Balanced 3-phase circuit?

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In summary, a balanced 3-phase circuit is an electrical circuit that has three voltage sources with equal magnitude and 120 degrees phase difference. It is commonly used in power distribution systems due to its efficiency and high power capacity. Some advantages of a balanced 3-phase circuit include efficiency, lower cost, higher power capacity, and less voltage drop. To calculate line voltage and current in a balanced 3-phase circuit, specific formulas can be used. The main difference between a balanced and unbalanced 3-phase circuit is the equal distribution of voltage and current in a balanced circuit, while an unbalanced circuit has unequal distribution. Common applications of a balanced 3-phase circuit include power distribution systems, electric motors, generators, and renewable energy systems.
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eehelp150
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Homework Statement


RMS value of line-to-line voltage between phase A and phase C is ##V_{CA}= 208 \angle 10° V##
Assume ABC positive phase sequence and that it is a balanced 3-phase circuit.

Find line-to-line voltages (magnitude and angle) ##V_{AB}## and ##V_{BC}##.
Find the phase-to-neutral voltages (magnitude and angle) ##V_{AN}, V_{BN}, V_{CN}##

Homework Equations


upload_2016-10-24_23-23-24.png


The Attempt at a Solution


Are the equations I posted the ones to use to solve this problem? I honestly have no idea where to start and any advice would be appreciated.
 
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Hello,

To solve this problem, you can use the following equations:

1. For line-to-line voltages:
##V_{AB} = V_{CA} \angle -120°##
##V_{BC} = V_{CA} \angle 120°##

2. For phase-to-neutral voltages:
##V_{AN} = \frac{V_{AB}}{\sqrt{3}}##
##V_{BN} = \frac{V_{BC}}{\sqrt{3}}##
##V_{CN} = \frac{V_{CA}}{\sqrt{3}}##

Using these equations, you can find the magnitudes and angles of the line-to-line and phase-to-neutral voltages. Just remember to convert the given voltage in polar form to rectangular form before using the equations.

Hope this helps! Let me know if you have any other questions.
 

What is a balanced 3-phase circuit?

A balanced 3-phase circuit is an electrical circuit that has three voltage sources, each with equal magnitude and 120 degrees phase difference from each other. This type of circuit is commonly used in power distribution systems due to its efficiency and ability to deliver high power.

What are the advantages of a balanced 3-phase circuit?

There are several advantages of a balanced 3-phase circuit, including:

  • Efficiency: A balanced 3-phase circuit can deliver power more efficiently compared to a single-phase circuit, as the power is evenly distributed among the three phases.
  • Lower cost: The use of three smaller conductors in a balanced 3-phase circuit results in lower material and installation costs compared to a single-phase circuit with larger conductors.
  • Higher power capacity: A balanced 3-phase circuit can deliver higher power capacity compared to a single-phase circuit, making it suitable for industrial and commercial applications.
  • Less voltage drop: Due to the use of three phases, the voltage drop in a balanced 3-phase circuit is lower compared to a single-phase circuit, resulting in more stable and reliable power delivery.

How do you calculate the line voltage and current in a balanced 3-phase circuit?

To calculate the line voltage in a balanced 3-phase circuit, you can use the following formula: Vline = Vphase * √3, where Vphase is the phase voltage. The line current can be calculated using the formula: Iline = Iphase / √3, where Iphase is the phase current.

What is the difference between a balanced and unbalanced 3-phase circuit?

A balanced 3-phase circuit has equal voltage and current in all three phases, while an unbalanced 3-phase circuit has unequal voltage and/or current in one or more phases. This can lead to inefficiency and uneven power distribution in the circuit.

What are the common applications of a balanced 3-phase circuit?

Balanced 3-phase circuits are commonly used in power distribution systems for industrial and commercial applications. They are also used in electric motors, generators, and other electrical equipment that require high power capacity. Additionally, they can be found in renewable energy systems, such as wind and solar power systems, due to their efficiency and ability to handle high power loads.

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