The equivalent resistance of series combination of two resistors is $s .$ When they are connected in parallel, the equivalent resistance is $p .$ If $s = n p,$ then the minimum value for $n$ is ______.
(Round off to the Nearest Integer)

Question

The equivalent resistance of series combination of two resistors is $s .$ When they are connected in parallel, the equivalent resistance is $p .$ If $s = n p,$ then the minimum value for $n$ is ______.

(Round off to the Nearest Integer)

TestHub · Accepted Answer

R 1 ​ + R 2 ​ = s … ( 1 ) R 1 ​ + R 2 ​ R 1 ​ R 2 ​ ​ = p … ( 2 ) R 1 ​ R 2 ​ = s p R 1 ​ R 2 ​ = n p 2 R 1 ​ + R 2 ​ = ( R 1 ​ + R 2 ​ ) n R 1 ​ R 2 ​ ​ R 1 ​ R 2 ​ ( R 1 ​ + R 2 ​ ) 2 ​ = n for minimum value of n R 1 ​ = R 2 ​ = R ∴ n = R 2 ( 2 R ) 2 ​ = 4

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