JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Current Electricity

Two known resistance of

R Ω

and

2 R 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 is ____

Ω

Answer: (A)

Solution

From the circuit, the equivalent resistance is

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

. Cross-multiplying:

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

, which gives

2 R^{2} + R X = 3 R X + X^{2}

. Rearranging:

X^{2} + 2 R X - 2 R^{2} = 0

. Using the quadratic formula:

X = \frac{- 2 R \pm 4 R ^{2} + 8 R ^{2}}{2} = \frac{- 2 R \pm 2 R 3}{2} = R (- 1 \pm 3)

. Taking the positive value:

X = (3 - 1) R

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option