Ratio
Vs / Vp = Ns / Np. More secondary turns raise voltage. For bounded power, current capacity moves the other way.
Induction, visible
Follow the energy
Vs / Vp = Ns / Np. More secondary turns raise voltage. For bounded power, current capacity moves the other way.
AC continuously changes core flux. At steady DC, flux stops changing and secondary voltage disappears.
Bmax = Vp / (4.44 f Np A). Low frequency, high voltage, too few primary turns, or too little core area push the core past its useful region.
Transfer evidence
Set the supply and frequency first. Control flux with primary turns and core area, then choose secondary turns for voltage and load resistance for current.