# Equivalent Resistance

**Figure 1.26** Individual Resistances

Figure 1.26 shows a transformer having primary resistance *R*_{1} and secondary resistance *R*_{2}, 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 *N*_{1} and *N*_{2} be the number of turns of primary and secondary winding respectively. Let the turns ratio be ‘*a*’. Let *I*_{1} and *I*_{2} be the currents in primary and secondary winding, respectively. Neglecting *I*_{0}, = a. Let the referred value of *R*_{2} be *R*_{2}^{′} when it is transferred to primary. The copper loss of secondary is *I*_{2}^{2}*R*_{2} when *R*_{2} is in secondary. The copper loss across *R*_{2}^{′} is *I*_{1}^{2}*R*_{2}^{′}when *R*_{2} has been transferred to primary. These two losses must be equal.

∴ *I*_{2}^{2}*R*_{2}=*I*_{1}^{2}*R*_{2}^{′}

i.e.,

The total resistance referred to as primary becomes *R*_{1} + *R*_{2}^{′} or *R*_{1} + *a*^{2}*R*_{2}. This is also known as equivalent or effective resistance of the transformer referred to as primary and is denoted by *R*_{01}.

*R*_{01}=*R*_{1}+*a*^{2}*R*_{2} (1.13)

Figure 1.27 is the equivalent of Figure 1.26 when the secondary resistance is transferred to the primary.

If *R*_{1} is transferred to secondary, having referred value *R*_{1}^{′}, we have

*I*_{1}^{2}*R*_{1}=*I*_{2}^{2}*R*_{1}^{′}

i.e.,

**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