Insulation Resistance of a Cable Capacitor

Insulation Resistance of a Cable Capacitor-

 In a cable capacitor, useful current flows along the axis of the core but there is always present some leakage of current. This leakage is radial i.e. at right angles to the flow of resistance useful current.The resistance offered to this radial leakage of current is called insulation resistance of the cable.
             
                              If cable length is greater,then leakage is also greater. It means that more current will leak.
                             In other words, insulation resistance is decreased.Hence, we find that insulation resistance is inversely proportional to the cable length. This insulation resistance  is not to be confused with conductor resistance which is directly proportional to the cable length.

                            Consider i metre of a single-core cable of inner radius  r₁ and outer radius r2 (Fig.). Imagin an annular ring of radius ''r" and radial thickness 'dr'.

                          If resistivity of insulating material is ρ then resistance of this narrow ring is

                               ρ dr
                   dR = ⸻⸻
                              2πr × l

ஃ  Insulation resistance of l meter length of cable is

               r2      ρ dr                                                                   

∫dR =   ∫     ----------------       Or     
               ʳ¹      2πr l                                                                 
                       
        



              ρ                     r2
R =    ---------   |logₑr|
          2πr l                   ʳ¹


           

                ρ
  R =    ----------  logₑ(r2/r1)
               2πl

It Should be noted that-

(A)R is inversely proportional to the cable length.
(B) R depends upon the ratio r2/r1 and NOT on the thickness of insulator itself.


ये भी पढ़ें👇
Energy stored in a capacitor in #Hindi



👍👍👍👍👍👍👍👍