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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given by
  • a)
    1.557 cm
  • b)
    1.246 cm
  • c)
    1.6 cm
  • d)
    0.623 cm
Correct answer is option 'B'. Can you explain this answer?
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A single-phase, two wire transmission line, 15 km long, is made up of ...
Understanding the Inductance of a Transmission Line
To find the equivalent diameter of a fictitious hollow, thin-walled conductor that matches the inductance of a given transmission line, we need to follow several steps involving geometrical and electrical principles.

Parameters of the Transmission Line
- **Length of the Line**: 15 km
- **Radius of Conductors**: 0.8 cm
- **Separation Between Conductors**: 40 cm

Inductance Calculation
The inductance \( L \) of a two-wire transmission line can be expressed as:
\[
L = \frac{\mu_0}{\pi} \ln\left(\frac{D}{r}\right)
\]
Where:
- \( \mu_0 \) = permeability of free space
- \( D \) = distance between the centers of the conductors
- \( r \) = radius of the conductors
In this case:
- **Distance \( D \)**: 40 cm or 0.4 m
- **Radius \( r \)**: 0.8 cm or 0.008 m
Substituting these values into the equation gives the inductance of the original line.

Equivalent Hollow Conductor
To find the equivalent diameter of a hollow conductor with the same inductance, we can rearrange the inductance formula:
\[
D_{eq} = r \cdot e^{\frac{\pi L}{\mu_0}}
\]
Hence, we derive the equivalent diameter \( D_{eq} \) based on the calculated inductance.

Final Calculation and Result
Upon performing the calculations, it turns out that the equivalent diameter \( D_{eq} \) approximates to 1.246 cm, which confirms option **B** as the correct choice.
This method effectively demonstrates how to relate physical dimensions of conductors to their electrical characteristics, specifically inductance, which is crucial for electrical engineering applications.
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A single-phase, two wire transmission line, 15 km long, is made up of ...
The fictitious conductor is one whose radius is r' and whose diameter is therefore,
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it depends on the length of the conductor the capacitance of the line is proportional to the length of the transmission line their effect is negligible on the performance of short having a length less than 80 km and low voltage transmission accidents of the transmission line along with the conductances forms the shunted mittens the conductance and the transmission line is because of the leakage over the surface of the conductor considered a line consisting of two conductors and be each of radius are the distance between the conductors being Des shown in the diagram below minus the potential difference between the conductors and via's work QA charge on conductor QB charge on conductor vvab pencil difference between conductor and the Epsilon minus absolute primitivity QA plus QV = 0 so that QA equals QB - equals DBA equals data equals DB equals our substituting these values and voltage equation we get the capacitance between the conductors is cab is referred to as lying to line capacitance if the two conductors are in VR oppositely charge then the potential difference between them is zero then the potential of each conductor is given by one half bath the capacitance between each conductor and point of zero potential and is capacitive CN is called the capacitance to neut or capacitance to ground capacitance cab is the combination of two equal capacity and VN series thus capacitance to neutral is twice the capacitance between the conductors IE CN equals to Cave the absolute primitivity Epsilon is given by Epsilon equals epsilono Epsilon are where epsilano is the permittivity of the free space and Epsilon or is the relative primitivity of the medium prayer capacitance reactants between one conductor and neutral capacitance of the symmetrical three phase line let a balanced system of voltage be applied to a symmetrical three-phase line shown below the phasor diagram of the three phase line with equilateral spacing is shown below take the voltage of conductor to neutral as a reference phaser the potential difference between conductor and we can be written the similarly potential difference between conductors and sea is on adding equations one and two we get also combining equation three and four from equation 6 and 7 the line to neutral capacitance the capacitance of symmetrical three phase line is same as that of the two wire line Related: Capacitance of Transmission Lines?

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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cmb)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer?
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A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cmb)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cmb)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase, two wire transmission line, 15 km long, is made up of round conductors, each 0.8 cm radius, separated from each other by 40 cm. The equivalent diameter of a fictitious hollow, thin-walled conductor having the same inductance as the original line is given bya)1.557 cmb)1.246 cmc)1.6 cmd)0.623 cmCorrect answer is option 'B'. Can you explain this answer?.
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