In a three-phase delta connection, the line voltage is equal to the phase voltage. Let's understand this concept in detail:

Three-Phase Delta Connection:
In electrical power systems, three-phase power is commonly used due to its efficiency and balanced load distribution. In a three-phase system, there are three conductors or phases that carry alternating current. These phases are typically represented as A, B, and C.

A delta connection is one of the ways to connect the three phases in a three-phase system. In a delta connection, the end of one phase is connected to the start of the next phase in a circular manner, forming a closed loop. This connection resembles the Greek letter delta (Δ), hence the name.

Line Voltage:
The line voltage refers to the voltage between any two line conductors in a three-phase system. In a delta connection, the line voltage is equal to the phase voltage, which means that the voltage measured between two line conductors is the same as the voltage measured across each phase.

Phase Voltage:
The phase voltage refers to the voltage between any one phase conductor and the neutral point in a three-phase system. In a delta connection, the phase voltage is the voltage across each individual phase. Since the line voltage is equal to the phase voltage in a delta connection, the voltage measured between any two line conductors is the same as the voltage measured across each phase.

Explanation:
In a delta connection, the line voltage is equal to the phase voltage because each phase is directly connected to the line conductors. The voltage across each phase is the same as the voltage between any two line conductors. This is due to the specific configuration of the delta connection, where the phases are connected in a closed loop.

For example, if the phase voltage is 230 volts, then the line voltage will also be 230 volts. This is true for all three phases in a delta connection.

Summary:
In a three-phase delta connection, the line voltage is equal to the phase voltage. This is because the phases are directly connected to the line conductors, forming a closed loop. The voltage across each phase is the same as the voltage between any two line conductors.