Insulation resistance of the cable decreases with the

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The correct answer is Option A: Increase in length of cable. The insulation resistance of a cable is inversely proportional to its length. As the length of the cable increases, the insulation resistance decreases because more leakage paths are connected in parallel.

Step-by-Step Solution & Concepts:
The insulation resistance of a cable is inversely proportional to its length. As the length of the cable increases, the insulation resistance decreases because more leakage paths are connected in parallel.

Working Principle: In an underground cable, the insulation can be modeled as a resistance $R$ between the core and the sheath. If a cable of length $L$ has a resistance $R$, then a longer cable can be thought of as several small segments of length $dx$ connected in parallel. Since the conductance $G = \frac{1}{R}$ is proportional to length, adding length increases total conductance, thereby decreasing total resistance.

Key Formulas: $R_i = \frac{\rho}{2 \pi L} \ln(\frac{D}{d})$ — where $R_i$ is insulation resistance, $\rho$ is resistivity, $L$ is length, $D$ is sheath diameter, and $d$ is core diameter.

Key Points: Insulation resistance is inversely proportional to length ($R \propto \frac{1}{L}$).; Leakage current increases as the length of the cable increases.; This relationship is critical for testing long-distance power distribution lines.; The resistivity of the insulating material ($\rho$) remains constant regardless of cable length.

Advantages: Predictability of leakage current based on cable segment length.; Easier fault location using resistance measurement techniques.

Disadvantages: Requires high-sensitivity instruments for very long cables where resistance becomes very low.; Vulnerability to environmental factors affecting large exposed lengths.

Applications: Power transmission and distribution network monitoring.; Maintenance testing of underground cable systems.

Additional Info: Standard industrial practice defines insulation resistance in $M\Omega-km$.. Option B is incorrect because a decrease in length would increase the insulation resistance, effectively 'shortening' the parallel leakage paths.

Answer: A is correct — Insulation resistance of a cable is inversely proportional to its length because total leakage conductance increases with the length of the cable.

Exam Tip: Always remember that while resistance of a *conductor* is directly proportional to length ($R = \frac{\rho L}{A}$), the insulation resistance of a *dielectric* follows an inverse relationship ($R_i \propto \frac{1}{L}$).

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Option B: Decrease in length of cable

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Option C: Electric stresses

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Option D: None of above

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