Power Factor using Area of X-Section(3-Phase 4-Wire OS) Solution

STEP 0: Pre-Calculation Summary
Formula Used
Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire))
PF = (P/Vm)*sqrt(2*ρ*L/(3*A))
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Power Factor - The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit.
Power Transmitted - (Measured in Watt) - Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end.
Maximum Voltage Overhead AC - (Measured in Volt) - Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire.
Resistivity - (Measured in Ohm Meter) - Resistivity is the measure of how strongly a material opposes the flow of current through them.
Length of Overhead AC Wire - (Measured in Meter) - Length of Overhead AC Wire is the total length of the wire from one end to other end.
Area of Overhead AC Wire - (Measured in Square Meter) - Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.
STEP 1: Convert Input(s) to Base Unit
Power Transmitted: 890 Watt --> 890 Watt No Conversion Required
Maximum Voltage Overhead AC: 62 Volt --> 62 Volt No Conversion Required
Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Length of Overhead AC Wire: 10.63 Meter --> 10.63 Meter No Conversion Required
Area of Overhead AC Wire: 0.79 Square Meter --> 0.79 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PF = (P/Vm)*sqrt(2*ρ*L/(3*A)) --> (890/62)*sqrt(2*1.7E-05*10.63/(3*0.79))
Evaluating ... ...
PF = 0.177267955125567
STEP 3: Convert Result to Output's Unit
0.177267955125567 --> No Conversion Required
FINAL ANSWER
0.177267955125567 0.177268 <-- Power Factor
(Calculation completed in 00.004 seconds)

Credits

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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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10+ Power & Power Factor Calculators

Power Transmitted using Area of X-Section(3-Phase 4-Wire OS)
Go Power Transmitted = sqrt((3*Area of Overhead AC Wire*(Maximum Voltage Overhead AC^2)*Line Losses*((cos(Phase Difference))^2))/(Resistivity*2*Length of Overhead AC Wire))
Angle of PF using Area of X-Section(3-Phase 4-Wire OS)
Go Phase Difference = acos(sqrt(2*Resistivity*Length of Overhead AC Wire*(Power Transmitted^2)/(3*Area of Overhead AC Wire*Line Losses*(Maximum Voltage Overhead AC^2))))
Power Transmitted using Volume of Conductor Material (3-Phase 4-Wire OS)
Go Power Transmitted = sqrt(3*Line Losses*Volume of Conductor*(Maximum Voltage Overhead AC*cos(Phase Difference))^2/(7*Resistivity*(Length of Overhead AC Wire)^2))
Power Factor using Area of X-Section(3-Phase 4-Wire OS)
Go Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire))
Power Transmitted using Load Current (3-Phase 4-Wire OS)
Go Power Transmitted = Current Overhead AC*Maximum Voltage Overhead AC*cos(Phase Difference)*(3/sqrt(2))
Angle of PF using Load Current (3-Phase 4-Wire OS)
Go Phase Difference = (sqrt(2)*Power Transmitted)/(3*Maximum Voltage Overhead AC*Current Overhead AC)
Angle of PF using Volume of Conductor Material (3-Phase 4-Wire OS)
Go Phase Difference = acos(sqrt((0.583)*Constant Overhead AC/Volume of Conductor))
Power Factor using Load Current (3-Phase 4-Wire OS)
Go Power Factor = (sqrt(2)*Power Transmitted)/(3*Maximum Voltage Overhead AC)
Power Factor using Volume of Conductor Material (3-Phase 4-Wire OS)
Go Power Factor = sqrt((0.583)*Constant Overhead AC/Volume of Conductor)
Power Transmitted(3-Phase 4-Wire OS)
Go Power Transmitted = (1/3)*Power Transmitted per Phase

Power Factor using Area of X-Section(3-Phase 4-Wire OS) Formula

Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire))
PF = (P/Vm)*sqrt(2*ρ*L/(3*A))

Why do we use 3 phase 4 wire?

The function of neutral wire in the 3 phase 4 wire system is to serve as a return wire for the general domestic supply system. The neutral is paired to each of the single-phase loads.

How to Calculate Power Factor using Area of X-Section(3-Phase 4-Wire OS)?

Power Factor using Area of X-Section(3-Phase 4-Wire OS) calculator uses Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire)) to calculate the Power Factor, The Power Factor using Area of X-section(3-phase 4-wire OS) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit. Power Factor is denoted by PF symbol.

How to calculate Power Factor using Area of X-Section(3-Phase 4-Wire OS) using this online calculator? To use this online calculator for Power Factor using Area of X-Section(3-Phase 4-Wire OS), enter Power Transmitted (P), Maximum Voltage Overhead AC (Vm), Resistivity (ρ), Length of Overhead AC Wire (L) & Area of Overhead AC Wire (A) and hit the calculate button. Here is how the Power Factor using Area of X-Section(3-Phase 4-Wire OS) calculation can be explained with given input values -> 0.177268 = (890/62)*sqrt(2*1.7E-05*10.63/(3*0.79)).

FAQ

What is Power Factor using Area of X-Section(3-Phase 4-Wire OS)?
The Power Factor using Area of X-section(3-phase 4-wire OS) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit and is represented as PF = (P/Vm)*sqrt(2*ρ*L/(3*A)) or Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire)). Power Transmitted is defined as the product of current and voltage phasor in a overhead ac line at the receiving end, Maximum Voltage Overhead AC is defined as the peak amplitude of the AC voltage supplied to the line or wire, Resistivity is the measure of how strongly a material opposes the flow of current through them, Length of Overhead AC Wire is the total length of the wire from one end to other end & Area of Overhead AC Wire is defined as the cross-sectional area of the wire of an AC supply system.
How to calculate Power Factor using Area of X-Section(3-Phase 4-Wire OS)?
The Power Factor using Area of X-section(3-phase 4-wire OS) formula is defined as the cosine of the angle between the voltage phasor and current phasor in an AC circuit is calculated using Power Factor = (Power Transmitted/Maximum Voltage Overhead AC)*sqrt(2*Resistivity*Length of Overhead AC Wire/(3*Area of Overhead AC Wire)). To calculate Power Factor using Area of X-Section(3-Phase 4-Wire OS), you need Power Transmitted (P), Maximum Voltage Overhead AC (Vm), Resistivity (ρ), Length of Overhead AC Wire (L) & Area of Overhead AC Wire (A). With our tool, you need to enter the respective value for Power Transmitted, Maximum Voltage Overhead AC, Resistivity, Length of Overhead AC Wire & Area of Overhead AC Wire and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Power Factor?
In this formula, Power Factor uses Power Transmitted, Maximum Voltage Overhead AC, Resistivity, Length of Overhead AC Wire & Area of Overhead AC Wire. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Power Factor = sqrt((0.583)*Constant Overhead AC/Volume of Conductor)
  • Power Factor = (sqrt(2)*Power Transmitted)/(3*Maximum Voltage Overhead AC)
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