# Equivalent Reactance

## MAGNETIC LEAKAGE

Till now we have assumed that all the flux linked with the primary also links with the secondary. But in practice, the permeability of the core of the transformer is finite. All the flux linked with the primary do not link with the secondary. As shown in Figure 1.29(a), *Φ*_{L1} and *Φ*_{L2} induce emf *e*_{L1} and *e*_{L2} in primary and secondary windings respectively. Therefore, in effect, we can consider it as an equivalent inductive coil in phase with the winding shown in Figure 1.29(b).

## EQUIVALENT REACTANCE

If *X*_{2} be transferred to primary, let its referred value be *X*_{2}^{′}. We have

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

i.e.,

If *X*_{1} be transferred to secondary, let the referred value be *X*_{1}^{′} We have

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

i.e.,

The total reactance referred to as primary (*X*_{01}) is *X*_{l} + *a*^{2}*X*_{2} and that of referred to as secondary (*X*_{02}) is *X*_{2}+. The total reactance is known as *equivalent reactance*. It is denoted by

*X*_{01}=*X*_{1}+*a*^{2}*X*_{2} (1.18)