In this theory, dielectric stress on cable, electric
intensity, maximum potential gradient, minimum potential gradient, ratio of
maximum to minimum potential gradient and dielectric stress on stranded cable is
given.

# Dielectric Stress

- It is electrostatic stress on cable insulation under operating conditions.
**The dielectric stress at any point is equal to potential gradient at that point**therefore in order to find dielectric stress at any point in cable, we have to find out potential gradient at that point.

## Electric intensity

The
electric intensity at any distance x from the center of cable O is given by

E_{x}
= [Q / 2πε_{0}ε_{r }] ( 1 / x )
volt / meter

Where

ε_{0
}=_{ }Absolute Permittivity = 8.854 × 10 ^{– 12} Farad /
meter_{}

ε_{r
}= Relative Permittivity

## Potential Gradient

The
potential gradient ( E ) at any point is equal to electric intensity ( g ) at
that point therefore

g
= [Q / 2πε_{0}ε_{r }] (
1 / x ) volt / meter… ( 1 )

As
capacitance C = 2πε_{0}ε_{r }/ Log_{e} ( D / d ) and C
= Q / V… ( 2 )

Q = CV

= [ 2πε_{0}ε_{r }/ Log_{e}
( D / d )] V…. ( 3 )

From
equation ( 1 ) and ( 3 )

g
= [ V_{ }/ Log_{e} ( D / d )] _{ }( 1 / x )

**g
= V / [ x Log _{e} ( D / d )] **

_{ }…. ( 4 )

**We
can say that the potential gradient at any point on cable is inversely
proportional to x. The potential gradient is minimum when x is maximum and
potential gradient is maximum when x is minimum. **

- X is maximum at distance = D ( Internal diameter of sheath ) / 2
- X is minimum at distance = d ( Diameter of conductor ) / 2

### Maximum & Minimum Potential Gradient

- Maximum potential gradient at x = d / 2

g_{max}
= 2V / [ d Log_{e} ( D / d )] _{ } (
⸫ x = d / 2 )….. ( 5 )

- Minimum potential gradient at x = D / 2

g_{min}
= 2V / [ D Log_{e} ( D / d )] _{ } (
⸫ x = D / 2 )…. ( 6 )

### Ratio of Maximum to Minimum Potential Gradient

- Therefore, the ratio of maximum potential gradient to the minimum potential gradient

( g_{max }/ g_{min} ) = {2V /
[ d Log_{e} ( D / d )] } / { 2V / [ D Log_{e} ( D / d )] } _{ } _{ }

**(
g _{max }/ g_{min} ) = D / d **

- The formula for maximum and minimum potential gradient is applicable only for smooth cylindrical cable.
**The dielectric stress for the stranded conductor increases by 20% due to conductor surface of the individual wires (strands).**

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