Consider the following statements 1. The insulation resistance of cable will increase if the length of cable is increased 2. For same overall diameter of cable, grading of cables will increase the safe working voltage 3. The normal operating temperature of PVC cable is 70 °C 4. The thermal resistance of soil increases as the moisture content of soil increases

The correct answer is Option B: 2 and 3 are correct. Statement 2 and 3 are correct. Grading of cables helps achieve uniform stress distribution, allowing higher working voltages for a given diameter, and 70°C is the standard maximum operating temperature for PVC insulation. Step-by-Step Solution & Concepts: Statement 2 and 3 are correct. Grading of cables helps achieve uniform stress distribution, allowing higher working voltages for a given diameter, and 70°C is the standard maximum operating temperature for PVC insulation. Working Principle: Insulation resistance is inversely proportional to length ($R_i = \frac{\rho}{2\pi L} \ln(\frac{R}{r})$), so it decreases as length increases. Thermal resistance of soil decreases with increased moisture because water acts as a superior heat conductor compared to air voids, enhancing heat dissipation from the buried cable. Key Formulas: $R_i = \frac{\rho}{2\pi L} \ln(\frac{R}{r})$ — Insulation resistance of a cable; $g_{max} = \frac{V}{r \ln(R/r)}$ — Maximum dielectric stress in a cable Key Points: Insulation resistance is inversely proportional to the length of the cable.; Cable grading (capacitance or inter-sheath) improves dielectric stress distribution.; PVC insulation is limited to 70°C, while XLPE can withstand up to 90°C.; Higher moisture content in soil lowers thermal resistivity, aiding in cooling. Advantages: Grading allows higher voltage ratings in smaller cable diameters.; Lower thermal resistance increases the current-carrying capacity (ampacity) of the cable. Disadvantages: Increased complexity and cost in manufactured graded cables.; PVC insulation can release toxic gases under fire conditions. Applications: Underground power distribution networks.; Submarine power cable installations. Additional Info: Statement 1 is incorrect because $R_i \propto 1/L$.. Statement 4 is incorrect because thermal resistivity decreases with higher moisture content.. PVC (Polyvinyl Chloride) is standard for low to medium voltage; XLPE (Cross-linked Polyethylene) is preferred for high voltage due to superior thermal properties. Answer: B is correct — Statements 2 and 3 are scientifically accurate regarding cable grading and thermal limits of PVC insulation. Exam Tip: Always remember that resistance ($R$) is proportional to length ($L$), whereas insulation resistance ($R_i$) is inversely proportional to length ($L$) because it acts as a parallel leakage path.

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Consider the following statements

The insulation resistance of cable will increase if the length of cable is increased
For same overall diameter of cable, grading of cables will increase the safe working voltage
The normal operating temperature of PVC cable is 70 °C
The thermal resistance of soil increases as the moisture content of soil increases

1 and 2 are correct

2 and 3 are correct

3 and 4 are correct

1 and 4 are correct

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option B

2 and 3 are correct

Quick Summary:

Statement 2 and 3 are correct. Grading of cables helps achieve uniform stress distribution, allowing higher working voltages for a given diameter, and 70°C is the standard maximum operating temperature for PVC insulation.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$R_i = \frac{\rho}{2\pi L} \ln(\frac{R}{r})$ — Insulation resistance of a cable

$g_{max} = \frac{V}{r \ln(R/r)}$ — Maximum dielectric stress in a cable

⚙️ Working Principle

Insulation resistance is inversely proportional to length ( $R_i = \frac{\rho}{2\pi L} \ln(\frac{R}{r})$ ), so it decreases as length increases. Thermal resistance of soil decreases with increased moisture because water acts as a superior heat conductor compared to air voids, enhancing heat dissipation from the buried cable.

📌 Key Points

▸
Insulation resistance is inversely proportional to the length of the cable.
▸
Cable grading (capacitance or inter-sheath) improves dielectric stress distribution.
▸
PVC insulation is limited to 70°C, while XLPE can withstand up to 90°C.
▸
Higher moisture content in soil lowers thermal resistivity, aiding in cooling.

✅ Advantages

▸
Grading allows higher voltage ratings in smaller cable diameters.
▸
Lower thermal resistance increases the current-carrying capacity (ampacity) of the cable.

❌ Disadvantages / Limitations

▸
Increased complexity and cost in manufactured graded cables.
▸
PVC insulation can release toxic gases under fire conditions.

🛠️ Applications / Uses

▸
Underground power distribution networks.
▸
Submarine power cable installations.

📄 Additional Information

▸
Statement 1 is incorrect because $R_i \propto 1/L$ .
▸
Statement 4 is incorrect because thermal resistivity decreases with higher moisture content.
▸
PVC (Polyvinyl Chloride) is standard for low to medium voltage; XLPE (Cross-linked Polyethylene) is preferred for high voltage due to superior thermal properties.

📊 Diagram / Illustration

✅

B is correct — Statements 2 and 3 are scientifically accurate regarding cable grading and thermal limits of PVC insulation.

Core Concepts Used

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Cable Insulation Resistance Dielectric Stress Grading Thermal Resistivity of Soil Material Temperature Ratings

💡 EXAM TIP

Always remember that resistance ( $R$ ) is proportional to length ( $L$ ), whereas insulation resistance ( $R_i$ ) is inversely proportional to length ( $L$ ) because it acts as a parallel leakage path.

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