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Equivalent Resistance of single phase Transformer

In a transformer, primary and secondary windings have some resistance. Let, R1 is the resistance of the primary winding and R2 is the resistance the Secondary winding which is shown in the figure.


Now, We can easily prove that the resistance of two winding can be transferred to any one of the two windings of the transformer. Let, I 2 secondary current flows through the secondary winding of the transformer, at that time the primary current is I1.

So , Copper loss in the secondary winding is I22 R2. This copper loss is supplied by Primary current I1. And R2 is the equivalent secondary resistance as refer to primary winding which is shown in the figure-2.


fig-2

So, the loss I12R2 will be same loss of secondary copper loss i.e I22R2

Therefore, I12R2’ = I22R2
∴R2’=I22R2/I12
∴R2’= (I2/I1)2 R2
If, no-load current I0 is neglect, then I2/I1= 1/K (where K = voltage transformation ratio of the transformer)
Hence, R2’=(1/K)2 R2
∴R2’=R2/K2


Similarly , equivalent primary resistance as referred to Secondary winding is R1’=K2R1.

In fig -2 shows , The secondary resistance is transferred to primary winding and secondary winding is resistance less. And the total resistance at primary winding is ( R1 + R2/K2 ) which is known as the equivalent resistance of the transformer as referred to primary . and It may be demarked as R01= R1+ R2’= R1 +R2/K2.

fig-3

And In fig.-3 shows , The primary resistance is transferred to secondary winding and primary winding is resistance less. And the total resistance at secondary winding is ( R2 + R1K2 ) which is known as the equivalent resistance of the transformer as referred to Secondary . and It may be demarked as R02= R2+ R1’= R2 +R1K2.



Therefore, The Equivalent resistance as referred to secondary and primary are,

  1. R1= Equivalent resistance as referred to secondary winding
  2. R2= Equivalent resistance as referred to primary winding
  3. R01=Effective resistance of the transformer as referred to primary of the transformer.
  4. R02= Effective resistance of the transformer as referred to secondary of the transformer.

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