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## Credits

Vishwakarma Government Engineering College (VGEC), Ahmedabad
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## Angle Of PF Using Area Of X-section(3-phase 4-wire OS) Solution

STEP 0: Pre-Calculation Summary
Formula Used
theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2))))
ϑ = acos(sqrt(2*ρ*l*(P^2)/(3*a10*W*(Vm^2))))
This formula uses 3 Functions, 6 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
acos - Inverse trigonometric cosine function, acos(Number)
sqrt - Squre root function, sqrt(Number)
Variables Used
Resistivity - Resistivity is the measure of how strongly a material opposes the flow of current through them. (Measured in Ohm Meter)
Length - Length is the measurement or extent of something from end to end. (Measured in Meter)
Power Transmitted - The Power Transmitted Value through a shaft. (Measured in Watt)
Area Of 3-Φ 4-wire system - The Area Of 3-Φ 4-wire system is the amount of two-dimensional space taken up by an object. (Measured in Square Meter)
Line Losses - Line Losses is defined as the losses that are produced in the line. (Measured in Watt)
Maximum Voltage - Maximum Voltage the highest voltage rating for electrical devices (Measured in Volt)
STEP 1: Convert Input(s) to Base Unit
Resistivity: 1.7E-05 Ohm Meter --> 1.7E-05 Ohm Meter No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required
Power Transmitted: 10 Watt --> 10 Watt No Conversion Required
Area Of 3-Φ 4-wire system: 10 Square Meter --> 10 Square Meter No Conversion Required
Line Losses: 0.6 Watt --> 0.6 Watt No Conversion Required
Maximum Voltage: 60 Volt --> 60 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ϑ = acos(sqrt(2*ρ*l*(P^2)/(3*a10*W*(Vm^2)))) --> acos(sqrt(2*1.7E-05*3*(10^2)/(3*10*0.6*(60^2))))
Evaluating ... ...
ϑ = 1.57039958076068
STEP 3: Convert Result to Output's Unit
1.57039958076068 Radian -->89.9772681267178 Degree (Check conversion here)
89.9772681267178 Degree <-- Theta
(Calculation completed in 00.025 seconds)

## < 8 Area Of X-Section Calculators

Power Transmitted Using Area Of X-section(3-phase 4-wire OS)
power_transmitted = sqrt((3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2))/(Resistivity*2*Length)) Go
Maximum Voltage Using Area Of X-section(3-phase 4-wire OS)
maximum_voltage = sqrt((2*Length*Resistivity*(Power Transmitted^2))/(3*Area Of 3-Φ 4-wire system*Line Losses*((cos(Theta))^2))) Go
Angle Of PF Using Area Of X-section(3-phase 4-wire OS)
theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2)))) Go
Line Losses Using Area Of X-section(3-phase 4-wire OS)
line_losses = (2*Length*Resistivity*(Power Transmitted^2))/(3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*((cos(Theta))^2)) Go
Length Of Wire Using Area Of X-section(3-phase 4-wire OS)
length = 3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2)/(2*Resistivity*(Power Transmitted^2)) Go
Resistivity Using Area Of X-section(3-phase 4-wire OS)
resistivity = 3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2)/(2*Length*(Power Transmitted^2)) Go
RMS Voltage Using Area Of X-section(3-phase 4-wire OS)
rms_voltage = (Power Transmitted/cos(Theta))*sqrt(Resistivity*Length/(3*Area Of 3-Φ 4-wire system)) Go
Power Factor Using Area Of X-section(3-phase 4-wire OS)
power_factor = (Power Transmitted/Maximum Voltage)*sqrt(2*Resistivity*Length/(3*Area Of 3-Φ 4-wire system)) Go

### Angle Of PF Using Area Of X-section(3-phase 4-wire OS) Formula

theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2))))
ϑ = acos(sqrt(2*ρ*l*(P^2)/(3*a10*W*(Vm^2))))

## 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 Angle Of PF Using Area Of X-section(3-phase 4-wire OS)?

Angle Of PF Using Area Of X-section(3-phase 4-wire OS) calculator uses theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2)))) to calculate the Theta, The Angle Of PF Using Area Of X-section(3-phase 4-wire OS) formula is defined as the phase angle between reactive and active power. Theta and is denoted by ϑ symbol.

