Find the expression for the resistors connected in series

Resistors connected in series: - If the number of resistance are connected one after another in such a way that the same current flows through each resistance, then the arrangement is called resistance in series.

LetR1, R2 and R3 are three resistances connected in a series combination and let  be their effective resistance in the circuit.  
Let V1, V2 and V3 be the P.D. across resistances R1, R2 and R3 respectively. Let ‘V’ be the P.D. of the cell.   Let ‘I’ be the current flow through each resistance.
 According to Ohm’s Law,

Conclusion:  If the resistors are connected in series then.
i.         In a circuit the current is the same in every part of the circuit.
ii.        The resistance of the combination of resistors is equal to the sum of the individual resistors.
iii.      The total voltage across the combination is equal to the sum of the voltage drop across the separate resistors.
iv.      The effective resistance in a series combination is greater than the individual resistances.

v.       This combination is used to increase resistance in a circuit.