Show that if a resistance connected in a parallel combination is much smaller than the other resistance of the combination,then the equivalent resistance of the combination is almost equal to the small resistance.

Explanation

IF R be the equivalent of the resistance `R_1,R_2,R_3…..` connected in a parallel combination , then
`1/R=1/R_1+1/R_2+1/R_3+…….`
Suppse `R_1` is much smaller than `R_2,R_3……`
i.e., `R_1 lt R_2,R_3……`
So, `1/R_1gt1/R_2+1/R_3,.....`
Therefore , the terms `1/R_2,1/R_3,.....` of the expression `(1/R_1+1/R_2+1/R_3+.....)` can be neglected.
So, `1/R=1/R_1or,RapproxR_1`