In a delta-connected three-phase system, the relationship between line voltage and phase voltage is crucial for understanding electrical systems, especially in power distribution.

Key Concepts:

• Delta Connection: In a delta-connected system, each end of the three-phase windings is connected in series, forming a closed loop.
• Line Voltage (\(V_L\)): The voltage measured across the terminals of each line of the delta connection.
• Phase Voltage (\(V_{ph}\)): The voltage across any one component (winding) of the connected system.

Relationship Explanation:

In a delta connection, the line voltage is the same as the phase voltage. The reason for this equality is due to the configuration of the connection:

• All three windings are connected end-to-end, forming an equilateral triangle (delta shape).
• The voltage across each line (line voltage) becomes the voltage across each corresponding winding (phase voltage).

Justification of the Correct Answer:

The provided options are:

1. Line voltage is zero
2. Line voltage is twice phase voltage
3. Line voltage is less than phase voltage
4. Line voltage equals phase voltage

Considering the delta connection properties, the correct answer is: Line voltage equals phase voltage.

Why Other Options Are Incorrect:

• Line voltage is zero: This is incorrect because there is always a measurable voltage in the connection.
• Line voltage is twice phase voltage: This is incorrect for a delta connection; it might apply to other configurations or misconceptions.
• Line voltage is less than phase voltage: This is incorrect as, in delta connection, they are equal, not less.

Conclusion:

In a delta-connected three-phase system, the line voltage and the phase voltage are equal. This holds a significant advantage in simplifying calculations for certain electrical systems, allowing direct application of Ohm's Law and related principles.