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A 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 kW at 0.8 pf lagging over 10 km. Resistance and reactance of each line conductor may be assumed to be0.5Ω/km and 0.56 Ω/km respectively. Efficiency of line in percentage is _______________. (Correct upto 2 decimal place)
Correct answer is '93'. Can you explain this answer?
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A 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 ...
Given data:
- Transmission line is 3-phase and operates at 50 Hz.
- Voltage level is 11 kV.
- Load is 1000 kW with a power factor of 0.8 lagging.
- The length of the transmission line is 10 km.
- The resistance and reactance of each line conductor are 0.5 Ω/km and 0.56 Ω/km respectively.
To find:
Efficiency of the line in percentage.
Calculations:
Step 1: Calculate the total line resistance and reactance
Total resistance of the transmission line = Resistance per km x Length of the line = 0.5 Ω/km x 10 km = 5 Ω
Total reactance of the transmission line = Reactance per km x Length of the line = 0.56 Ω/km x 10 km = 5.6 Ω
Step 2: Calculate the total line impedance
The total line impedance (Z) can be calculated using the resistance and reactance as follows:
Z = √(Resistance^2 + Reactance^2)
Z = √(5^2 + 5.6^2) = √(25 + 31.36) = √56.36 = 7.51 Ω
Step 3: Calculate the total line current
The total line current (I) can be calculated using the load power and voltage as follows:
I = P / (√3 x V x Power factor)
I = 1000 kW / (√3 x 11 kV x 0.8) = 1000 / (1.732 x 11 x 0.8) = 61.62 A
Step 4: Calculate the line losses
The line losses (Ploss) can be calculated using the formula:
Ploss = 3 x I^2 x R
Ploss = 3 x (61.62 A)^2 x 5 Ω = 56821.5 W = 56.82 kW
Step 5: Calculate the delivered power
The delivered power can be calculated by subtracting the line losses from the load power:
Delivered power = Load power - Line losses = 1000 kW - 56.82 kW = 943.18 kW
Step 6: Calculate the efficiency
Efficiency = (Delivered power / Load power) x 100
Efficiency = (943.18 kW / 1000 kW) x 100 = 94.32%
Result:
The efficiency of the transmission line is 94.32%, which can be approximated to 94% when rounded to the nearest whole number.
- Transmission line is 3-phase and operates at 50 Hz.
- Voltage level is 11 kV.
- Load is 1000 kW with a power factor of 0.8 lagging.
- The length of the transmission line is 10 km.
- The resistance and reactance of each line conductor are 0.5 Ω/km and 0.56 Ω/km respectively.
To find:
Efficiency of the line in percentage.
Calculations:
Step 1: Calculate the total line resistance and reactance
Total resistance of the transmission line = Resistance per km x Length of the line = 0.5 Ω/km x 10 km = 5 Ω
Total reactance of the transmission line = Reactance per km x Length of the line = 0.56 Ω/km x 10 km = 5.6 Ω
Step 2: Calculate the total line impedance
The total line impedance (Z) can be calculated using the resistance and reactance as follows:
Z = √(Resistance^2 + Reactance^2)
Z = √(5^2 + 5.6^2) = √(25 + 31.36) = √56.36 = 7.51 Ω
Step 3: Calculate the total line current
The total line current (I) can be calculated using the load power and voltage as follows:
I = P / (√3 x V x Power factor)
I = 1000 kW / (√3 x 11 kV x 0.8) = 1000 / (1.732 x 11 x 0.8) = 61.62 A
Step 4: Calculate the line losses
The line losses (Ploss) can be calculated using the formula:
Ploss = 3 x I^2 x R
Ploss = 3 x (61.62 A)^2 x 5 Ω = 56821.5 W = 56.82 kW
Step 5: Calculate the delivered power
The delivered power can be calculated by subtracting the line losses from the load power:
Delivered power = Load power - Line losses = 1000 kW - 56.82 kW = 943.18 kW
Step 6: Calculate the efficiency
Efficiency = (Delivered power / Load power) x 100
Efficiency = (943.18 kW / 1000 kW) x 100 = 94.32%
Result:
The efficiency of the transmission line is 94.32%, which can be approximated to 94% when rounded to the nearest whole number.
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A 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 kW at 0.8 pf lagging over 10 km. Resistance and reactance of each line conductor may be assumed to be0.5Ω/km and 0.56 Ω/km respectively. Efficiency of line in percentage is _______________. (Correct upto 2 decimal place)Correct answer is '93'. Can you explain this answer?
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A 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 kW at 0.8 pf lagging over 10 km. Resistance and reactance of each line conductor may be assumed to be0.5Ω/km and 0.56 Ω/km respectively. Efficiency of line in percentage is _______________. (Correct upto 2 decimal place)Correct answer is '93'. 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 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 kW at 0.8 pf lagging over 10 km. Resistance and reactance of each line conductor may be assumed to be0.5Ω/km and 0.56 Ω/km respectively. Efficiency of line in percentage is _______________. (Correct upto 2 decimal place)Correct answer is '93'. 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 3-phase, 50 Hz transmission line at 11 kV delivers at load of 1000 kW at 0.8 pf lagging over 10 km. Resistance and reactance of each line conductor may be assumed to be0.5Ω/km and 0.56 Ω/km respectively. Efficiency of line in percentage is _______________. (Correct upto 2 decimal place)Correct answer is '93'. Can you explain this answer?.
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