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 = VR (voltage in red phase) = VY (voltage in yellow phase) = VB (voltage in blue phase).

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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 system.

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 is 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:

\[V_{line} = \sqrt{3} V_{phase}\];

While line current = phase current.

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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.

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Difference between phase voltage and line voltage is given as follows:

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

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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,

Vphase = Vline / √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?

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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: Vline = √3 Vphase.

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.

FAQ (Frequently Asked Questions)

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

Answer: 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 V_{γ} - V_{B} 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 which 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?

Answer: 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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