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JEE Main 2004 (AIEEE) · Combination of Resistors

Combination of Resistors question from JEE Main 2004 (AIEEE)

Q76JEE Main 2004 · AIEEEMedium

Combination of Resistors

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

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Answer: (c)

$S = R_1 + R_2$ , $P = \dfrac{R_1 R_2}{R_1 + R_2}$ , so $n = \dfrac{S}{P} = \dfrac{(R_1 + R_2)^2}{R_1 R_2}$ .
By AM–GM, $(R_1 + R_2)^2 \ge 4R_1R_2$ , so $n \ge 4$ (equality when $R_1 = R_2$ ).
So the answer is (c) 4.

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