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

Question

Two known resistances of $R Ω and 2 R Ω$ 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 ______ $Ω .$ [2026]

Smart Achievers · Accepted Answer

(1)

$\frac{(2 R + x) (R)}{3 R + x} = x$

$x^{2} + 2 R x - 2 R^{2} = 0$

$x = (\sqrt{3} - 1) R$

Solution

Q.
Two known resistances of $R Ω and 2 R Ω$ 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 ______ $Ω .$ [2026]

1 $(\sqrt{3} - 1) R$

2 $2 (\sqrt{3} - 1) R$

3 R

4 $(\sqrt{3} + 1) R$

Ans.
(1)

$\frac{(2 R + x) (R)}{3 R + x} = x$

$x^{2} + 2 R x - 2 R^{2} = 0$

$x = (\sqrt{3} - 1) R$

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Solution

Q. Two known resistances of RΩ and 2RΩ and one unknown resistance XΩ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is XΩ then the value of X is ______Ω. [2026]

1 (3-1)R

2 2(3-1)R

3 R

4 (3+1)R