Leakage reactance can also be transferred from one winding to the
other in the same way as resistance \[\begin{array}{ccc}
X_{2}^{'}=X_{2}/K^{2} & \mbox{and} &
X_{1}^{'}=K^{2}X_{1}\\
X_{01}=X_{1}+X_{2}^{'} & \mbox{and} &
X_{02}=X_{2}+X_{1}^{'}
\end{array}\]

At no load: \[\begin{aligned}
V_{1} & \thickapprox E_{1}\\
E_{2} & =KE_{1}=KV_{1}\\
E_{2} & =_{0}V_{2}
\end{aligned}\] At load:

The approximate voltage drop is: \[I_{2}R_{02}\cos\Phi\pm
I_{2}X_{02}\sin\Phi\] where \(+\) is for lagging pf and \(-\) is for leading pf

Similarly, approximate voltage drop referred to primary is \[I_{1}R_{01}\cos\Phi\pm
I_{1}X_{01}\sin\Phi\] % voltage drop in secondary is \[\begin{aligned}
= & \dfrac{I_{2}R_{02}cos\Phi\pm
I_{2}X_{02}sin\Phi}{_{0}V_{2}}\times100\\
= & v_{r}cos\Phi\pm v_{x}sin\Phi
\end{aligned}\] where \[\begin{aligned}
v_{r} &
=\dfrac{I_{2}R_{02}}{_{0}V_{2}}\times100=\dfrac{I_{1}R_{01}}{V_{1}}\times100=\mbox{percentage
resistive drop}\\
v_{x} &
=\dfrac{I_{2}X_{02}}{_{0}V_{2}}\times100=\dfrac{I_{1}X_{01}}{V_{1}}\times100=\mbox{percentage
reactive drop}
\end{aligned}\]

Equivalent Circuit of a Transformer

Equivalent circuit is basically a diagram in which the resistance and
leakage reactance of the transformer are imagined to be external to the
winding

The equivalent circuit diagram of transformer is given below:-

The secondary circuit and its equivalent primary value

The total equivalent circuit is obtained by adding in the primary
impedance

It can be simplified

At last, the circuit is simplified by omitting \(I_0\) altogether

The total impedance between the input terminal: \[\begin{aligned}
Z &
=Z_{1}+Z_{m}\bigparallel\left(Z_{2}^{'}+Z_{L}^{'}\right)\\
&
=Z_{1}+\dfrac{Z_{m}\left(Z_{2}^{'}+Z_{L}^{'}\right)}{Z_{m}+\left(Z_{2}^{'}+Z_{L}^{'}\right)}
\end{aligned}\] Therefore the input voltage is given by \[V_{1}=I_{1}\left[Z_{1}+\dfrac{Z_{m}\left(Z_{2}^{'}+Z_{L}^{'}\right)}{Z_{m}+\left(Z_{2}^{'}+Z_{L}^{'}\right)}\right]\]