Types of Conductors MCQ Quiz - Objective Question with Answer for Types of Conductors - Download Free PDF

Kelvin's Law 

The Kelvin's law states that the most economical size of a conductor is that for which annual interest and depreciation on the capital cost of the conductor is equal to the annual cost of energy loss.

Graphical representation of Kelvin's law:

Limitations of Kelvin's law:

• Interest and depreciation on the capital cost cannot be determined accurately.
• It gives different conductor sizes for two identical systems due to variations in interest rates, depreciation, and energy costs.
• This law does not take into account several factors like safe current carrying capacity, corona loss, etc.
• The economical size of a conductor may cause the voltage drop beyond the acceptable limits.

Cadmium Copper Alloy

• Cadmium copper alloy is a copper-based alloy containing 1% to 2% cadmium (Cd). 
• When 1% or 2% cadmium is added to copper, it increases the tensile strength significantly. This makes it suitable for applications requiring durability, such as overhead transmission lines.
• However, the electrical conductivity of copper decreases slightly due to the addition of cadmium. This is because cadmium introduces impurities, increasing electrical resistance.
• Even though conductivity decreases slightly, the mechanical strength gain outweighs the loss in many industrial uses.

Explanation:

The I-V characteristics of a material indicate whether it follows Ohm’s law or not.

For ohmic conductors , the graph of current (I) vs. voltage (V) is a straight line passing through the origin, indicating that resistance remains constant.

For non-ohmic conductors , the graph is nonlinear, meaning the resistance changes with applied voltage.

The given graph is nonlinear, indicating a non-ohmic conductor .

Since the curve deviates from a straight line, it does not obey Ohm’s law.

Examples of non-ohmic conductors include:

- Semiconductor diodes

- Transistors

- Filament lamps

- Electrolytes

∴ The I-V characteristics represent a non-ohmic conductor.

Explanation:

Stranded Conductor with Multiple Layers of Wire

Definition: A stranded conductor is composed of multiple layers of wire strands twisted together. The structure typically enhances flexibility and mechanical strength compared to a single solid wire.

Working Principle: In a stranded conductor, the individual strands are arranged in concentric layers. Each layer contains a specific number of strands that follow a geometric progression. The diameter of the entire conductor increases with each additional layer of strands.

Calculation:

To determine the diameter of a stranded conductor with multiple layers of wire, follow these steps:

Step 1: Understand the arrangement of strands in each layer. The number of strands in each layer follows a specific pattern. For instance, the first layer (center) has 1 strand, the second layer has 6 strands, the third layer has 12 strands, and so on.

Step 2: Calculate the total number of layers and their respective radii. The radius of each layer can be found by adding the diameter of one strand to the radius of the previous layer.

Step 3: Determine the overall diameter of the conductor.

Given:

• Diameter of each strand = 5 mm
• Number of layers = 3

Let's calculate the diameter step-by-step:

Layer 1:

• Number of strands = 1
• Radius = (1/2) * Diameter of one strand = (1/2) * 5 mm = 2.5 mm

Layer 2:

• Number of strands = 6
• Radius = Diameter of one strand + Radius of Layer 1 = 5 mm + 2.5 mm = 7.5 mm

Layer 3:

• Number of strands = 12
• Radius = Diameter of one strand + Radius of Layer 2 = 5 mm + 7.5 mm = 12.5 mm

Total Diameter:

The total diameter of the conductor is twice the radius of the outermost layer:

Total Diameter = 2 * Radius of Layer 3 = 2 * 12.5 mm = 25 mm

Conclusion:

The diameter of the conductor with 3 layers of wire, each strand having a diameter of 5 mm, is 25 mm.

Important Information:

Now, let's analyze the other options:

Option 1: 40 mm

This option is incorrect. The calculation of 40 mm does not align with the geometric progression and layering structure of the strands. The diameter of each layer follows a specific pattern that does not result in such a large value.

