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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?
    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
    Let R be the resistance of one conductor.
    Line losses = 2I2R
    ⇒27.78 × 10= 2(83.33)2R
    ⇒ R = 2 Ω

    = 8 km
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    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.
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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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