Question

Two resistances X and Y are connected turn by turn:

1. in parallel, and
2. in series.

In which case the resultant resistance will be less than either of the individual resistances?

Answer 1

When two resistances, x and y, are connected:

i. In parallel:

The resultant resistance is given by:

`1/R_p = 1/x + 1/y`

R_p = `(x y)/(x + y)`

Since R_p​ is the reciprocal of the sum of reciprocals, it is always less than either x or y individually (provided both x and y are positive).

ii. In series:

The resultant resistance is given by:

R_s​ = x + y

This is always greater than either x or y individually.

∴ The resultant resistance will be less than either of the individual resistances when the resistors are connected in parallel.