Find the effective resistance of series connection of parallel resistors.

Explanation

The connection of a set of parallel resistors that are connected in series, is a series - parallel circuit.
(i) Let `R_(1)` and `R_(2)` be connected in parallel to give an effective resistance of `R_(p1)`.
(ii) Similarly , Let `R_(3)` and `R_(4)` be connected in parallel to give an effective resistance of `R_(p2)`.
(iii) Then , both of these parallel segments are connected in series (Figure).

For parallel connection, the effective resistance is `(1)/(R_(p)) = (1)/(R_(1))+(1)/(R_(2))`
Using equation
`(1)/(R_(p1)) = (1)/(R_(1))+(1)/(R_(2))`
`(1)/(R_(p2)) =(1)/(R_(3)+(1)/(R_(4))`
`R_(p1)` and `R_(p2)` are connected in series
Finally , using equation `R_(s) = R_(1)+R_(2)` the net effective resistance is given by
`R_("total") = R_(p1)+R_(p2)`