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A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.
What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)
Correct answer is '0.0377'. Can you explain this answer?
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A single-phase 60 Hz power line is supported on a horizontal cross-ar...
Given data:
- Power line frequency: 60 Hz
- Spacing between power line conductors: 2.5 m
- Spacing between telephone line conductors: 0.6 m
- Distance between nearest conductors of both lines: 20 m
- Current flowing in the power line: 150 A
Step 1: Calculate the magnetic field induced by the power line at the location of the telephone line.
The magnetic field induced by a current-carrying conductor can be calculated using Ampere's Law:
B = (μ₀ * I) / (2π * r)
Where:
B = Magnetic field strength
μ₀ = Permeability of free space (4π × 10^-7 T*m/A)
I = Current in the power line
r = Distance from the power line conductor to the point of interest
Considering a single power line conductor, the distance from the power line conductor to the nearest telephone line conductor is 10 m (half of the given distance of 20 m). Therefore, the magnetic field at the location of the telephone line conductor is:
B = (4π × 10^-7 T*m/A * 150 A) / (2π * 10 m)
B = 3 × 10^-6 T
Step 2: Calculate the magnetic flux through the telephone line loop.
The magnetic flux through a loop can be calculated using Faraday's Law of electromagnetic induction:
Φ = B * A
Where:
Φ = Magnetic flux
B = Magnetic field strength
A = Area of the loop
The area of the telephone line loop can be calculated as follows:
- The spacing between telephone line conductors is 0.6 m.
- The length of the telephone line loop is equal to the spacing between power line conductors, which is 2.5 m.
- The height of the telephone line loop can be considered negligible.
Therefore, the area of the telephone line loop is:
A = 0.6 m * 2.5 m
A = 1.5 m²
Thus, the magnetic flux through the telephone line loop is:
Φ = 3 × 10^-6 T * 1.5 m²
Φ = 4.5 × 10^-6 Wb
Step 3: Calculate the voltage induced in the telephone line loop.
The voltage induced in a loop can be calculated using Faraday's Law of electromagnetic induction:
V = N * dΦ/dt
Where:
V = Induced voltage
N = Number of turns in the loop
dΦ/dt = Rate of change of magnetic flux
Since there is only one telephone line conductor, the number of turns in the loop is considered as 1.
The rate of change of magnetic flux can be calculated by considering the time period of one cycle at the power line frequency:
dt = 1 / f
dt = 1 / 60 s
Therefore, the rate of change of magnetic flux is:
dΦ/dt = 4.5 × 10^-6 Wb / (1 / 60 s)
dΦ/dt = 2.7 × 10^-4 Wb/s
Thus, the induced voltage in the telephone line loop is:
V = 1 * 2.7 × 10
- Power line frequency: 60 Hz
- Spacing between power line conductors: 2.5 m
- Spacing between telephone line conductors: 0.6 m
- Distance between nearest conductors of both lines: 20 m
- Current flowing in the power line: 150 A
Step 1: Calculate the magnetic field induced by the power line at the location of the telephone line.
The magnetic field induced by a current-carrying conductor can be calculated using Ampere's Law:
B = (μ₀ * I) / (2π * r)
Where:
B = Magnetic field strength
μ₀ = Permeability of free space (4π × 10^-7 T*m/A)
I = Current in the power line
r = Distance from the power line conductor to the point of interest
Considering a single power line conductor, the distance from the power line conductor to the nearest telephone line conductor is 10 m (half of the given distance of 20 m). Therefore, the magnetic field at the location of the telephone line conductor is:
B = (4π × 10^-7 T*m/A * 150 A) / (2π * 10 m)
B = 3 × 10^-6 T
Step 2: Calculate the magnetic flux through the telephone line loop.
The magnetic flux through a loop can be calculated using Faraday's Law of electromagnetic induction:
Φ = B * A
Where:
Φ = Magnetic flux
B = Magnetic field strength
A = Area of the loop
The area of the telephone line loop can be calculated as follows:
- The spacing between telephone line conductors is 0.6 m.
- The length of the telephone line loop is equal to the spacing between power line conductors, which is 2.5 m.
- The height of the telephone line loop can be considered negligible.
Therefore, the area of the telephone line loop is:
A = 0.6 m * 2.5 m
A = 1.5 m²
Thus, the magnetic flux through the telephone line loop is:
Φ = 3 × 10^-6 T * 1.5 m²
Φ = 4.5 × 10^-6 Wb
Step 3: Calculate the voltage induced in the telephone line loop.
The voltage induced in a loop can be calculated using Faraday's Law of electromagnetic induction:
V = N * dΦ/dt
Where:
V = Induced voltage
N = Number of turns in the loop
dΦ/dt = Rate of change of magnetic flux
Since there is only one telephone line conductor, the number of turns in the loop is considered as 1.
The rate of change of magnetic flux can be calculated by considering the time period of one cycle at the power line frequency:
dt = 1 / f
dt = 1 / 60 s
Therefore, the rate of change of magnetic flux is:
dΦ/dt = 4.5 × 10^-6 Wb / (1 / 60 s)
dΦ/dt = 2.7 × 10^-4 Wb/s
Thus, the induced voltage in the telephone line loop is:
V = 1 * 2.7 × 10
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Community Answer
A single-phase 60 Hz power line is supported on a horizontal cross-ar...
Induced voltage in telephone line = 377 x 0.01 x 10-5 x 103
= 0.0377 V/km
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A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer?
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A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. 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 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. 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 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer?.
A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. 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 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. 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 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer?.
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A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer?, a detailed solution for A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer? has been provided alongside types of A single-phase 60 Hz power line is supported on a horizontal cross-arm. The spacing between conductors is 2.5 m. A telephone line is also supported on a horizontal cross-arm in the same horizontal plane as the power line. The conductors of the telephone line are of solid copper spaced 0.6 m between centres. The distance between the nearest conductors of the two lines is 20 m. A current of 150 A is flowing over the power line.What is the value of voltage per kilometre induced in the telephone line? (Answer up to four decimal places)Correct answer is '0.0377'. Can you explain this answer? theory, EduRev gives you an
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