Figure 1.26 Individual Resistances
Figure 1.26 shows a transformer having primary resistance R1 and secondary resistance R2, where resistances have been shown external to the wind-ings. In Figure 1.26, it is assumed that there is no fringing, i.e. no leakage of flux. It is possible to transfer resistance from one winding to another to simplify the calculation. Let N1 and N2 be the number of turns of primary and secondary winding respectively. Let the turns ratio be ‘a’. Let I1 and I2 be the currents in primary and secondary winding, respectively. Neglecting I0, = a. Let the referred value of R2 be R2′ when it is transferred to primary. The copper loss of secondary is I22R2 when R2 is in secondary. The copper loss across R2′ is I12R2′when R2 has been transferred to primary. These two losses must be equal.
The total resistance referred to as primary becomes R1 + R2′ or R1 + a2R2. This is also known as equivalent or effective resistance of the transformer referred to as primary and is denoted by R01.
Figure 1.27 is the equivalent of Figure 1.26 when the secondary resistance is transferred to the primary.
If R1 is transferred to secondary, having referred value R1′, we have
Figure 1.27 Resistance Referred to as Primary
Therefore, the equivalent resistance of the transformer referred to as secondary becomes
Figure 1.28 is the equivalent of Figure 1.26 when the primary resistance is trans-ferred to the secondary.
Figure 1.28 Resistance Referred to as Secondary
Figure 1.29 Magnetic Leakage and Equivalent Circuit