We are going to discuss three circuits
Then, the resistors are called, connected in series. Here, this right end of R1, is connected to left end of R2, again, the right end of R2
is connected to left end of R3. Now, we can say, these resistors are connected in series
Voltage, V is connected across the resistors, R1, R2, and, R3. The current, drawn from the battery is, I
This current gets only one path through R1, R2, and R3. Say, voltage drop due to this current, I, across R1 is V1, across R2 is V2, and across
R3 is V3. Therefore, V1 equals I dot R1, V2 equals I dot R2, and V3 equals I dot R3
Now, as per laws of circuit theory, entire voltage V, applied to the circuit is equal
to the sum of the voltage drops across individual resistor. That means, V equals V1, plus V2, plus V3 equals I dot R1, plus I dot R2, plus I dot
R3, say, this is equation 1. Now, we consider the equivalent resistance of this series combined resistors is, R so
at that case, entire supply voltage will drop across this single equivalent resistor of
the system. That means, in this case, V equals I dot R, say this is equation 2
From, equations 1 and 2, we get, I dot R equals I dot R1 plus I dot R2 plus I dot R3
Cancelling, I, from both sides of the equations, we get, R equals, R1, plus R2, plus R3
From this equation, we can say, equivalent resistance of the series connected resistors
is nothing but simple sum of resistance of individual resistor. Instead of 3, if we connect any number of resistors in series, we can write this equation
as, R equals, R1, plus R2, plus R3 plus, dot dot dot, plus Rn
Where, n is the total number of resistors connected in series. Hope you got a basic idea
Thank you