The grading done by using the layers of dielectrics having different permittivities between the core and the sheath is called capacitance grading.

In intersheath grading, the permittivity of dielectric is same everywhere and the dielectric is said to be homogeneous. But in case of capacitance grading, a composite dielectric is used.

Let d

_{1}= Diameter of the dielectric with permittivity ε_{1} and D = Diameter of the dielectric with permittivity ε

_{2} This is shown in the Fig. 1.

Fig. 1 Capacitance grading |

The stress at a point which is at a distance x is inversely proportional to the distance x and given by,

g

_{x }= Q/(2πε x)Hence the stress at point in the inner dielectric is,

g

_{1 }= Q/(2πε_{1}x)Similarly the dielectric stress in the outer dielectric is,

g

_{2 }= Q/(2πε_{2}x) Hence the total voltage V can be expressed as,

The stress is maximum at surface of conductor i.e. x =d/2.

And the stress is maximum at inner surface of dielectric i.e. at x = d

_{1}/2. Substituting Q interms of V we get,

**Key Point**: Thus the electric stress is inversely proportional to the permittivities and the inner radii of the dielectrics.

__1.1 Condition for Equal Maximum Stress__

Let us obtain the condition under which the maximum values of the stresses in the two regions are equal.

The maximum stresses are given by,

g

_{1max }= Q/(πε_{1}d) and g

_{2max}= Q/(πε_{2}d_{1}) Equating the two stresses,

Q/(πε

_{1}d) = Q/(πε_{2}d_{1}) Now d

_{1}is greater than d so to satisfy above equation ε_{2}must be less than ε_{1}. Thus the dielectric nearest to the conductor must have the highest permittivity.

Similar for the grading with three dielectrics with permittivities ε

_{1}, ε_{2 }and ε_{3}, for equal maximum stress the condition is,And

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