I have a car inverter (DC 12 V to AC 240 V). Inverter's frequency is 60 Hz.
I want to connect the output (240 V) of the inverter to an transformer (AC 240 V to AC 16 V) which indicates input frequency 50 Hz.
Is it ok to connect them? Will the frequency difference damage the transformer?
It's almost certainly okay with the same ratings, with 60Hz and the same voltage in.
Flux density is 20% lower decreasing core losses as transformers are usually optimized to run close to saturation, probably more than compensating for any small increase due to the frequency. Copper (\$I^2R\$) losses will be the same at the same RMS current.
This characteristic is used to advantage in aircraft systems by running transformers at 400Hz rather than 50 or 60Hz which allows proportionally more VA for the same core mass. Because of the relatively high frequency the laminations have to be thinner to reduce eddy current losses though.
Going the other way- running a transformer optimized for 60Hz on 50Hz is a different matter. You can do it if you lower the input voltage by 20%, but at full rated voltage it would most likely overheat, and perhaps dramatically so, since transformers are typically designed to operate just at the edge of saturation with maximum input voltage in order to minimize materials, weight and cost. Saturation means that the dissipation can increase drastically, causing insulation failure and premature death of the transformer. That occurs because the effective inductance drops dramatically when the core saturates.
It is sort of OK. You will not damage it, but the efficiency probably will be lower. It could be a problem for a motor, but a transformer will probably work.
Are you sure 12V isn't enough where you are going to use 16V? Perhaps you could skip the transformer.
A 50 Hz transformer may be safely operated at 60 Hz.
An increase in losses at 60 Hz would be offset by reduction of the same due to lower flux density in the larger 50 Hz core area.
A 50Hz transformer will happily run at 60Hz with minimal change in efficiency (it may be positive or negative, depending on the transformer design compromises).
Then again, connecting whatever transformer to whatever inverter is usually not very good idea.
Cheap inverters tend to generate square-ish wave rich in harmonics (higher frequencies) that may heat the transformer core. Even if the transformer is OK with this, the load that expects AC may not like the square AC either.
Inverters (even the more expensive "pure sine wave" type) may not like the inductive character of the transformer or its not-so-mild transient behavior on power-on. The inverter may shutdown (or even get damaged) in response to the transformer startup current.
And finally, all these problems are solvable, but the whole idea doesn't look very much efficient. 12V sources tend to be limited in available energy and the energy from them is expensive in the first place.
You may get better result by powering whatever needs these 16V by other means.
