why are the line voltage and phase voltage same in delta configuration of three phase system
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In a delta configuration of a three-phase system, the line voltage and phase voltage are equal. This diagram shows a delta connection where three phase windings are connected end-to-end forming a triangle. The line terminals L1, L2, and L3 are connected to the vertices of this triangle.
The key insight is that in a delta configuration, the line terminals connect directly to the vertices of the triangle. When we measure the voltage between line terminals L1 and L2, we are measuring directly across the phase winding that connects these two points. There is no intermediate connection or transformation.
Mathematically, we can prove this relationship. The line voltage V line equals the voltage measured between L1 and L2. Since L1 and L2 are directly connected to the endpoints of phase winding AB, the voltage between L1 and L2 equals the phase voltage of winding AB. Therefore, line voltage equals phase voltage in delta configuration.
To better understand why delta configuration has equal line and phase voltages, let's compare it with star configuration. In delta, line voltage equals phase voltage. In star configuration, line voltage equals square root of 3 times phase voltage. This difference occurs because in delta, line terminals connect directly to phase windings, while in star, they connect through a neutral point.
To summarize what we have learned: In a delta configuration, the line voltage equals the phase voltage because line terminals connect directly to the triangle vertices. There are no intermediate connections or transformations. This fundamental difference from star configuration makes delta systems particularly useful in high-power applications.