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JEE Main 2021 (17 Mar, Shift 1) · Combination of Resistors

Combination of Resistors question from JEE Main 2021 (17 Mar, Shift 1)

Q50JEE Main 2021 · 17 MAR · SHIFT 1Medium

Combination of Resistors

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

Numerical answer type. Work it out, then open the answer.

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Answer: 4

$n = \dfrac{s}{p} = \dfrac{(R_1 + R_2)^2}{R_1 R_2}$ .
Since $(R_1 + R_2)^2 \ge 4R_1R_2$ , $n \ge 4$ , with equality for $R_1 = R_2$ .
Minimum $n = 4$

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