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

Question

G1 Physics · Accepted Answer

Between A and B, one branch has resistance R. The second branch contains 2R and X in series, so its resistance is 2R + X. Therefore the equivalent resistance is R(eq) = R(2R + X)/(3R + X). The question states that R(eq) = X. Hence, X = R(2R + X)/(3R + X). Cross-multiplying: X(3R + X) = R(2R + X). Therefore, X² + 2RX - 2R² = 0. Solving the quadratic, X = [-2R + √(4R² + 8R²)]/2 = [-2R + 2√3R]/2 = (√3 - 1)R. The other root is negative and is not a physical resistance. Correct option: A.

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