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Impedance Ratio
In many problems that involve transformers it is convenient to refer the impedance in one side of the transformer to the other side of the transformer.
For example, Fig. 65(a) shows an ideal transformer with a load impedance of Z_{L} ohms connected across its secondary terminals. The load impedance referred to the primary is the value of impedance that, if connected directly across the source of voltage V_{1}, would draw the same value of current I_{1} as the transformer with its connected load impedance Z_{L}. This is shown in Fig. 65(b). When Eq. 614 is divided by Eq. 617 the result is
or
But the load impedance is
and an impedance that would draw a current of I_{1} amp when connected directly across the source of voltage of V_{1} v must have a value of
A comparison of Eqs. 618, 619, and 620 shows that
where Z_{1} is the value of the load impedance referred to the primary of the transformer. The impedance ratio is, therefore
or the square of the turns ratio of the transformer. The turns ratio of a transformer is sometimes represented by the letter a, which means that
and the impedance ratio is


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