I just started learning about circuits in Chapter 6 of "Computational Complexity". There is an emphasis on the fact this model of computation allows different circuits for different input sizes of the problem. The authors refer to this as a nonuniform model of computation.
My question is: why do we need to use circuits for this type of model? Couldn't we just as well allow for a different Turing machine for each input size? Is there some subtle reason for why we need to use circuits in order to study this model of computation?