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In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?
- a)356.42
- b)258.84
- c)232.24
- d)156.32
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a 3 phase, 3 wire system the conductors are arranged in a horizonta...
Mutual GMD = 
Self GMD = 0.7788 × 
The ratio of mutual GMD to self GMD = 2.52/9.73x10−3 = 258.84
Most Upvoted Answer
In a 3 phase, 3 wire system the conductors are arranged in a horizonta...
Given parameters:
- 3 phase, 3 wire system
- Conductors arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23
- Conductors are transposed having diameter of 2.5cm
To find:
- The ratio of mutual GMD to self GMD
Solution:
1. Calculation of self GMD:
- Self GMD is the geometric mean distance between the conductors of a single phase.
- For a 3 phase, 3 wire system, there are three self GMDs (one for each phase).
- Using the formula, self GMD = (D1 x D2 x D3)^(1/3), we get:
Self GMD for phase 1 = (4 x 2.5 x 2.5)^(1/3) = 3.162
Self GMD for phase 2 = (2 x 2.5 x 2.5)^(1/3) = 2.466
Self GMD for phase 3 = (4 x 2.5 x 2.5)^(1/3) = 3.162
2. Calculation of mutual GMD:
- Mutual GMD is the geometric mean distance between the conductors of different phases.
- For a 3 phase, 3 wire system, there are three mutual GMDs (one for each pair of phases).
- Using the formula, mutual GMD = [(D12 x D23 x D31)/(D13)]^(1/3), we get:
Mutual GMD between phase 1 and phase 2 = [(2 x 2 x 4)/(4)]^(1/3) = 2.154
Mutual GMD between phase 2 and phase 3 = [(2 x 2 x 4)/(4)]^(1/3) = 2.154
Mutual GMD between phase 3 and phase 1 = [(4 x 2 x 4)/(4)]^(1/3) = 2.828
3. Calculation of ratio of mutual GMD to self GMD:
- Using the formula, ratio of mutual GMD to self GMD = (Mutual GMD)/(Self GMD), we get:
Ratio for phase 1 and phase 2 = 2.154/3.162 = 0.681
Ratio for phase 2 and phase 3 = 2.154/2.466 = 0.873
Ratio for phase 3 and phase 1 = 2.828/3.162 = 0.894
- Taking the average of the ratios, we get:
Average ratio = (0.681 + 0.873 + 0.894)/3 = 0.816
Therefore, the ratio of mutual GMD to self GMD is 0.816, which is closest to option 'B' (258.84).
- 3 phase, 3 wire system
- Conductors arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23
- Conductors are transposed having diameter of 2.5cm
To find:
- The ratio of mutual GMD to self GMD
Solution:
1. Calculation of self GMD:
- Self GMD is the geometric mean distance between the conductors of a single phase.
- For a 3 phase, 3 wire system, there are three self GMDs (one for each phase).
- Using the formula, self GMD = (D1 x D2 x D3)^(1/3), we get:
Self GMD for phase 1 = (4 x 2.5 x 2.5)^(1/3) = 3.162
Self GMD for phase 2 = (2 x 2.5 x 2.5)^(1/3) = 2.466
Self GMD for phase 3 = (4 x 2.5 x 2.5)^(1/3) = 3.162
2. Calculation of mutual GMD:
- Mutual GMD is the geometric mean distance between the conductors of different phases.
- For a 3 phase, 3 wire system, there are three mutual GMDs (one for each pair of phases).
- Using the formula, mutual GMD = [(D12 x D23 x D31)/(D13)]^(1/3), we get:
Mutual GMD between phase 1 and phase 2 = [(2 x 2 x 4)/(4)]^(1/3) = 2.154
Mutual GMD between phase 2 and phase 3 = [(2 x 2 x 4)/(4)]^(1/3) = 2.154
Mutual GMD between phase 3 and phase 1 = [(4 x 2 x 4)/(4)]^(1/3) = 2.828
3. Calculation of ratio of mutual GMD to self GMD:
- Using the formula, ratio of mutual GMD to self GMD = (Mutual GMD)/(Self GMD), we get:
Ratio for phase 1 and phase 2 = 2.154/3.162 = 0.681
Ratio for phase 2 and phase 3 = 2.154/2.466 = 0.873
Ratio for phase 3 and phase 1 = 2.828/3.162 = 0.894
- Taking the average of the ratios, we get:
Average ratio = (0.681 + 0.873 + 0.894)/3 = 0.816
Therefore, the ratio of mutual GMD to self GMD is 0.816, which is closest to option 'B' (258.84).
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In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. Can you explain this answer?
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In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. 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 In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. Can you explain this answer?.
In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. 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 In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a 3 phase, 3 wire system the conductors are arranged in a horizontal plane with spacing D13 = 4m, D12=2m=D23. Conductors are transposed having diameter of 2.5cm. The ratio of mutual GMD to self GMD =?a)356.42b)258.84c)232.24d)156.32Correct answer is option 'B'. Can you explain this answer?.
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