Cylindrical Capacitor

A capacitor is a device that stores electrical charge and energy. It’s used to store a lot of electric current in a tiny amount of area. A distance in capacitors usually separates two electrical conductors. Capacitors are used for various things, from filtering static from radio reception to storing energy in defibrillators. 

A cylindrical capacitor consists of a radius x conducting cylinder or wire enclosed by a radius y concentric cylindrical shell (y>x). A concentric hollow spherical cylinder encloses a hollow or solid cylindrical conductor in the cylindrical capacitor.

A well-known example of a cylindrical capacitor is an electrical power cable.

The simplest capacitor is a pair of isolated conductors separated by a small distance. For a capacitor, the charge q and the potential difference V are proportional; that is, q = C V. The capacitance of the capacitor is the proportionality constant C. Farad is the unit of capacitance. For the same applied voltage V across their plates, capacitors with different physical characteristics, including the shape and size of their plates, store different amounts of charge.

Capacitors are divided into three types: (a) parallel plate capacitors, (b) cylindrical capacitors (c) spherical capacitors.

A dielectric is used to separate the capacitor’s space in most circumstances.

Introduction to the cylindrical capacitor

A cylindrical capacitor is composed of two concentric cylindrical shells or wires separated by a dielectric in between them.

A cylindrical conductor with linear charge density is enclosed by a coaxial cylindrical conducting shell with charge density in this form of capacitor. Capacitors are mainly used in electric motors and other electronic equipment. 

Capacitance Of a Cylindrical Capacitor

Let ‘a’ be the radius of the inner cylinder, and ‘b’ be the radius of the outer cylinder. Let epsilon r be the relative permittivity of the medium between the two cylinders.

Allow for a charge of +Q coulombs on the outer surface of the inner cylinder and -Q coulombs on the inner surface of the outer cylinder per metre length of cable. The charge of +Q coulombs/m on the surface of the core can be considered to be localised near its axis for all practical purposes. The cylinder on the outside is earthed.

Assume there is a charge Q on the capacitor.

The electrical field E between the conductors must be determined. You might be able to apply Gauss’s law for this calculation if the conductor configuration is symmetric.

Determine the difference in potential between the conductors

Where the integration path connects one conductor to the next, V=|VBVA| is the magnitude of the potential difference.

With V known, use the above-mentioned equation to calculate capacitance.

The equation for the cylindrical capacitor is:

C = capacitance of the cylinder

L = length of the cylinder

a = inner radius of the cylinder

b = outer radius of the cylinder

Capacitance is usually measured as the charge per unit voltage.

One farad is calculated as one coulomb per one volt.

Other Types of Capacitors

• Parallel Plate Capacitors: A parallel plate capacitor is the most basic capacitor, consisting of two parallel conducting plates. C = (e0A) / d is the capacitance of this capacitor, where A is the area of each plate and d is the distance between them.

• Spherical capacitor: A spherical capacitor comprises two concentric conducting spheres with radii of r1 and r2 and charges of +q and –q, respectively. 

C = 4πεo(r1r2) / (r2 – r1) is the capacitance of the spherical capacitor.

The conductor arrangement’s geometry solely determines capacitance.

Electrolytic capacitors are another common type of capacitor. It’s made up of an oxidised metal suspended in a conducting paste. The major benefit of an electrolytic capacitor is its high capacitance compared to other capacitor types.

Two pairs of parallel plates make up a variable capacitor.

Cell biology provides an intriguing application of the capacitor concept, which deals with the electrical potential in a live cell’s plasma membrane. Cell membranes keep cells distinct from their environment while allowing certain ions to move in and out. A membrane’s potential differential is around 70 mV. The thickness of the cell membrane can range from 7 to 10 nanometers.

Energy Stored in a Capacitor

The energy stored in a capacitor may be described in terms of the work performed by the battery. Because voltage represents energy per unit charge, the work required to transfer a charge element dq from the negative to positive plates equals V dq, where V is the capacitor’s voltage. The voltage V is proportional to the quantity of charge on the capacitor at any given time. 

The work done is stored as potential energy by U = Q2 / 2C = (1/2)CV2 = (1/2)QV (V = Q/C).

When a capacitor is charged by connecting it to a battery or other source with a set potential difference V, raising the value of C results in a higher charge (Q = C).

When a capacitor is charged by connecting it to a battery or another source that offers a set potential difference V, raising the value of C results in a higher charge (Q = C V) and more stored energy.

Conclusion

A capacitor is an electronic device that stores electrical charge and energy. A distance in capacitors usually separates two electrical conductors. Electrodes are a term used to describe these types of electrical conductors. When the distance between capacitors is merely a vacuum, the capacitor is called a “vacuum capacitor.” The gap is normally filled with a dielectric, an insulating substance. Capacitance is a characteristic that determines how much storage a capacitor has.