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Question
Two resistances X and Y are connected turn by turn:
- in parallel, and
- in series.
In which case the resultant resistance will be less than either of the individual resistances?
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Solution
When two resistances, x and y, are connected:
i. In parallel:
The resultant resistance is given by:
`1/R_p = 1/x + 1/y`
Rp = `(x y)/(x + y)`
Since Rp 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:
Rs = 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.
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