Option 2: 30 mm

This option is also incorrect. As calculated, the correct diameter for the given configuration is 25 mm. The value of 30 mm does not fit the arrangement and layering structure.

Option 3: 25 mm

This option is correct. The calculations align with the geometric progression and layering structure, confirming that the diameter of the conductor with 3 layers of wire, each strand having a diameter of 5 mm, is indeed 25 mm.

Option 4: 35 mm

This option is incorrect. The value of 35 mm does not match the calculated diameter for the given configuration of the conductor. The layering structure results in a diameter of 25 mm.

Conclusion:

Understanding the arrangement and geometric progression of strands in a stranded conductor is essential for accurately determining its diameter. The correct diameter for a stranded conductor with 3 layers of wire, each strand having a diameter of 5 mm, is 25 mm. This calculation is crucial for applications requiring precise conductor dimensions to ensure proper functionality and performance.

Representation of ACSR Conductor:

A standard conductor is represented as A/S/D for ACSR conductor.
Where,

• A is the number of aluminum strands.
• S is the number of steel strands.
• D is the diameter of each strand.
   

Example: If the ACSR conductor having 6 steel strands surrounded by 70 aluminum conductors will be specified as 70/6.

Additional Information

Calculation of the number of strands in a stranded conductor:

• If there are ‘n’ layers of strands in a stranded conductor.
• Number of strands of the conductor = 3n² - 3n + 1
   

Calculation of overall diameter of a stranded conductor:

• If d mm is the diameter of a single strand in the conductor.
• The overall diameter of the conductor = (2n + 1) d unit

Generally, the total number of strands in any conductor is given by the formulae

N = 3x² – 3x + 1

Where x = no. of layers

Bundled conductor are those conductors which form from two or more stranded conductors, bundled together to get more current carrying capacity.

By using bundle conductors instead of the single conductor in the transmission line increases the GMR of the conductors.

So, inductance  reduces according to the following equation

\(\downarrow L = \frac{{{\mu _0}}}{{2\pi }}\ln \left( {\frac{{GMD}}{{ \uparrow GMR}}} \right)\) H/m/ph

Hence, the inductance per phase of the conductor decreases

So, capacitance  increases according to the following equation

\(\uparrow C = \frac{{2\pi {\varepsilon _0}{\varepsilon _r}}}{{\ln \left( {\frac{{GMD}}{{ \uparrow GMR}}} \right)}}\) F/m/ph

Hence, by using bundle conductors GMR is increased, so inductance L decrease and capacitance C increases.

Advantages of Bundled Conductors:

• Bundling of conductors leads to a reduction in line inductance.
• Bundling of conductors leads to increases in capacitance.
• An important advantage of bundled conductors is its ability to reduce corona discharge
• Reduction in the formation of corona discharge leads to less power loss and hence improved transmission efficiency of the line.
• Reduction in communication line interference.

Generally, the total number of strands in any conductor is given by the formulae

N = 3x2 – 3x + 1

Where x = no. of layers

Bundled conductor are those conductors which form from two or more stranded conductors, bundled together to get more current carrying capacity.

By using bundle conductors instead of the single conductor in the transmission line increases the GMR of the conductors.

So, inductance reduces according to the following equation

\(\downarrow L = \frac{{{\mu _0}}}{{2\pi }}\ln \left( {\frac{{GMD}}{{ \uparrow GMR}}} \right)\) H/m/ph

Hence, the inductance per phase of the conductor decreases

So, capacitance increases according to the following equation

\(\uparrow C = \frac{{2\pi {\varepsilon _0}{\varepsilon _r}}}{{\ln \left( {\frac{{GMD}}{{ \uparrow GMR}}} \right)}}\) F/m/ph

Hence, by using bundle conductors GMR is increased, so inductance L decreases and capacitance C increases.

Advantages of Bundled Conductors:

• Bundling of conductors leads to a reduction in line inductance.
• Bundling of conductors leads to increases in capacitance.
• An important advantage of bundled conductors is their ability to reduce corona discharge
• Reduction in the formation of corona discharge leads to less power loss and hence improved transmission efficiency of the line.
• Reduction in communication line interference.

