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.