Electrical Engineering ⇒ Topic : Cylindrical Capacitor

CYLINDRICAL CAPACITOR

A single core cable or cylindrical capacitor is shown in Figure (a). Let the inner and outer radio of the cylindrical capacitor be b and a metre, respectively. Let the permittivity of the dielectric medium between inner and outer cylinders be ε_r.

Let us consider an imaginary co-axial cylinder of radius x metres (b < x < a) having length one metre. Therefore, total flux coming out from the imaginary surface is Q coulomb. Area of this n curved surface is = 2πx. 1 = 2πx m²

                                                           Figure (a) Cylindrical capacitor.

The value of the electric flux density on the surface of the imaginary sphere is given by

A cylindrical capacitor consists of two co-axial cylinders separated by an insulating medium.This is an important practical case since a single core cable is in effect a capacitor of this kind. The conductor (or core) of the cable is the inner cylinder while the outer cylinder is represented by lead sheath which is at earth potential. The two co-axial cylinders have insulation between them.

Consider a single core cable with conductor diameter a metres and inner sheath diameter D metres (See Figure (a).Let the charge per metre axial length of the cable be Q coulombs and ε_r be the relative permittivity of the insulating material. Consider a cylinder of radius x metres. According to Gauss's theorem, electric flux passing through this cylinder is Q coulombs. The surface area of this cylinder is

Electric flux density at any point P on the considered cylinder is given by ;

                                           FIGURE  (A)

Electric intensity at point P is given by;

The work done in moving a unit positive charge from point P through a distance dx in the direction of electric field is E_X dx. Hence the work done in moving a unit positive charge from conductor to sheath, which is the p.d. V between the conductor and sheath, is given by

If the cable has a length of I metres, then capacitance of the cable is