# Transformer with Leakage Reactance & Leakage Flux

## What is Leakage Flux in a Transformer ?

We know that all the flux linked with primary winding is also linked with the secondary winding. But, in the actual transformer the total flux created does not link with the primary and secondary winding but is divided into three parts as follows :

#### The main flux 'Φ' linking both primary and secondary windings.Primary leakage flux ΦL1 linking with primary winding only. andSecondary leakage flux ΦL2 linking with secondary winding only as shown in the figure.

The primary leakage flux ΦL1, is proportional to primary ampere-turns alone, (because the secondary turns do not link with ΦL1). The ΦL1 is in phase with I1 and produces self-induced EMF eL1 in primary given by,

eL1 = (2π f L1) × I1

#### Where, L1 is self-inductance of the primary winding produced by primary leakage flux ΦL1. So, Primary leakage reactance.

X1 = 2π f L1 = eL1/I1

Similarly secondary leakage flux, ΦL2 is produced by secondary ampere-turns. On no-load, there is no current in secondary and therefore no leakage flux exists across it. On load leakage flux ΦL2 is in phase with I2 and produces self-induced EMF

eL2 = (2π f L2) × I2

#### Where L2 is self-inductance of the secondary winding produced by secondary leakage flux ΦL2. Secondary leakage reactance.

X2 = 2π f L2 = eL2/I2

## Leakage Reactance of a Transformer :

By knowing the leakage reactance of the primary and secondary winding of the transformer. We can calculate the total leakage reactance of a transformer.

### i. Leakage reactance of a transformer referred to primary :

#### Total equivalent leakage reactance referred to secondary is given by,

While shifting the secondary reactance to the primary side we have to divide it with the square of the transformation ratio K of the transformer. i.e., X2/K2.

### ii. Leakage reactance of a transformer referred to secondary :

#### Total equivalent leakage reactance referred to secondary is given by,

While shifting the primary reactance to the secondary side we have to multiply it with the square of the transformation ratio K of the transformer. i.e., X1*K2.

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