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JEE Main 2022 (27 Jun, Shift 2) · Combination of Resistors

Combination of Resistors question from JEE Main 2022 (27 Jun, Shift 2)

Q44JEE Main 2022 · 27 JUN · SHIFT 2Difficult

Combination of Resistors

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be x2\sqrt{\frac{x}{2}}. The value of x is __________.

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

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Answer: 3

  1. Three mama in parallel give ma3\frac{ma}{3}; two am\frac{a}{m} in parallel give a2m\frac{a}{2m}.
  2. Req=ma3+a2mR_{eq} = \frac{ma}{3} + \frac{a}{2m}
  3. For minimum: dReqdm=a3−a2m2=0⇒m2=32\frac{dR_{eq}}{dm} = \frac{a}{3} - \frac{a}{2m^2} = 0 \Rightarrow m^2 = \frac{3}{2}
  4. m=32=x2⇒x=3m = \sqrt{\frac{3}{2}} = \sqrt{\frac{x}{2}} \Rightarrow x = 3
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