I want to know what will happen when the inverter output is shorted to input. and what is the application of this circuit? According to me,it will settle where Vout=Vin. Correct me if i am wrong.
I think you're referring to an invert gate?
There is in fact a workable analog amplifier design based on 3 such gates in series. In particular the 4069 UBE (unbuffered). A couple of resistors form a suitable feedback circuit as you describe, so that both input and output hover at 1/2 supply voltage. The unbuffered version permits this condition.
I saw it in a Forrest Mims book. He calls it an analog role for a digital IC.
Results with a buffered invert gate are hard to predict.
I want to know what will happen when the inverter output is shorted to input. and what is the application of this circuit? According to me,it will settle where Vout=Vin. Correct me if i am wrong.