You had a water powered motor whose speed was proportional to current flow.
The motor itself offered very little resistance to current flow - you had to control the current flow external to a pump.
You has a pump able to pump 10 litres per second through a 10 metre pipe to the motor then through the motor and then through another 10 metre pipe to the suction side of the pump. (Flow rate was related to the pressure that the pump made and pipeline resistance - ie NOT a positive displacement pump.
When the pump was operated you found that the motor ran MUCH too fast and that you needed to limit flow to about 1 litre/second.
To achieve the requirement you could place a reducing valve in the circuit to drop most of the pressure and to limit the flow. The valve worked to drop a certain amount of pressure across it at a given flow rate and as adjustable. (This is about how many rel water valves do work).
You could place the valve ANYWHERE in the circuit and it would achieve the desired result. It could be at the pump inlet or exit or at the motor exit or inlet or anywhere in either pipe.
This is a close analogy to you LED question. The current needs to be limited as it is too high without a limiter. The limiter may be placed anywhere in circuit.
With the Battery - resistor LED circuit
The LED has a certain defined voltage drop at a chosen current.
To be specific lets say that at 20 mA the LED drops exactly 3.00 Volt. This is typical of some modern LEDs.
If we wish to run the LED at 20 mA we MUST arrange for it to drop 3 V - not more and not less.
If we wish to use a 9V supply to operate the LED we N=MUST "get rid of" 9-3 = 6B somehow.
The resistor does this.
To drop 6V at 20 mA the resistor needed is R = V/I = 6 / 0.02 = 300 ohms.
In this example a 9V battery + a resistor + an LED will operate at 20 mA. The resistor can be placed before or after the LED. The current is dropped across it in either location.
It is not relevant to this question but extremely important to know that your statement that
- "we know that series ciircuit, the current is constant at every point."
There are many circuits where this is rue -but also many circuits where it is not true.
In DC circuits with only resistive components, such as this 1 LED, 1 resistor circuit, then it is true. BUT when there are reactive components present such as inductors and capacitors or certain other non linear elements then it is often NOT true.