It took me a long time to understand that current is constant throughout the circuit. And now I am stuck at one last thing: The speed of charge. Here is what I am thinking:
Current is defined as quantity of charge passing through a point at a given time, and from this we can deduce that current is constant throughout a circuit. But, if this is true, then wouldn't the speed of charge through a resistor be increased? Let us think about an analogy, water flowing through a pipe. Suppose water is flowing through a broader pipe(analogous to a less-resistance wire), and a greater quantity of water can flow past a point because of larger cross-sectional area. Now, suddenly water encounters a smaller pipe(analogous to the resistor). So, less quantity of charge can flow through it because of less cross-sectional area. But, if the volume of water flowing in a time $T$(analogous to current) is same, won't the rate of flow of water in the narrower pipe(the resistor) be more?
I am asking this question because while seeing some answers for the question that "Why is current constant?" , I saw some people saying that speed of charge slows down a bit through a resistor, which seems incorrect to me.