Some small transformers for low-power applications are constructed with air between the two coils. Such transformers are inefficient because the percentage of the flux from the first coil that links the second coil is small. The voltage induced in the second coil is determined as follows.
E=NdΦ/dt108
where N is the number of turns in the coil, dϕ/dt is the time rate of change of flux linking the coil, and ϕ is the flux in lines.
At a time when the applied voltage to the coil is E and the flux linking the coils is ϕ lines, the
instantaneous voltage of the supply is:
Since the amount of flux ϕ linking the second coil is a small percentage of the flux from the first coil, the voltage induced into the second coil is small. The number of turns can be increased to increase the voltage output, but this will increase costs. The need then is to increase the amount of flux from the first coil that links the second coil.