Q.1. Define capacitance of a capacitor, Give its unit. Derive an
expression for the capacitance of a parallel plate capacitor in
which a dielectric medium of dielectric constant K fills the
space between the plates.
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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=
V
Q
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=
Kε
o
σ
E=
Kε
o
A
Q
as σ=
A
Q
Electric field is defined as the gradient of potential.
E=
d
V
⟹V=
Kε
o
A
Qd
By definition of capacitance,
C=
V
Q
=
d
Kε
o
A
....,....
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