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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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