How To Find Capacitance Of A Capacitor

The capacitance of a capacitor is the ability of a capacitor to store an electric charge per unit of measurement of voltage across its plates of a capacitor. Capacitance is found by dividing electrical charge with voltage by the formula C=Q/V. Its unit is Farad.

Formula

Its formula is given as:

C=Q/V

Where C is capacitance, Q is voltage, and V is voltage. Nosotros can as well notice charge Q and voltage 5 by rearranging the to a higher place formula every bit:

Q=CV

V=Q/C

Farad is the unit of measurement of capacitance. One Farad is the amount of capacitance when one coulomb of charge is stored with one volt across its plates.

Most capacitors that are used in electronics piece of work accept capacitance values that are specified in microfarad (µF) and picofarads(pF) . A microfarad is one-millionth of a farad, and a picofarad is 1-trillionth of a farad.

What are the factors that event the capacitance of capacitor?

It depends on the following factors:

Area of plates

Capacitance is directly proportional to the physical size of the plates as adamant by the plate area,A. A larger plate area produces a larger capacitance and a smaller capacitance.Fig(a) shows that the plate area of a parallel plate capacitor is the area of 1 of the plates. If the plates are moved in relation to each other, as shown in fig(b), the overlapping area determines the effective plate area. This variation in the effective plate surface area is basic for a certain type of variable capacitor.

Plates seperation

`Capacitance is inversely proportional to the altitude between the plates. The plate separation is designated d, as shown in fig(a). Greater separation of the plates produces a smaller capacitance, equally illustrated in fig(b). As previously discussed, the breakdown voltage is straight proportional to the plate separation. The further the plates are separated, the greater the breakdown voltage.

Dielectric Constant of cloth

As you know, the insulating material betwixt the plates of a capacitor is called the dielectric. Dielectric materials tend to reduce the voltage betwixt plates for a given charge and thus increase the capacitance. If the voltage is fixed, more accuse tin exist stored due to the presence of a dielectric than tin be stored without a dielectric. The measure out of a material'southward power to establish an electric field is called dielectric abiding or relative permittivity, symbolized past ∈_r.

Capacitance is directly proportional to the dielectric constant. The dielectric abiding of a vacuum is divers every bit 1 and that of air is very close to 1. These values are used as a reference, and all other materials have values of ∈r specified with respect to that of a vacuum or air. For case, a material with ∈r=8 can consequence in a capacitance viii times greater than that of air with all other factors being equal.

The dielectric abiding ∈r is dimensionless considering information technology is a relative measure. It is a ratio of the absolute permittivity of a cloth,∈r, to the absolute permittivity of a vacuum,∈₀, as expressed by the post-obit formula:

∈_r=∈/∈₀

Beneath given some common dielectric materials and typical dielectric constants for each. Values tin can vary because they depend on the specific composition of the cloth.

Fabric Typical ∈r values

Air 1.0
Teflon 2.0
Paper 2.v
Oil 4.0
Mica 5.0
Glass vii.5
Ceramic 1200

The dielectric constant ∈r is dimensionless because it is a relative mensurate. It is a ratio of the absolute permittivity of a material,∈r, to the absolute permittivity of a vacuum,∈0, equally expressed past the following formula:

∈r=∈/∈0

The value of ∈0 is eight.85×ten-12 F/m.

Formula of capacitance in terms of physical parameters

You have seen how capacitance is straight related to plate area, A, and the dielectric constant,∈r, and inversely related to plate separation, d. An verbal formula for calculating the capacitance in terms of these 3 quantities is:

C=A ∈_r∈/d

where ∈= ∈_r∈₀=∈r(8.85×10-12F/m)

Capacitance of parallel plate capacitor derivation

Consider a parallel plate capacitor. The size of the plate is large and the distance between the plates is very small, and then the electric field between the plates is compatible.

The electrical field 'E' between the parallel plate capacitor is:

Capacitance of cylindrical capacitors physics

Consider a cylindrical capacitor of length L, formed by two coaxial cylinders of radii 'a' and 'b'.Suppose L >> b, such that there is no fringing field at the ends of cylinders.

Permit 'q' is the accuse in the capacitor and 'V' is the potential difference between plates. The inner cylinder is positively charged while the outer cylinder is negatively charged. We want to find out the expression of capacitance for the cylindrical capacitor. For this, nosotros consider a cylindrical Gaussian surface of radius 'r' such that a<<b.

If 'Eastward' is the electric field intensity on any point of the cylindrical Gaussian surface, then by Gauss's law:

If 'Five' is the potential difference between plates, then