How to calculate Angle Of PF Using Area Of X-section(3-phase 4-wire OS) using this online calculator? To use this online calculator for Angle Of PF Using Area Of X-section(3-phase 4-wire OS), enter Resistivity (ρ), Length (l), Power Transmitted (P), Area Of 3-Φ 4-wire system (a10), Line Losses (W) and Maximum Voltage (Vm) and hit the calculate button. Here is how the Angle Of PF Using Area Of X-section(3-phase 4-wire OS) calculation can be explained with given input values -> 89.97727 = acos(sqrt(2*1.7E-05*3*(10^2)/(3*10*0.6*(60^2)))).

### FAQ

What is Angle Of PF Using Area Of X-section(3-phase 4-wire OS)?
The Angle Of PF Using Area Of X-section(3-phase 4-wire OS) formula is defined as the phase angle between reactive and active power and is represented as ϑ = acos(sqrt(2*ρ*l*(P^2)/(3*a10*W*(Vm^2)))) or theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2)))). Resistivity is the measure of how strongly a material opposes the flow of current through them, Length is the measurement or extent of something from end to end, The Power Transmitted Value through a shaft, The Area Of 3-Φ 4-wire system is the amount of two-dimensional space taken up by an object, Line Losses is defined as the losses that are produced in the line and Maximum Voltage the highest voltage rating for electrical devices.
How to calculate Angle Of PF Using Area Of X-section(3-phase 4-wire OS)?
The Angle Of PF Using Area Of X-section(3-phase 4-wire OS) formula is defined as the phase angle between reactive and active power is calculated using theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2)))). To calculate Angle Of PF Using Area Of X-section(3-phase 4-wire OS), you need Resistivity (ρ), Length (l), Power Transmitted (P), Area Of 3-Φ 4-wire system (a10), Line Losses (W) and Maximum Voltage (Vm). With our tool, you need to enter the respective value for Resistivity, Length, Power Transmitted, Area Of 3-Φ 4-wire system, Line Losses and Maximum Voltage 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 Theta?
In this formula, Theta uses Resistivity, Length, Power Transmitted, Area Of 3-Φ 4-wire system, Line Losses and Maximum Voltage. We can use 8 other way(s) to calculate the same, which is/are as follows -
• length = 3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2)/(2*Resistivity*(Power Transmitted^2))
• resistivity = 3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2)/(2*Length*(Power Transmitted^2))
• power_transmitted = sqrt((3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*Line Losses*((cos(Theta))^2))/(Resistivity*2*Length))
• line_losses = (2*Length*Resistivity*(Power Transmitted^2))/(3*Area Of 3-Φ 4-wire system*(Maximum Voltage^2)*((cos(Theta))^2))
• maximum_voltage = sqrt((2*Length*Resistivity*(Power Transmitted^2))/(3*Area Of 3-Φ 4-wire system*Line Losses*((cos(Theta))^2)))
• rms_voltage = (Power Transmitted/cos(Theta))*sqrt(Resistivity*Length/(3*Area Of 3-Φ 4-wire system))
• power_factor = (Power Transmitted/Maximum Voltage)*sqrt(2*Resistivity*Length/(3*Area Of 3-Φ 4-wire system))
• theta = acos(sqrt(2*Resistivity*Length*(Power Transmitted^2)/(3*Area Of 3-Φ 4-wire system*Line Losses*(Maximum Voltage^2))))
Where is the Angle Of PF Using Area Of X-section(3-phase 4-wire OS) calculator used?
Among many, Angle Of PF Using Area Of X-section(3-phase 4-wire OS) calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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