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A single core 5 km long has an insulation resistance of 0.4 megaohm. The core diameter is 20 mm and the diameter of cable over insulation is 50mm .calculate resistivity of insulating material?
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A single core 5 km long has an insulation resistance of 0.4 megaohm. T...
Calculation of Resistivity of Insulating Material

Given Parameters:

  • Length of core (L) = 5 km = 5000 m

  • Insulation resistance (R) = 0.4 megaohm = 400000 ohm

  • Diameter of core (d) = 20 mm

  • Diameter of cable over insulation (D) = 50 mm



Calculation:

  • Area of cross-section of core (A) = pi * d^2 / 4

  • Area of cross-section of cable over insulation (A') = pi * D^2 / 4

  • Resistance of core (Rc) = R * A / L

  • Resistance of cable over insulation (R') = R * A' / L



Assumptions:

  • The core and cable over insulation are made of the same insulating material.

  • The insulation resistance is considered to be the resistance of the insulating material.

  • The resistance of the metal conductor is negligible.



Formula:

  • Resistivity (p) = R * A / L



Calculation of Resistivity:

  • Resistance of core (Rc) = R * A / L = 400000 * pi * (20/1000)^2 / 5000 = 0.502 ohm

  • Resistance of cable over insulation (R') = R * A' / L = 400000 * pi * (50/1000)^2 / 5000 = 5.026 ohm

  • Total resistance of cable (Rtotal) = Rc + R' = 0.502 + 5.026 = 5.528 ohm

  • Resistance of insulation (Rinsulation) = Rtotal - Rc = 5.528 - 0.502 = 5.026 ohm

  • Resistivity of insulation (p) = Rinsulation * A' / L = 5.026 * pi * (50/1000)^2 / 5000 = 3.183 * 10^(-12) ohm-m



Explanation:

  • The calculation of resistivity of insulating material requires the calculation of resistance of the core and cable over insulation.

  • The resistance of the core and cable over insulation is calculated using the formula R = p * L / A.

  • The resistivity of the insulating material is then calculated using the formula p = R * A' / L.

  • The diameter of the core and cable over insulation is used to calculate the area of cross-section, which is then used to calculate the resistance.

  • The total resistance of the cable is calculated by adding the resistance of the core and cable over insulation.

  • The resistance of the insulation is calculated by subtracting the resistance of the core from the total resistance of the cable.

  • The resistivity of the insulation is then calculated using the resistance of the insulation and the
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A single core 5 km long has an insulation resistance of 0.4 megaohm. The core diameter is 20 mm and the diameter of cable over insulation is 50mm .calculate resistivity of insulating material?
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