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The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10−12 . The capacitance to ground per kilometer of each line is
- a)4.2 × 10-9F
- b)8.4 × 10-9F
- c)4.2 × 10-12F
- d)8.4 × 10-12F
Correct answer is option 'B'. Can you explain this answer?
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× 10^-12 F/m.
To find the capacitance per unit length (C), we can use the formula:
C = (2πε) / ln(D/d)
Where:
- C is the capacitance per unit length
- ε is the permittivity of free space
- D is the outside diameter of the conductors
- d is the spacing between centers of the conductors
Plugging in the given values:
C = (2π * 8.854 × 10^-12 F/m) / ln(0.016 m / 6 m)
Simplifying the expression:
C = (2π * 8.854 × 10^-12 F/m) / ln(0.0026667)
Using ln(0.0026667) = -5.926, we get:
C = (2π * 8.854 × 10^-12 F/m) / -5.926
Calculating:
C ≈ - (2π * 8.854 × 10^-12 F/m) / 5.926
C ≈ -2.984 × 10^-11 F/m
Therefore, the capacitance per unit length of the single phase line is approximately -2.984 × 10^-11 F/m.
To find the capacitance per unit length (C), we can use the formula:
C = (2πε) / ln(D/d)
Where:
- C is the capacitance per unit length
- ε is the permittivity of free space
- D is the outside diameter of the conductors
- d is the spacing between centers of the conductors
Plugging in the given values:
C = (2π * 8.854 × 10^-12 F/m) / ln(0.016 m / 6 m)
Simplifying the expression:
C = (2π * 8.854 × 10^-12 F/m) / ln(0.0026667)
Using ln(0.0026667) = -5.926, we get:
C = (2π * 8.854 × 10^-12 F/m) / -5.926
Calculating:
C ≈ - (2π * 8.854 × 10^-12 F/m) / 5.926
C ≈ -2.984 × 10^-11 F/m
Therefore, the capacitance per unit length of the single phase line is approximately -2.984 × 10^-11 F/m.
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The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10−12 . The capacitance to ground per kilometer of each line isa)4.2 × 10-9Fb)8.4 × 10-9Fc)4.2 × 10-12Fd)8.4 × 10-12FCorrect answer is option 'B'. Can you explain this answer?
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The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10−12 . The capacitance to ground per kilometer of each line isa)4.2 × 10-9Fb)8.4 × 10-9Fc)4.2 × 10-12Fd)8.4 × 10-12FCorrect 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 The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10−12 . The capacitance to ground per kilometer of each line isa)4.2 × 10-9Fb)8.4 × 10-9Fc)4.2 × 10-12Fd)8.4 × 10-12FCorrect 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 The horizontally placed conductors of a single phase line operating at 50 Hz are havingoutside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854×10−12 . The capacitance to ground per kilometer of each line isa)4.2 × 10-9Fb)8.4 × 10-9Fc)4.2 × 10-12Fd)8.4 × 10-12FCorrect answer is option 'B'. Can you explain this answer?.
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