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Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit length
- a)doubles
- b)halves
- c)increase but does not double
- d)decreases but does not halve
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider a long two wire line composed of solid round-conductors. The ...
Inductance per wait length = 
μ = Permeability of material
D = Distance between their
cont res
r = Effective radius
L α lo D
If D is double, 1 will increase but does not double.
D = Distance between their
cont res
r = Effective radius
L α lo D
If D is double, 1 will increase but does not double.
Most Upvoted Answer
Consider a long two wire line composed of solid round-conductors. The ...
Explanation:
Inductance per unit length of a long two-wire line can be given by the formula:
L = (μ/8π) * [(2πd) / ln(b/a)]
Where,
μ = permeability of free space
d = distance between the two conductors
a = radius of each conductor
b = distance between the centres of the conductors
Given that the radius of both conductors is 0.20 cm and the distance between their centres is 2m.
Thus, a = 0.20 cm = 0.002 m
b = 2 m
d = b - 2a = 1.996 m
Using the above formula, we can calculate the inductance per unit length to be:
L = (4π × 10^-7 / 8π) * [(2π × 1.996) / ln(2.002/0.002)]
L = 2.00 × 10^-7 H/m
Now if the distance between the centres of the conductors is doubled i.e. b = 4 m, then d = 3.996 m.
Using the same formula, we can calculate the inductance per unit length to be:
L' = (4π × 10^-7 / 8π) * [(2π × 3.996) / ln(4.002/0.002)]
L' = 2.58 × 10^-7 H/m
Comparing L and L', we can see that the inductance per unit length has increased but not doubled. Therefore, option (c) is the correct answer.
Reasoning:
The inductance of a two-wire line is dependent on the distance between the two conductors. When the distance between the centres of the conductors is increased, the inductance per unit length increases as well. However, the increase is not proportional to the increase in distance. This is because the inductance also depends on the natural logarithm of the ratio of the distance between the centres of the conductors to the radius of the conductors. Therefore, doubling the distance between the centres of the conductors will not result in a doubling of the inductance per unit length.
Inductance per unit length of a long two-wire line can be given by the formula:
L = (μ/8π) * [(2πd) / ln(b/a)]
Where,
μ = permeability of free space
d = distance between the two conductors
a = radius of each conductor
b = distance between the centres of the conductors
Given that the radius of both conductors is 0.20 cm and the distance between their centres is 2m.
Thus, a = 0.20 cm = 0.002 m
b = 2 m
d = b - 2a = 1.996 m
Using the above formula, we can calculate the inductance per unit length to be:
L = (4π × 10^-7 / 8π) * [(2π × 1.996) / ln(2.002/0.002)]
L = 2.00 × 10^-7 H/m
Now if the distance between the centres of the conductors is doubled i.e. b = 4 m, then d = 3.996 m.
Using the same formula, we can calculate the inductance per unit length to be:
L' = (4π × 10^-7 / 8π) * [(2π × 3.996) / ln(4.002/0.002)]
L' = 2.58 × 10^-7 H/m
Comparing L and L', we can see that the inductance per unit length has increased but not doubled. Therefore, option (c) is the correct answer.
Reasoning:
The inductance of a two-wire line is dependent on the distance between the two conductors. When the distance between the centres of the conductors is increased, the inductance per unit length increases as well. However, the increase is not proportional to the increase in distance. This is because the inductance also depends on the natural logarithm of the ratio of the distance between the centres of the conductors to the radius of the conductors. Therefore, doubling the distance between the centres of the conductors will not result in a doubling of the inductance per unit length.
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Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer?
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Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. 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 Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer?.
Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. 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 Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer?.
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Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider a long two wire line composed of solid round-conductors. The radius of bot h conductors is 0.20 cm and the distance between their centres is 2m. If this distance is doubled, t hen the inductance per unit lengtha)doublesb)halvesc)increase but does not doubled)decreases but does not halveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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