The Ideal Transformer

An ideal transformer is a loseless device with an input winding and an output winding.The relationships between the iput voltage and the output voltage and between the input current and the output current are given by two simple equations.

             The transformer shown above has Np turns of wire on its primary side and Ns turns wire on its secondary side.The relationship between the voltage Vp(t) applied to the primary side of the transfomer and the voltage Vs(t) produced on the secondary side is
                                                   
                                                       Vp(t)  = Np
                                                       Vs(t)      Ns
where a is defined to be the turns ratio of the transformer.
                                                          a= Np
                                                               Ns
The relationship between the current i p(t) flowing into the primary side of the transformer and the current i s(t) flowing out of the secondary side of the transformer is
                                                   Np ip(t) = Ns is(t)
or
                                                ip(t) = 1
                                                is(t)     a

Notice that the phase angle of Vp is the same as angle of Vs and the phase angle of Ip is the same as the phase angle of Is.
Dot And Cross Convention :
                                                                      The realtionship in dot and cross product will become.

• If the primary voltage is positive at the dotted end of the winding with respect to the undotted end , then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the dots on each side of the core.
• If the primary current of the transformer flows into the dotted end of the primary winding , the secondary current will flow out of the dotted end of the secondary winding.