The resistance of the series combination of two resistances is S. When they are joined in parallel the total resistance is P. If S= nP then the minimum possible value of n is

Options

A. 4
B. 3
C. 2
D. 1

Answer

A

Explanation

(a) If two resistance are `R_(1)` and `R_(2)` then
`S = R_(1) + R_(2)` and `P = (R_(1) R_(2))/((R_(1) + R_(2)))`
For given condition `S = nP`
or `(R_(1) + R_(2)) = n (R_(1) R_(2))/((R_(1) + R_(2)))`
`implies (R_(1) + R_(2))^(2) = n R_(1) R_(2) implies (R_(1) - R_(2))^(2) + 4 R_(1) R_(2) = n R_(1) R_(2)`
So `n = 4 + ((R_(1) + R_(2))^(2))/(R_(1) R_(2))`