8/4/2019 Capacitance of a Single Core Cable
1/21
Capacitance of a single core
cable
8/4/2019 Capacitance of a Single Core Cable
2/21
Capacitance of a single core cable
Single core cable consists of two long co-axial cylinders.Inner cylinder is conductor and outer cylinder is a lead sheath.
R=D/2
R=d/2
Radius of the cylinder is = x
8/4/2019 Capacitance of a Single Core Cable
3/21
Flux density =
Here charge=Q
Surface area =2
Radius=2 x
Flux density , Dx Cm
According to gauss law
8/4/2019 Capacitance of a Single Core Cable
4/21
Electric Field intensity at point P is given by,
Since
Potential Difference between Conductor and
sheath is given by
R=D/2r=d/2
8/4/2019 Capacitance of a Single Core Cable
5/21
V
Since
or
Capacitance for cable is given by
or
Substitute the values of
F/mor
8/4/2019 Capacitance of a Single Core Cable
6/21
Dielectric Stress
8/4/2019 Capacitance of a Single Core Cable
7/21
Dielectric Stress:
Here dielectric stress is equal to electric field
intensity at point p
Now voltage is given by
Since
8/4/2019 Capacitance of a Single Core Cable
8/21
Substitute Q in
Maximum stress will be at the surface of the conductor, x=r
Since,r=d/2
Minimum stress will be at the Sheath, x=R
Since,R=D/2
So dielectric stress is
8/4/2019 Capacitance of a Single Core Cable
9/21
Grading of cables
8/4/2019 Capacitance of a Single Core Cable
10/21
Grading of cables
Maximum stress will be at the surface of theconductor and minimum stress will be at thesheath.
To avoid breakdown of insulation it isnecessary to have uniform distribution ofstress all along the insulator
The process of obtaining uniform distributionof stress in the insulation of cables is calledgrading of cables
8/4/2019 Capacitance of a Single Core Cable
11/21
Types of Grading
Use of inter sheaths for grading
Capacitance grading
8/4/2019 Capacitance of a Single Core Cable
12/21
Use of inter sheaths for grading
In this method of
grading the between
the core and lead
sheaths number ofmetallic sheaths are
placed which are called
as inter sheaths
Radius of the conductor =d/2
Radius of the intersheath1=d1/2
Radius of the intersheath1=d2/2
Radius of the lead sheath=D/2
8/4/2019 Capacitance of a Single Core Cable
13/21
Use of intersheaths for grading
Let V1 be the voltage
between core and inter
sheath1
Let V2 be the voltagebetween intersheath1
and inter sheath2
Let V3 be the voltage
between intersheath2
and Lead sheath
8/4/2019 Capacitance of a Single Core Cable
14/21
Maximum stress between core and sheath given by
We can write Maximum stress between core and inter sheath1 as
Similarly, Maximum stress between inter sheath1 andinter sheath2 is
Similarly, Maximum stress between inter sheath2 and Lead sheath is
Let V1 be the voltage between core and inter sheath1Let V2 be the voltage between intersheath1 and intersheath2
Let V3 be the voltage between intersheath2 and Lead sheath
8/4/2019 Capacitance of a Single Core Cable
15/21
Now
Voltage between conductor and lead sheath is
8/4/2019 Capacitance of a Single Core Cable
16/21
Capacitance grading
8/4/2019 Capacitance of a Single Core Cable
17/21
Capacitance grading
In this type grading is done by using layers of
dielectrics having different permittivitties between
core and sheath
Let d be the diameter ofconductor
Let d1 be the diameter of
dielectric with permittivity Let d2 be the diameter of
dielectric with permittivity
8/4/2019 Capacitance of a Single Core Cable
18/21
As we know, dielectric stress isgiven by
Here the stress at inner dielectric is given by
Here the stress at outer dielectric is given by
(1)
(2)
8/4/2019 Capacitance of a Single Core Cable
19/21
8/4/2019 Capacitance of a Single Core Cable
20/21
We know
From (1) the maximum stress at the surface of conductor is ,i.e x=d/2
From (2) the maximum stress at the surface inner dielectric is , i.e x=d1/2
(3)
(4)
Substitute the value of Q in (3)
8/4/2019 Capacitance of a Single Core Cable
21/21
Substitute the value of Q in (3)
Similarly Substitute the value of Q in (4)