What is the purpose of the resistor in a RC circuit?

I answered this SE EE question yesterday.

My answer

Unlike the other "frequency" explanations, I will use the more intuitive "time" explanations.

V-to-I converter

The purpose of the resistor in an RC circuit is to "convert" the input voltage into output current; so it acts as a voltage-to-current converter (actually, the resistor does not convert but only determines the current according to Ohm's law).

I-to-V integrator

The single capacitor converts the constant input current into linearly changing output voltage; so it acts as a current-to-voltage integrator.

V-to-V integrator

The combination of the two cascaded converters converts the constant input voltage into exponentially changing output voltage; so it acts as a bad voltage-to-voltage integrator. It is interesting to see how we can make it perfect again...

Generalization

Besides in an RC circuit, we can see the same resistor in an R1R2 voltage divider, RD logarithmic converter, RLED voltage indicator, RBE transistor switch, RL differentiator, RA voltmeter made through an ammeter, etc. The resistor converts all these current-input devices into voltage-input devices.

You can follow the RC circuit evolution in detail in my other two answers:

Charging of capacitor in RC circuit

What is an integrator topology?

My comments

1. @Scott Seidman, Very useful practical explanations... But just to add that when we explain circuit ideas, principles, concepts... we use "ideal" elements... simply because the ideas are "ideal". In this case, the details get in the way of understanding the main thing...
2. @比尔盖子Very interesting... I feel like I wrote this nice story because it does not repeat well-known things about circuits but reveals the philosophy behind them... It gives me hope that in addition to concrete thinking people, there are also "circuit philosophers" here...