Obtain an expression for equivalent resistance of two resistors connected in a series combination.

Explanation

Resistors are said to be connected in series, when (i) the same current passes through each of the resistors (ii) net voltage gets divided such that `V = V_(1) + V_(2)` From Ohm.s law V = IR.
i.e., `V_(1)=IR_(1) , V_(2) = IR_(2)`
`thereforeV=I(R_(1)+R_(2))`
or `R_(x)=(V/I)=R_(1)+R_(2)`
For two resistors in series `R_(x)=R_(1)+R_(2)`
Hence when a number of resistors are connected in series, their equivalent resistance is equal to the algebraic sum of the individual resistances.
Note: For n number of resistors in series `R_(x)=sum_(i=1)^(n)R_(i)`
For n identical resistors in series `R_(x) = nR`.