## Introduction

Line voltage in a three-phase system is the potential difference between any two lines or phases present in the system, denoted by V_{line} or V_{L-L}. The phases present here are conductors or windings of a coil. If R, Y and B are the three phases ( red phase, yellow phase, blue phase ) then the voltage difference between R and Y, Y and B or B and R forms the line voltage. Phase voltage, on the other hand, is the potential difference between one phase (R, Y or B) and neutral junction point, denoted by V_{phase} = V_{R} (voltage in red phase) = V_{Y} (voltage in yellow phase) = V_{B} (voltage in blue phase).

Similarly line current is the current in one phase while phase current is the current inside the three-phase connection.

To understand line voltage and phase voltage relation, the first thing we need to understand is the different types of three-phase connection systems.

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### Relation Between Line Voltage and Phase Voltage in Star Connection

Consider three coils of wire or winding of a transformer attached by a common connection point. The three wires going away from each coil to the load are known as the line wires, and the conductors themselves are the phases. This system is a typical three-phase three-wire star connection system. If a neutral wire is attached to the shared middle point, then it is known as a three-phase four-wire star connection system.

The terms line voltage and phase voltage has already been explained before, and they are related as follows:

V_{line}= 3–√V_{phase} ;

While line current = phase current.

### Relation Between Line Voltage And Phase Voltage In Delta Connection

In delta connection, all the three ends of the phases are connected to form a closed triangular loop, and it has no common neutral point as in a star connection. Here, the line and phase voltage are related as follows:

V_{line}=V_{phase};

While line current = √3× phase current.

### Difference Between Line Voltage and Phase Voltage

For Delta connection, the line voltage and phase voltage are equal.

### Solved Examples

1. Calculate the phase voltage if the line voltage is 460 volts, given that the system is a three-phase balanced star connected system.

Answer: We know,

V_{phase} = V_{line} / √3 = 460 / √3 = 265.59 volts.

2. In which of the following circuit line voltage and phase voltage are equal? And what about the line voltage and phase voltage relationship in the other circuit?

Answer: As we know, in a delta connection (second figure), the line voltage and phase voltage are equal. While for a star connection line voltage is higher than phase voltage which is given by the relation: V_{line} = √3 V_{phase}.

### Fun Facts

In any problem or question, the voltage given is generally line voltage. In the case of phase voltage, it should be mentioned. If not mentioned, consider it as the line voltage.

Our domestic three-phase power supply or 440 volts is the line voltage.

The single-phase 230 volts AC supply is the voltage difference between a phase and the neutral junction or rather the phase voltage.

The polyphase system where all the line voltages and line currents are equal is known as a three-phase balanced system. In the case of unsymmetrical loads, the system is generally an unbalanced one.

### Single-Phase System

A single-phase system is one of the most commonly used types of systems that people are familiar with. This is also what most people tend to have at their homes. For normal plugs and appliances, this type of system is used. However when it comes to needing a larger amount of power then the three-phase system is necessary. The electricity is generated by using a coil of wire which keeps on moving through the magnetic fields. As there are three coils involved the system will be called a three-phase system. Whereas when the connection is between a line and a neutral it is called a single-phase system. It is hence necessary to understand the Difference Between Line Voltage and Phase Voltage with Solved Examples via Vedantu to check out the power that both systems provide.

### What is the Meaning of Star Connection?

Star connection is also known as the three-phase four-wire system where there are 3 phases being involved and are connected by four wires. This is one of the most preferred systems for alternating current distribution whereas for transmission the Delta connection is used. In the star which is also denoted by Y the system of interconnection, the starting and the finishing points of the three coils are connected together to form the neutral point.

Star connection is obtained by connecting together the similar ends of three coils which the two other ends are joined to line wires. The common point is also said to be the neutral or star point which is represented by N.

### What Does Delta Connection Mean?

The Delta connection is also said to be the Mesh connection where there is the presence of three phases connected with three wires. It is also one of the most preferred AC power systems for transmission.

In simpler words, it can also be said that the three coils that are connected in series seem like they form a close mesh and when the three wires are taken out from the three junctions all the outgoing currents are assumed to be positive. It is seen that if the system is balanced then the value of the algebraic sum of all voltages within the mesh will remain zero.

### Advantages of Using a Three-Phase System:

There are certain advantages of three-phase systems and can be provided as follows:

The three-phase currents that are present tend to cancel out each other and hence the sum will be zero making it a linear balanced load. This hence makes it possible to reduce the size of the neutral conductor as it carries little to no current.

Power transfer into the linear balanced load is constant and this helps in the reduction of vibrations in motor or generator applications.

A three-phase system will also create a rotating magnetic field that has a specific magnitude and direction allowing the design of electric motors to be simplified as no starting circuit will be needed.

Students can now also learn more about the Difference Between Line Voltage and Phase Voltage with Solved Examples via Vedantu NCERT Solutions for Physics.

## FAQs on Difference Between Line Voltage and Phase Voltage

**1. How can it be Shown that Phase Voltage Equals 1/√3 Times the Line Voltage?**

Firstly, we need to understand a basic phasor diagram for a three-phase supply, where all the phases are 120 degrees apart.

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Now, the difference between the two-phase voltages gives us the line voltage.

For example, line voltage between yellow and blue phase (V_γB) will be given by Vγ - VB which is a vector difference that means the vector addition of V_{Y} and - V_{B}. Now we know, V_{R}=V_{Y}=V_{B}=V volts as the magnitude of all phase voltages are the same. Therefore, V_{YB}= √3 V, which is the resultant of two vectors that are equal in magnitude and 60 degrees apart. Now, V_{YB} is the line voltage or potential difference between the yellow and blue phase. V_{L-L}=√3V_{Phase}. Therefore, from the above equation, we get the phase voltage as 1/√3 times the line voltage.

**2. How can Power be Calculated Using Line Voltage and Phase Voltage in a Star Connection?**

The most widely used power generation technology is a three-phase power system. Here, the calculations are a bit different and complex than a single-phase system. The alternating current takes the shape of a sine wave as the current varies in direction and amplitude. In a single-phase system there is one such wave. But in a three-phase system, there are three such components of current which remain out of phase by each third of a cycle. Each of the components is opposite in direction to the combination of the other two parts but are equal in magnitude.

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