what is the effect of the gap(core gap) in transformer on the output so if the gap bigger what will happen if it is smaller what will happen and if no gap what will happen

 

The simplest explanation is to not allow the core to go into saturation. You can find gap equations from the data based upon the material you are using. Saturating a core means excessive current which means HEAT!

Cheers, DPW [ Everything has limitations...and I hate limitations.]

 

In general, increasing gap of the core will reduce the amount of inductance you get but make the inductance more stable with applied current. It also moves the "saturation point" to a higher value of current.

 

open air gap on the core, one is for storage energy. other is what core is not saturation at DC current, air gap is relation inductance coefficient, air gap is bigger, inductance coefficient is lower.