Representation of ACSR Conductor:

A standard conductor is represented as A/S/D for ACSR conductor.

Where,

A is the number of aluminum strands.

S is the number of steel strands.

D is the diameter of each strand.

Example: If the ACSR conductor having 7 steel strands surrounded by 25 aluminum conductors will be specified as 25/7.

Additional Information

Calculation of the number of strands in a stranded conductor:

If there are ‘n’ layers of strands in a stranded conductor.

Number of strands of the conductor = 3n² - 3n + 1

Calculation of overall diameter of a stranded conductor:

If d mm is the diameter of a single strand in the conductor.

The overall diameter of the conductor = (2n + 1) d unit

Spiraling of conductor

• The overhead transmission line needs a conductor which is light in weight and also has greater conductivity. For this spiraling of the conductor is done.
• It is a process in which the core is of the material which has greater conductivity while the outer strands are of lighter material.
• ACSR (aluminum-conductor-steel-reinforced) is one of the most used conductors in transmission lines.
• It consists of alternate layers of stranded conductors, spiraled in opposite directions to hold the strands together, surrounding a core of steel strands.
• The purpose of introducing a steel core inside the stranded aluminum conductors is to obtain a high strength-to-weight ratio.
• A stranded conductor offers more flexibility and is easier to manufacture than a solid large conductor.
• Since the resistance is inversely proportional to the cross-sectional area, therefore the total resistance increases due to spiraling.​

Aluminum conductor steel reinforced(ACSR):

• It is one of the stranded conductors composed of one or more layers of hard-drawn 1350-H19 aluminum wire that is on galvanized coated steel core.

• The ACSR conductors are mainly used in distribution and transmission lines due to their high tensile strength, economical design, less weight, suitable for medium and long periods with fewer supports, and good properties of sag and high voltage overhead lines.

Advantages of ACSR conductors over copper conductors:

• The conductivity of the ACSR is less than the copper conductor.
• ACSR conductor can be used for medium and long spans and needs less support.
• The mechanical performance and Tensile strength of the ACSR conductor are High.
• It provides lesser Sag than copper conductors.

Concept :

ACSR Cable :

• It is an Aluminium conductor steel reinforced cable.
• It is of very high capacity.
• It has high mechanical and electrical strength.
• It has low maintenance and low cost.
• It will reduce corona loss.

The Correct Answer is option (3)

Explanation:

Generally, the diameter of the conductor can be calculated by,

D = (2n - 1)d

\(\frac{D}{d}= 2n-1\ \)

Where D = Diameter of n-layered stranded conductor

d = Diameter of each strand.
Additional InformationStranding of Conductor:

• The strands of each layer are laid in a helical fashion over the preceding layer is called stranding.
• Generally, in the successive layer, the stranding is done in opposite direction to the preceding layer.
• This means, that if the strands of one layer are twisted in a clockwise direction, the strands of the next layer will be twisted in an anticlockwise direction, and so on.

Generally, the total number of strands in any conductor is given by,

Total number of strands in a stranded conductor (N) = 3n(n-1) + 1

N = 3n² - 3n + 1

The correct answer for this question is option 4: 30 cm.

Concept:

Bundled conductors are those conductors which form from two or more sub-conductors, bundled together to get more current carrying capacity.

Using bundle conductors instead of the single conductor in the transmission line increases the GMR of the conductors. The individual conductor of any bundle is defined as a sub conductor.

Important points:

Advantages of Bundled Conductors:

• The bundling of conductors leads to a reduction in line inductance.
• The bundling of conductors leads to increases in capacitance.
• An important advantage of bundled conductors is its ability to reduce corona discharge.
• Reduction in the formation of corona discharge leads to less power loss and hence improved transmission efficiency of the line.
• Reduction in communication line interference.
• The voltage gradient gets reduced.
• The surge impedance of the line is reduced.