Two known resistances of R and 2 R and one unknown resistance X are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is X , then the value of X is

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Quantrex Academy · Accepted Answer

Correct answer: A. ( 3 -1) R

The circuit has 2R and X in series (top branch) parallel to R (bottom branch).
The equivalent resistance is

R_{eq} = \frac{(2R + X) \cdot R}{3R + X} = X

.
Setting up the equation:

X(3R + X) = R(2R + X)

, which simplifies to

X^2 + 2RX - 2R^2 = 0

.
Using the quadratic formula:

X = \frac{-2R \pm 2R\sqrt{3}}{2} = R(-1 \pm \sqrt{3})

.
Since resistance must be positive,

X = (\sqrt{3} - 1)R

Ω.

Two known resistances of R and 2 R and one unknown resistance X are...

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