# Delta Connection In a 3 Phase System

In **Delta (Δ) or Mesh connection**, the finished terminal of one winding is connected to start terminal of the other phase and so on which gives a closed circuit. The three line conductors are run from the three junctions of the mesh called Line Conductors.

**Contents:**

- Relation Between Phase Voltage and Line Voltage in Delta Connection
- Relation Between Phase Current and Line Current in Delta Connection

The connection in Delta form is shown in the figure below.

To obtain the **Delta connections**, a_{2 }is connected with b_{1}, b_{2} is connected with c_{1} and c_{2} is connected with a_{1} as shown in the above figure. The three conductors R, Y and B are running from the three junctions known as **Line Conductors**.

The current flowing through each phase is called **Phase Current (Iph)**, and the current flowing through each line conductor is called** Line Current (I _{L}).**

The voltage across each phase is called** Phase Voltage (E _{ph})**, and the voltage across two line conductors is called

**Line Voltage (E**

_{L}).## Relation Between Phase Voltage and Line Voltage in Delta Connection

To understand the relationship between the phase voltage and line voltage in the Delta consider the figure A shown below.

It is clear from the figure that the voltage across terminals 1 and 2 is the same as across the terminals R and Y. Therefore,

Similarly,

Where, the phase voltages are

The line voltages are

**Hence, in Delta Connection Line Voltage is equal to Phase Voltage.**

## Relation Between Phase Current and Line Current in Delta Connection

As in the balanced system the three phase current I_{12}, I_{23} and I_{31} are equal in magnitude but are displaced from one another by 120 degrees electrical.

The **phasor diagram** is shown below.

If we look at figure A, it is seen that the current is divided at every junction 1, 2 and 3.

Applying Kirchhoff’s Law at junction 1

The Incoming currents are equal to outgoing currents.

And their vector difference will be given as

The vector I_{12} is reversed and is added in the vector I_{31} to get the vector sum of I_{31} and –I_{12} as shown above in the phasor diagram. Therefore,

As we know, I_{R} = I_{L}, therefore,

Similarly,

Hence, in Delta connection line current is root three times of phase current.