**9.9. Equivalent Circuit**. In transformers, the problems concerning voltages and currents can be solved by the use of phasor diagrams. However, it is more convenient to represent the transformer by an equivalent circuit. If an equivalent circuit is available the computations can be of the equations direct application of circuit theory. An *equivalent circuit is merely a circuit interpretation of the equation which describe the behaviour of the device. *

The transformer windings, in the equivalent circuit, are shown as ideal. The resistance and leakage reactance of the primary and secondary are shown separately in the primary and secondary circuits. The effect of magnetising current is represented by Xo connected in parallel across the winding. The effect of core loss is represented by a non-inductive resistance *R _{0} *as shown in Fig. 35.

Fig. 35. Equivalent circuit of a transtormer.

The equivalent circuit can be simplified by transferring the secondary resistances and reactance to the primary aide in such a way that the ratio of *E _{2} *to

*E*

_{1}*is not affected in magnitude or phase. Let R*

_{2}’ be the resistance which must be placed in the primary circuit to produce the same drop as produced by R

_{2}in the secondary. Then R

_{2}’ causes a voltage drop in primary equal to I

_{2}’ R

_{2}’.

The ration of I_{2}’ and R_{2}’ must be the same as the turn ration N_{1}/N_{2}.

The load resistance and reactance can be transferred to the primary side in the same way. When all the secondary impedances have been transferred to the primary side, the winding need not be shown in the equivalent circuit. The exact equivalent circuit of the transformer with all impedance transferred to the primary side is shown in Fig. 36.

Fig. 36. Equivalent circuit with secondary impedances transferred to primary.

Just as the secondary impedances have been transferred to the primary it is possible to transfer the primary winding resistance and reactance to the secondary side. The primary resistance *R _{1} *and leakage reactance X

_{1}when transferred to secondary are denoted by

*R*and X

_{1}’_{1}’ and are given by

R_{1}’ = K^{2}R_{1}

X_{1}’ = K^{2}X_{1}.

**Approximate equivalent circuit. **It is seen that *E _{1} *differs from

*V*by a very small amount. Moreover, the no-load current

_{1}*I*is only a small fraction of full-load primary current so that I

_{0}_{2}‘ is practically equal to I

_{1}. Consequently the equivalent circuit can be simplified by transferring the parallel branch consisting of

*R*and X

_{0}_{0}to the extreme left position of the circuit as shown in Fig. 37. This circuit is known as

*approximate equivalent circuit.*Analysis with the approximate equivalent circuit gives almost the same results as the analysis with the exact equivalent circuit.

*However, the analysis with approximate equivalent circuit is simple because the resistances R*

_{1}

*and R*

_{2}*‘*

*and*

*leakage*

*reactance X*

_{1}and X_{2}’ can be combined.Fig. 37. Approximate equivalent circuit of transformer.

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