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What is the maximum length (in km) for a single phase transmission line having a copper conductor of 0.8 cm2 cross-section over which 250 kW at unity power factor and at 3 kV are to be delivered?
The efficiency of transmission is 90%. The specific resistance as 2 μΩ-cm.
Correct answer is between '7,9'. Can you explain this answer?
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Verified Answer
What is the maximum length (in km) for a single phase transmission lin...
Receiving end power = 250 kW
Efficiency of transmission = 90%
Sending end power =
Line losses = 277.78− 250 = 27.78kW
Line current, I
Sending end power =
Line losses = 277.78− 250 = 27.78kW
Line current, I
Let R be the resistance of one conductor.
Line losses = 2I2R
⇒27.78 × 103 = 2(83.33)2R
⇒ R = 2 Ω
= 8 km
⇒27.78 × 103 = 2(83.33)2R
⇒ R = 2 Ω
= 8 km
Most Upvoted Answer
What is the maximum length (in km) for a single phase transmission lin...
The maximum length of a single phase transmission line can be calculated using the formula:
L = (P * V^2) / (I^2 * R * η)
where:
L is the maximum length of the transmission line
P is the power to be delivered (in watts) - 250 kW or 250,000 W
V is the voltage (in volts) - 3 kV or 3000 V
I is the current (in amperes) - calculated using P and V as I = P / V
R is the specific resistance of the copper conductor (in ohms/km) - given as 2 ohms/km
η is the efficiency of transmission (in decimal form) - given as 0.9
First, calculate the current (I):
I = P / V
I = 250,000 W / 3000 V
I ≈ 83.33 A
Now, substitute the values into the formula:
L = (250,000 * (3000)^2) / ((83.33)^2 * 2 * 0.9)
L = (250,000 * 9,000,000) / (6,944.44 * 2 * 0.9)
L = 2,250,000,000,000 / 12,499,999.6
L ≈ 180,000 km
Therefore, the maximum length of the single phase transmission line is approximately 180,000 km.
L = (P * V^2) / (I^2 * R * η)
where:
L is the maximum length of the transmission line
P is the power to be delivered (in watts) - 250 kW or 250,000 W
V is the voltage (in volts) - 3 kV or 3000 V
I is the current (in amperes) - calculated using P and V as I = P / V
R is the specific resistance of the copper conductor (in ohms/km) - given as 2 ohms/km
η is the efficiency of transmission (in decimal form) - given as 0.9
First, calculate the current (I):
I = P / V
I = 250,000 W / 3000 V
I ≈ 83.33 A
Now, substitute the values into the formula:
L = (250,000 * (3000)^2) / ((83.33)^2 * 2 * 0.9)
L = (250,000 * 9,000,000) / (6,944.44 * 2 * 0.9)
L = 2,250,000,000,000 / 12,499,999.6
L ≈ 180,000 km
Therefore, the maximum length of the single phase transmission line is approximately 180,000 km.
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What is the maximum length (in km) for a single phase transmission line having a copper conductor of 0.8 cm2cross-section over which 250 kW at unity power factor and at 3 kV are to be delivered?The efficiency of transmission is 90%. The specific resistance as 2 μΩ-cm.Correct answer is between '7,9'. Can you explain this answer?
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What is the maximum length (in km) for a single phase transmission line having a copper conductor of 0.8 cm2cross-section over which 250 kW at unity power factor and at 3 kV are to be delivered?The efficiency of transmission is 90%. The specific resistance as 2 μΩ-cm.Correct answer is between '7,9'. 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 What is the maximum length (in km) for a single phase transmission line having a copper conductor of 0.8 cm2cross-section over which 250 kW at unity power factor and at 3 kV are to be delivered?The efficiency of transmission is 90%. The specific resistance as 2 μΩ-cm.Correct answer is between '7,9'. 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 What is the maximum length (in km) for a single phase transmission line having a copper conductor of 0.8 cm2cross-section over which 250 kW at unity power factor and at 3 kV are to be delivered?The efficiency of transmission is 90%. The specific resistance as 2 μΩ-cm.Correct answer is between '7,9'. Can you explain this answer?.
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