In electrical engineering, star (wye) and delta (mesh) connections refer to two different methods of wiring three-phase electrical systems. Understanding the relationship between current and voltage in each type of connection is crucial for designing and analyzing electrical circuits. Let’s delve into these relationships in detail:
### Star (Wye) Connection
In a star (or wye) connection, each phase of the electrical system is connected to a common neutral point, and the load is connected between each phase and the neutral.
1. **Voltage Relationships:**
- **Phase Voltage (\(V_{ph}\))**: This is the voltage across each individual phase of the load and the neutral point. It is the voltage between one phase and the neutral.
- **Line Voltage (\(V_{L}\))**: This is the voltage between any two lines (phases). It is higher than the phase voltage in a star connection.
The relationship between the line voltage (\(V_L\)) and phase voltage (\(V_{ph}\)) in a star connection is given by:
\[
V_{L} = \sqrt{3} \times V_{ph}
\]
Therefore, the phase voltage is:
\[
V_{ph} = \frac{V_{L}}{\sqrt{3}}
\]
2. **Current Relationships:**
- **Phase Current (\(I_{ph}\))**: This is the current flowing through each phase of the load.
- **Line Current (\(I_{L}\))**: This is the current flowing through each line (or phase conductor) and is the same as the phase current in a star connection.
In a star connection:
\[
I_{L} = I_{ph}
\]
### Delta (Mesh) Connection
In a delta (or mesh) connection, the load is connected in a loop or mesh with each load element connected end-to-end to form a triangle.
1. **Voltage Relationships:**
- **Phase Voltage (\(V_{ph}\))**: In the delta connection, the phase voltage is the voltage across each load element in the delta configuration.
- **Line Voltage (\(V_{L}\))**: This is the voltage between any two lines (phases). In a delta connection, the line voltage is the same as the phase voltage.
Therefore:
\[
V_{L} = V_{ph}
\]
2. **Current Relationships:**
- **Phase Current (\(I_{ph}\))**: This is the current flowing through each load element in the delta configuration.
- **Line Current (\(I_{L}\))**: This is the current flowing through each line (or phase conductor).
The relationship between the line current (\(I_L\)) and the phase current (\(I_{ph}\)) in a delta connection is given by:
\[
I_{L} = \sqrt{3} \times I_{ph}
\]
Therefore, the phase current is:
\[
I_{ph} = \frac{I_{L}}{\sqrt{3}}
\]
### Summary
- **Star Connection:**
- **Voltage Relationship:** \( V_{L} = \sqrt{3} \times V_{ph} \)
- **Current Relationship:** \( I_{L} = I_{ph} \)
- **Delta Connection:**
- **Voltage Relationship:** \( V_{L} = V_{ph} \)
- **Current Relationship:** \( I_{L} = \sqrt{3} \times I_{ph} \)
Understanding these relationships helps in converting between different connection types, sizing components correctly, and ensuring proper operation of three-phase systems.