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JEE Main 2026 (21 Jan, Shift 2) · Combination of Resistors

Combination of Resistors question from JEE Main 2026 (21 Jan, Shift 2)

Q4JEE Main 2026 · 21 JAN · SHIFT 2Medium

Combination of Resistors

Two known resistances of R ΩR\ \Omega and 2R Ω2R\ \Omega and one unknown resistance X ΩX\ \Omega are connected in a circuit as shown in the figure. If the equivalent resistance between points AA and BB in the circuit is X ΩX\ \Omega, then the value of XX is __________ Ω\Omega.

Figure

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Answer: (c)

  1. (2R+X)(2R + X) is in parallel with RR: X=R(2R+X)3R+XX = \dfrac{R(2R + X)}{3R + X}
  2. 3RX+X2=2R2+RX⇒X2+2RX−2R2=03RX + X^2 = 2R^2 + RX \Rightarrow X^2 + 2RX - 2R^2 = 0
  3. X=−R+R2+2R2=(3−1)RX = -R + \sqrt{R^2 + 2R^2} = (\sqrt{3} - 1)R
  4. So the answer is (c) (3−1)R(\sqrt{3}-1)R.
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