Question

why the current in series coonection remains same through connected resistances?

Answer 1

In series connection the current passing through the wire is voltage / total resistance.
So every resistor have its potential difference according to its resistance . And if you add all potential difference across a single resistor , it comes equal to potential difference across the battery . I mean potential of the battery is distributed on wire according to its resistance . When the resistance is more then the potential difference is more . But you can say that if potential difference is more (across the high resistance resistor) then there should be more current , but you have to understand that the resistance of that resistor is high . Therefore if there is more potential difference across the resistor then it means it have resistance more (in series case) .
2nd reason : You know that . CURRENT = VOLTAGE / RESISTANCE . From above we get that : DUE TO HIGH RESISTANCE THERE IS HIGH VOLTAGE . SO CURRENT WILL BE SAME , AS VOLTAGE INCREASE THE CURRENT , BUT DUE TO RESISTANCE THE CURRENT GET DECREASES .
NOW ONE MORE THING
CURRENT DECREASE BECAUSE OF MORE COLLISION OF ELECTRON IN THE WIRE . But it has more potential difference , therefore it has more drift velocity or you can say that it has more acceleration .but due to collision the current get decreases EVEN IF THERE IS MORE POTENTIAL DIFFERENCE ACROSS THE HIGH RESISTANCE (high resistance which is connected in series) the current is low due to high resistance .

**IN CASE OF LOW RESISTANCE**
Since this low resistance is connected in series therefore it has potential difference according to its resistance . Therefore it has low potential difference (as the potential is distributed across the resistor and these sum of potential difference across the resistor is equal to the potential difference of batter , eliminate internal resistance )
DUE TO LOW POTENTIAL DIFFERENCE AND LOW RESISTANCE (the low potential difference is due to low resistance , which is in the series) there is the same current . BECAUSE LOW POTENTIAL DIFFERENCE WILL DECREASE THE CURRENT , AND LOW RESISTANCE WILL INCREASE THE CURRENT . BOTH QUANTITY WILL DELETE ITS EFFECT TO PRODUCE SAME CURRENT . CURRENT = POTENTIAL DIFFERENCE / RESISTANCE .

*** SO WE GET HAT : NO MATTER WHAT THE RESISTANCE IS ADDED TO THE CIRCUIT IN SERIES THE CURRENT WILL REMAIN SAME , FOR SAME BATTERY . AND THAT IS EQUALS TO
I = VOLTAGE OF THAT BATTERY / TOTAL RESISTANCE ..

WE TAKE TOTAL RESISTANCE BECAUSE IN THIS TOTAL RESISTANCE THE WHOLE POTENTIAL DIFFERENCE(of the battery) IS GOING TO BE APPLIED . AND VOLTAGE OF THE BATTERY REMAINS SAME (IF IT HAS NO INTERNAL RESISTANCE) THEREFORE O MATTER WHAT THE RESISTANCE IS ADDED TO THE CIRCUIT IN SERIES THE CURRENT WILL REMAIN SAME , FOR SAME BATTERY ....

Answer 2

The simple answer is because current abides by Kirkoff's Law.

"The algebraic sum of all the currents at any node in a circuit equals zero."

So if you pick a spot (node) on a line of a schematic, the currents going into that spot (or node) equal the currents exiting the node. If you're asking for an explanation of Kirkoff's Law, then that is fundamentally an electromagnetic question, which is a very difficult explanation. You need a good understanding of integration of vector fields, differential equations, and electromagnetics. When ever you finally get to your electromagnetics courses, you should ask your professor to derive/explain Kirkoff's Law.