Why are resistance connected in series ?

Explanation

Resistors in Series Combination : Two or more resistors are said to be connected in series when these are connected one after the other and current flowing through each resistor remains same.
Let we have three resistors of resistances `R_1, R_2 and R_3`
V = Total potential difference applied by the battery.
I = Total current flowing through the circuit.
Let `V_1, V_2 and V_3` be the potential difference across resistors `R_1, R_2 and R_3` respectively, then
`V=V_1 + V_2 + V_3" "...(1)`
Using Ohm.s law for `1^(st)` resistor, `V_1 = IR_1`
Using Ohm.s law for `2^(nd)` resistor, `V_2 = IR_2`
Using Ohm.s law for `3^(rd)` resistor, `V_3 = IR_3`
Putting these values in eqn. (1), we get
`V = IR_1 + IR_2 + IR_3`
Let `R_s` = Net resistance in series combination
`V=IR_s`
`implies IR_s =IR_1+IR_2+IR_3`
`IR_s=I(R_1+R_2+R_3)`
`R_s = R_1 +R_2+R_3`

Thus, the equivalent resistance of a number of resistors connected in series is equal to the sum of individual resistances,
Resistors in Parallel Combination