = ϵ 0 A d , when the plates are separated by air or free space. ... A parallel plate capacitor with a dielectric between its plates has a capacitance given by C=κϵ0Ad C = κ ϵ 0 A d , where κ is the dielectric constant of the material.

Answer 2

• Capacitance or electric capacity indicates the ability of a system to store charge.
• It is defined as the ratio of charge stored in the conductors to the potential difference across the conductors.
• Its SI unit is Farad (F). Hence:

《C=VQ》

●To derive the expression of capacitance of parallel plate capacitor of conductor area A and distance between the conductors as d with a dielectric of dielectric constant K carrying a charge Q and potential difference V, refer to the attached figure.

●Electric field between plates of the capacitor can be found using Gauss Law.

E=Kεoσ

E=KεoAQ  as σ=AQ

●Electric field is defined as the gradient of potential.

E=dV

⟹V=KεoAQd

By definition of capacitance, 

C=VQ

   =dKεoA