Let us discuss in this topic what will be effect in a transformer due to the presence of resistance & leakage reactance. The resistance of Transformer means the resistance of primary and secondary winding of the transformer. And leakage reactance of Transformer means there is some magnetic leaking in the both of the windings that should be equal to inductive coils connected in both primary & secondary winding which is shown in fig-1.
Fig-1
Where, the R_{1}= Resistance of primary winding,
Therefore, Primary impedance of transformer is
Therefore, Secondary impedance of transformer is
Due to the presence of resistance and leakage reactance, some voltage drop will occur in the primary winding.
If,
Then, we can write , that
V_{1} = E_{1} + I_{1}Z_{1},
Similarly, The voltage drop will occur in secondary winding,
If
and
Then, we can write, that
E_{2} =V_{2} +I_{2}Z_{2}
Now, we draw the vector diagram below for different kinds of the load is shown in figs.
Fig-2 ( When Load is Non-Inductive)
Fig-3 ( When Load is Inductive)
Fig-4 ( When Load is Capacitive)
In these diagrams, the vector for resistive drops is parallel to current vector whereas reactive drops are perpendicular to the current vectors. The angle φ_{1} between V_{1} & I_{1} is the power factor angle of the transformer. And we can also transfer leakage reactance from one winding to another winding in the same way as resistance transfer.
Therefore, the equivalent secondary reactance as referred to primary
(X_{2}’) = X_{2}/K^{2} and
The equivalent primary reactance as referred to secondary (X_{1}’)=K^{2}X_{1},
And The reactance of the transformer as referred to primary
(X_{01})=X_{1} +X_{2}’ = X_{1} + X_{2}/K^{2},
Similarly, The reactance of the transformer as referred to secondary
(X_{02})=X_{2} +X_{1}’ = X_{2} + X_{1}K^{2},
Fig-5
Fig-6
We have discussed in the topic of equivalent resistance of transformer,
That, Effective resistance of the transformer as referred to primary of transformer
And Effective resistance of the transformer as referred to secondary of transformer,
Hence, The total impedance of the transformer as referred to primary is given by,
And, the total impedance of the transformer as referred to secondary is given by,
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