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The insulation resistance of a single-core cable is 200 MΩ/km. The insulation resistance for 5 km length is
40 MΩ
1000 MΩ
200 MΩ
8 MΩ
40 MΩ
A is correct because the insulation resistance of a cable is inversely proportional to its length, so dividing 200 MΩ/km by 5 km results in 40 MΩ.
Insulation resistance per unit length Rl = 200 MΩ/km, Total length L = 5 km.
RL=LRl
Understand the relationship
Insulation resistance of a cable is inversely proportional to its length. Therefore, the total insulation resistance is given by dividing the resistance per unit length by the total length.
RL=LRunit
Identify given values
The resistance per km is Runit=200 MΩ/km and the length is L=5 km.
Runit=200,L=5
Calculate the total resistance
Substitute the values into the formula to find the resistance for the 5 km length.
RL=5200=40 MΩ
A is correct because the insulation resistance of a cable is inversely proportional to its length, so dividing 200 MΩ/km by 5 km results in 40 MΩ.
Always remember that while metallic conductor resistance is directly proportional to length (R = ρL/A), insulation resistance is inversely proportional to length because leakage current flows radially through the insulation.