I built a simple circuit with two resistors of the same value connected in serie

Question

I built a simple circuit with two resistors of the same value connected in series. For trial 1, I would measure the resistors and voltage(across the 2nd resistor) values of let's say 1kohm using a DMM. Then I would switch those resistors for two other higher ohm resistor such two 10kohms and repeat the steps. After measuring what the values needed, i would switch the resistors to an other higher ohms value all the way to 10M ohms. by the way a 9V battery was used for everything.  When I recorded everything, I noticed that the measured voltage values were very close to each other even though I was switching the resistors everytime. Then I used the voltage divider to calculate the voltage across the 2nd resistor by hand. even so, I was getting approximately the same result. I'm not sure of my recorded and calculated results because isn't the voltage supposed to increase since I'm using higher ohms for each trials? could it have anything to do with the internal resistance of my DDM?

Explanation / Answer

Since voltage source is same for all cases let resistance be R

Since both resistance are same say R.let internal resistance is r

Current across circuit=V/(2R+r)

Voltage across any R=VR/(2R+r)

But since r is very small as compared to R

Voltage is almost equal to V/2 no matter what is R. Actuallt when R is increased, current across circuit will decrease but voltage across R will remain same. It will change very very slightly (almost negligible) due to internal resistance.

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