Question

The equivalent resistance between point $\text{A}$ and $\text{B}$ is-

• A. $2(\sqrt{3}+2)\Omega$
• B. $2(1+\sqrt{3})\Omega$
• C. $3(\sqrt{3}+2)\Omega$
• D. $3(1+\sqrt{3})\Omega$

Answer 1

The correct option is B $2(1+\sqrt{3})\Omega$



Let, equivalent resistance between $\text{A}$ and $\text{B}$ be $R_{AB}=X$

$R_{AB}=2+\frac{2X}{2+X}+2$

$\Rightarrow X=\frac{8+6X}{2+X}$

$\Rightarrow 2X+X^2=8+6X$

$\Rightarrow X^2-4X-8=0$

$X=\frac{4\pm \sqrt{16+32}}{2}=\frac{4+\sqrt{48}}{2}$

$X=\frac{4+\sqrt{3\times 16}}{2}=\frac{4+4\sqrt{3}}{2}$

$=2(1+\sqrt{3})\Omega$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.