Let's say that we have a transformer with two windings
a busy cat http://www.circuitstoday.com/wp-content/uploads/2011/11/Transformer-Circuit-Symbol.jpg
with nominal power \$S\$, nominal voltages \$V_1\$ and \$V_2\$ and windings \$N_1\$ and \$N_2\$ respectively. The equivalent impedance is \$R+jX\$ referred to the primary winding.
Now we rewire this transformer to become an autotransformer.
and the secondary has nominal load with lagging factor \$\cos \phi\$.
I am a little confused so my questions are: Does that mean that the voltage \$V_x\$ is equal to \$V_2\$? What about \$I_x\$ or \$I_H\$? How can we find the voltage \$V_H\$?