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A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.
Correct answer is '48'. Can you explain this answer?
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Verified Answer
A three-phase cable is supplying 800 kW and 600 kVAr to an inductive l...
Initial load = (800 + j600)
load after modification = (900 + j600) to maintain same heat dissipation magnitude of power should be same
Load with compensation = (900 + j 600 + Compensation) = 900 + jx)
Equating magnitude of power= 8002 + 6002 = 9002 + x2
load after modification = (900 + j600) to maintain same heat dissipation magnitude of power should be same
Load with compensation = (900 + j 600 + Compensation) = 900 + jx)
Equating magnitude of power= 8002 + 6002 = 9002 + x2
Reactive power to be compensated by capacitor to achieve this is 164.11 kVAr
Most Upvoted Answer
A three-phase cable is supplying 800 kW and 600 kVAr to an inductive l...
Given Data:
- Three-phase cable is supplying 800 kW and 600 kVAr to an inductive load.
- The line voltage is 3.3 kV and the frequency is 50 Hz.
- An additional resistive load of 100 kW needs to be supplied without increasing the heat dissipation in the cable.
Approach:
To supply the additional resistive load without increasing the heat dissipation in the cable, a three-phase bank of capacitors connected in star across the load can be used. The capacitors will compensate for the reactive power demand of the inductive load, resulting in a balanced power factor and reduced heat dissipation in the cable.
Calculating the Power Factor:
To calculate the required capacitance per phase of the bank, we first need to calculate the power factor of the existing inductive load.
Given,
Active power (P) = 800 kW
Reactive power (Q) = 600 kVAr
Using the formula:
Apparent power (S) = √(P^2 + Q^2)
We can calculate the apparent power as:
S = √(800^2 + 600^2)
S ≈ 1000 kVA
The power factor (PF) can be calculated as:
PF = P / S
PF = 800 kW / 1000 kVA
PF = 0.8
Calculating the Reactive Power of the Resistive Load:
Since the additional load is resistive, it does not have a reactive power component. Therefore, the reactive power of the resistive load is zero.
Calculating the Required Capacitive Reactive Power:
To compensate for the reactive power demand of the inductive load and achieve a balanced power factor, the capacitive reactive power to be supplied by the bank can be calculated as:
Qc = Qinductive - Qresistive
Qc = 600 kVAr - 0 kVAr
Qc = 600 kVAr
Calculating the Capacitance per Phase:
The reactive power (Qc) can be calculated using the formula:
Qc = √3 * Vline * Iline * Xc
Where,
Vline = Line voltage = 3.3 kV
Iline = Line current
Xc = Capacitive reactance per phase
The line current (Iline) can be calculated as:
Iline = S / Vline
Iline = 1000 kVA / 3.3 kV
Iline ≈ 303.03 A
The capacitive reactance per phase (Xc) can be calculated using the formula:
Xc = Vline / Iline
Xc = 3.3 kV / 303.03 A
Xc ≈ 10.89 Ω
The capacitance per phase (C) can be calculated using the formula:
C = 1 / (2πfXc)
Where,
f = Frequency = 50 Hz
C = 1 / (2π * 50 Hz * 10.89 Ω)
C ≈ 0.000029 F
Converting capacitance to microfarads:
C_microfarads = C * 10^6
C_microfarads ≈ 29 μF
Final
- Three-phase cable is supplying 800 kW and 600 kVAr to an inductive load.
- The line voltage is 3.3 kV and the frequency is 50 Hz.
- An additional resistive load of 100 kW needs to be supplied without increasing the heat dissipation in the cable.
Approach:
To supply the additional resistive load without increasing the heat dissipation in the cable, a three-phase bank of capacitors connected in star across the load can be used. The capacitors will compensate for the reactive power demand of the inductive load, resulting in a balanced power factor and reduced heat dissipation in the cable.
Calculating the Power Factor:
To calculate the required capacitance per phase of the bank, we first need to calculate the power factor of the existing inductive load.
Given,
Active power (P) = 800 kW
Reactive power (Q) = 600 kVAr
Using the formula:
Apparent power (S) = √(P^2 + Q^2)
We can calculate the apparent power as:
S = √(800^2 + 600^2)
S ≈ 1000 kVA
The power factor (PF) can be calculated as:
PF = P / S
PF = 800 kW / 1000 kVA
PF = 0.8
Calculating the Reactive Power of the Resistive Load:
Since the additional load is resistive, it does not have a reactive power component. Therefore, the reactive power of the resistive load is zero.
Calculating the Required Capacitive Reactive Power:
To compensate for the reactive power demand of the inductive load and achieve a balanced power factor, the capacitive reactive power to be supplied by the bank can be calculated as:
Qc = Qinductive - Qresistive
Qc = 600 kVAr - 0 kVAr
Qc = 600 kVAr
Calculating the Capacitance per Phase:
The reactive power (Qc) can be calculated using the formula:
Qc = √3 * Vline * Iline * Xc
Where,
Vline = Line voltage = 3.3 kV
Iline = Line current
Xc = Capacitive reactance per phase
The line current (Iline) can be calculated as:
Iline = S / Vline
Iline = 1000 kVA / 3.3 kV
Iline ≈ 303.03 A
The capacitive reactance per phase (Xc) can be calculated using the formula:
Xc = Vline / Iline
Xc = 3.3 kV / 303.03 A
Xc ≈ 10.89 Ω
The capacitance per phase (C) can be calculated using the formula:
C = 1 / (2πfXc)
Where,
f = Frequency = 50 Hz
C = 1 / (2π * 50 Hz * 10.89 Ω)
C ≈ 0.000029 F
Converting capacitance to microfarads:
C_microfarads = C * 10^6
C_microfarads ≈ 29 μF
Final
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A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer?
Question Description
A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer?.
A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to supply an additional resistive load of 100 kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is 3.3 kV, 50 Hz the capacitance per phase of the bank expressed in microfarads, is _______________.Correct answer is '48'. Can you explain this answer?.
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