I am learning about 1st order transfer functions, and I am trying to understand it with practical examples of systems, because it still looks weird to me how a same function can describe various physical systems. I am currently looking at the transfer function of a simple RC circuit.
It is denoted as
lookig at the standard function, we can tell we have a gain of 1 in this function, as explained in this post
I am ok with the fact that the time constant tau is equal to RC in this particular real world example, as a resistance multiplied by a capacitance can be simplified to time units, a little bit like a speed multiplied by a distance.
however, I am not sure how to look at this and, set apart all the math, intuitively understand why the gain should be 1, rather than anything else. I need help understanding what is the concept behind the gain here, because I am completely lost.
Thank you so much!