Question 22.9: Write the mesh equations for the transformer network in Fig....

For each coil, the mutual term is positive, and the sign of M in X _{m}=\omega M \angle 90^{\circ} \text { is positive, as determined by the direction of } I _{1} and I _{2}. Thus,

E _{1}- I _{1} R_{1}- I _{1} X_{L_{1}} \angle 90^{\circ}- I _{2} X_{m} \angle 90^{\circ}=0.

or    E _{1}- I _{1}\left(R_{1}+j X_{L_{1}}\right)- I _{2} X_{m} \angle 90^{\circ}=0.

For the other loop,

– I _{2} X_{L_{2}} \angle 90^{\circ}- I _{1} X_{m} \angle 90^{\circ}- I _{2} R_{L}=0.

or    I _{2}\left(R_{L}+j X_{L_{2}}\right)- I _{1} X_{m} \angle 90^{\circ}=0.