Resistance and Leakage Reactance or Impedance of Transformer

Leakage Reactance of Transformer

The flux generated in the primary winding of the transformer gets linked with both the primary and secondary winding. However, all the flux generated do not link  with both the primary and secondary winding.  A small portion of flux will link either winding but not both. The flux which does not link with both the primary and secondary winding is called Leakage Flux in transformer. The leakage flux cause self rectance in the concerned winding. The self rectance is also called leakage reactance. The transformer winding also has certain resistance. The combination of the resistance and the leakage reactance called impedance of the transformer winding  cause voltage drop in the primary and secondary winding.

Resistance of Transformer 

The  primary and secondary winding of transformer is made of copper or aluminium.  The copper is widely used as a  winding material for coils and winding.  The copper is very good conductor of electricity because it has lower resistance compared to aluminium. However, the copper does not have zero resistance, even the resistance of copper increase with an increase of temperature. 

Thus, the winding resistance can not be zero in any case, and therfore , the primary and secondary winding of the transformer have some resistance. The resistance of the winding depends on the specific conductivity of the material, number of turns and the area of the conducting material. So primary and secondary winding have some resistance. This total internal resistance of both the primary and secondary windings is known as resistance of transformer. The secondary winding resistance can be refereed at primary side, and also the primary winding resistance can be referrred at the secondary side.

Impedance of Transformer

The primary and secondary winding of the transformer has both the leakage reactance and resistance. The leakage reactance and the resistance can not be zero for a practical transformer.The combination of resistance and leakage reactance is called impedance of transformer.  If R1 and R2 and X1 and X2 are primary and secondary resistance and leakage reactance of transformer  respectively, then Z1 and Z2 impedance of primary and secondary windings are respectively,

The voltage drop in transformer winding depends on the impedance of the transformer.

Leakage Flux in Transformer

In an ideal condition the leakge flux in the transformer should be zero. However, there would be some part of the flux which does not link to both the primary and secondary winding and thus, the some part of the flux remains unutilized. The leakage flux pass through the winding insulation instead of passing through the core. The leakage flux produce leakage reactance in both the primary and secondary winding of transformer. This phenomenon in transformer is known as Magnetic leakage.

The voltage drop takes place in the winding due to impedance of the transformer. If  voltage V1 is applied across primary of transformer, there will be a voltage drop  I1X1  in the primary to compensate the primary self induced emf due to leakage rectance. Let X1 is the primary leakge reactance. The voltage equation at primary side of the transformer is:

Similarly, considering secondary leakge flux, the voltage equation of secondary side is,

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