hi thanks very much for the clarifications i'm beginning to see where i've been going astray let me check one more thing if you would be so kind if we attach a load of impedance zs which may be frequency dependent across the secondary then the equation should hold provided that the load is a linear system these variables are the complex fourier transforms of their time domain counterparts such as is t and vs t i'm asking this only because i think this is where i'm going astray personally i think that we should avoid complex quantities phasors at least in the initial sections for lay people transformers seem hard enough to understand without introducing complex voltages and currents i suspect most people would feel confused by them leibniz says that complex numbers are amphibians caught halfway between being and non being do you measure an imaginary current with an imaginary meter i'll stop by again in a few days i need to read up some more before i can feel that i have a clue but i'm trying sincerely and i hope you can hang on a little longer