- Cylindrical Capacitor Definition: A cylindrical capacitor is defined as a type of capacitor with a central conductor, an insulating layer, and an outer grounded metallic cover.
- Power Cable Example: Electrical power cables act as cylindrical capacitors with their conductor, insulation, and outer grounded cover.
- Charge Distribution: Charge per meter length (Q coulombs) in the cable is used in capacitance calculations.
- Capacitance Formula: The capacitance per unit length is calculated using the radii of the conductor and the cable.
- The capacitance per unit length is calculated using the radii of the conductor and the cable.: Understanding cylindrical capacitors helps in analyzing the capacitance in power cables.
Capacitance of a Cylindrical Power Cable
A common example of a cylindrical capacitor is an Electrical Power Cable. It consists of a central conductor, an insulating layer around it, and an outer metallic cover that is grounded.
When current flows through the conductor, the cable has a charge of Q coulombs per meter. The conductor’s radius is r1, and the outer radius of the cable is r2.
To calculate the capacitance of this cylindrical capacitor, imagine a concentric cylinder with a radius of x meters.
Now, the surface area of 1m long such imaginary cylinder is,
According to the definition, the flux density on this surface is calculated as follows:
Again, as per definition, electrical field intensity at any point on that imaginary surface will be,
Again, electrical field intensity is defined as the ratio incremental change in voltage to incremental change in distance.
By integrating both sides from r1 to r2, we obtain the following:
Where, surface voltage of conductor of radius r1 m is V1 volt and surface voltage of outer surface of cable of radius r2 m is V2 volt.
Now, if outer surface is grounded, then
Now, capacitance of the cable per unit length i.e. per meter is given as,
This is expression of capacitance per unit length i.e. per meter of the cable.
Hence, the capacitance of L meter cable will be,
