Question

What is the relationship between voltage and current in star delta connection?

Answer 1

In a star-delta (Y-Δ) connection, the relationship between voltage and current varies based on whether you're looking at the star (Y) or delta (Δ) configuration.

### Star Connection (Y)
1. **Line Voltage (V_L)**: The voltage across each phase (V_Ph) is related to the line voltage by:
   \[
   V_L = \sqrt{3} \cdot V_{Ph}
   \]

2. **Line Current (I_L)**: The line current is equal to the phase current:
   \[
   I_L = I_{Ph}
   \]

### Delta Connection (Δ)
1. **Line Voltage (V_L)**: The phase voltage is equal to the line voltage:
   \[
   V_{Ph} = V_L
   \]

2. **Line Current (I_L)**: The line current is related to the phase current by:
   \[
   I_L = \sqrt{3} \cdot I_{Ph}
   \]

### Summary
- In a **star connection**, the line voltage is higher than the phase voltage, while the line current equals the phase current.
- In a **delta connection**, the line voltage equals the phase voltage, while the line current is higher than the phase current.

This relationship is crucial for understanding the behavior of three-phase systems and how they can be transformed between these configurations for various applications.

Answer 2

In three-phase systems, star (Y) and delta (Δ) connections are used to connect loads or transformers. The relationship between voltage and current in these configurations can be understood by examining how they interrelate in each type of connection.

### Star (Y) Connection

**1. Line Voltage (V_L) and Phase Voltage (V_Ph):**
   - In a star connection, the line voltage (\( V_L \)) is related to the phase voltage (\( V_Ph \)) by the following equation:
     \[
     V_L = \sqrt{3} \cdot V_Ph
     \]
   - This is because the line voltage is the voltage between any two of the three lines (phases), whereas the phase voltage is the voltage between each phase and the neutral point.

**2. Line Current (I_L) and Phase Current (I_Ph):**
   - In a star connection, the line current (\( I_L \)) is equal to the phase current (\( I_Ph \)):
     \[
     I_L = I_Ph
     \]

### Delta (Δ) Connection

**1. Line Voltage (V_L) and Phase Voltage (V_Ph):**
   - In a delta connection, the phase voltage (\( V_Ph \)) is equal to the line voltage (\( V_L \)):
     \[
     V_L = V_Ph
     \]

**2. Line Current (I_L) and Phase Current (I_Ph):**
   - In a delta connection, the line current (\( I_L \)) is related to the phase current (\( I_Ph \)) by the following equation:
     \[
     I_L = \sqrt{3} \cdot I_Ph
     \]
   - This is because the line current is the sum of the currents in the two phases that are connected to each line.

### Summary

- **Star Connection:**
  - \( V_L = \sqrt{3} \cdot V_Ph \)
  - \( I_L = I_Ph \)

- **Delta Connection:**
  - \( V_L = V_Ph \)
  - \( I_L = \sqrt{3} \cdot I_Ph \)

These relationships are crucial for analyzing and designing three-phase electrical systems, ensuring proper operation and safety of electrical equipment.