What type of three-phase connection exists if the line voltage equals the phase voltage?

In a three-phase system, the relationship between line voltage and phase voltage depends on the type of connection being used. When the line voltage equals the phase voltage, this indicates a specific configuration of the system.

In the case of a delta connection, each phase is connected end-to-end, forming a closed loop, which means that the voltage across each phase is equal to the line voltage. In this arrangement, the phase voltage is taken across the individual components of the delta (the load or generator phases), which creates a scenario where the line voltage and the phase voltage are equal. This is a fundamental characteristic of the delta configuration.

In contrast, a wye (or star) connection would show that the line voltage is greater than the phase voltage. Specifically, in a wye connection, the line voltage is √3 times the phase voltage, which is a critical point distinguishing the two configurations. The series connection mentioned does not pertain to three-phase systems but is a different arrangement altogether, while the star connection also cannot produce equality of line and phase voltages.

Thus, the correct answer is rooted in the properties of the delta connection and its unique voltage relationships in a three-phase system.