(a) 1 MΩ
(b) 10 MΩ
(c) 0.1 MΩ
(d) 0.01 MΩ
Correct Answer: (c) 0.1
MΩ
Explanation
Insulation resistance is inversely proportional to
cable length.
Notes for
More Information
CONCEPT: Insulation Resistance
vs Length
1. Insulation
resistance is the resistance offered by the insulating material surrounding a
conductor to the leakage current.
2. Unlike
conductor resistance, insulation resistance is inversely proportional
to the length of the cable.
3. This is
because a longer cable provides more parallel leakage paths through
the insulation.
4. Hence:
5. Therefore,
the product of insulation resistance and length is constant:
Mathematical Relation
6. For the
same cable under identical conditions:
Where:
= insulation resistance at
length 
= insulation resistance at
length 
Given Data
7. Initial
insulation resistance:
8. Initial
length:
9. New length:
Calculation
10.
Using the relation:
11.
Substituting values:
12.
Solving for :
13.
Hence:
Final Answer
✅ Insulation resistance of the 100
km cable = 0.1 MΩ
Explanation (Physical Reason)
14.
Increasing cable length increases the surface area of insulation.
15.
This is equivalent to adding more resistances in parallel.
16.
Parallel resistances reduce the equivalent insulation resistance.
17.
Hence, longer cable → lower insulation resistance.
Important Exam Notes
18.
Conductor resistance ∝
length
19.
Insulation resistance ∝ 1 /
length
20.
Always use:
for insulation-resistance problems.
✔️ Key
One-Liner for Exams
Insulation resistance of a cable
is inversely proportional to its length.