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A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.
Correct answer is '1.438'. Can you explain this answer?
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To find the distance D in meters, we need to analyze the given information step by step.
1. Calculation of single-phase transmission line inductance per conductor:
- The radius of each conductor is given as 10 mm, which is equivalent to 0.01 meters.
- The center-to-center distance between the conductors is given as 1 meter.
- The inductance per conductor of a single-phase transmission line can be calculated using the formula:
L = (μ₀ / 2π) * ln(D/r)
where L is the inductance per conductor, μ₀ is the permeability of free space, and r is the radius of the conductor.
- Substituting the given values, we get:
L_single = (4π × 10^(-7) / 2π) * ln(1/0.01)
= (2 × 10^(-7)) * ln(100)
≈ 2 × 10^(-7) * 4.605
≈ 9.21 × 10^(-7) H/m
2. Calculation of positive sequence inductance per phase of the three-phase system:
- The positive sequence inductance per phase of the three-phase system is given to be 5% more than the inductance per conductor of the single-phase system.
- Let's assume the positive sequence inductance per phase of the three-phase system as L_three.
- According to the given information, we can write the equation:
L_three = L_single + 0.05 * L_single
= 1.05 * L_single
- Substituting the value of L_single, we get:
L_three = 1.05 * 9.21 × 10^(-7)
≈ 9.67 × 10^(-7) H/m
3. Calculation of distance D:
- Since the three-phase line is fully transposed, the distance D is equal to the center-to-center distance between any two adjacent conductors.
- Let's assume the center-to-center distance between the single-phase conductors as D_single.
- According to the given information, we can write the equation:
L_single = (μ₀ / 2π) * ln(D_single/r)
- Solving this equation for D_single, we get:
D_single = e^(L_single * 2π / μ₀)
= e^(9.21 × 10^(-7) * 2π / 4π × 10^(-7))
= e^(9.21 / 4)
≈ 8.738 meters
- Now, since the three-phase line is fully transposed, D_single is equal to D.
Therefore, D ≈ 8.738 meters.
- However, the correct answer is given as '1.438' meters. There might be an error in the calculations or the given information. Please double-check the values provided in the question.
1. Calculation of single-phase transmission line inductance per conductor:
- The radius of each conductor is given as 10 mm, which is equivalent to 0.01 meters.
- The center-to-center distance between the conductors is given as 1 meter.
- The inductance per conductor of a single-phase transmission line can be calculated using the formula:
L = (μ₀ / 2π) * ln(D/r)
where L is the inductance per conductor, μ₀ is the permeability of free space, and r is the radius of the conductor.
- Substituting the given values, we get:
L_single = (4π × 10^(-7) / 2π) * ln(1/0.01)
= (2 × 10^(-7)) * ln(100)
≈ 2 × 10^(-7) * 4.605
≈ 9.21 × 10^(-7) H/m
2. Calculation of positive sequence inductance per phase of the three-phase system:
- The positive sequence inductance per phase of the three-phase system is given to be 5% more than the inductance per conductor of the single-phase system.
- Let's assume the positive sequence inductance per phase of the three-phase system as L_three.
- According to the given information, we can write the equation:
L_three = L_single + 0.05 * L_single
= 1.05 * L_single
- Substituting the value of L_single, we get:
L_three = 1.05 * 9.21 × 10^(-7)
≈ 9.67 × 10^(-7) H/m
3. Calculation of distance D:
- Since the three-phase line is fully transposed, the distance D is equal to the center-to-center distance between any two adjacent conductors.
- Let's assume the center-to-center distance between the single-phase conductors as D_single.
- According to the given information, we can write the equation:
L_single = (μ₀ / 2π) * ln(D_single/r)
- Solving this equation for D_single, we get:
D_single = e^(L_single * 2π / μ₀)
= e^(9.21 × 10^(-7) * 2π / 4π × 10^(-7))
= e^(9.21 / 4)
≈ 8.738 meters
- Now, since the three-phase line is fully transposed, D_single is equal to D.
Therefore, D ≈ 8.738 meters.
- However, the correct answer is given as '1.438' meters. There might be an error in the calculations or the given information. Please double-check the values provided in the question.
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A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer?
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A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer?.
A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer?.
Solutions for A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ____________.Correct answer is '1.438'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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