Question

The value of effective resistance between $A$ and $B$ is ? $(R=2k\Omega )$

Answer 1

$R_{AB}=2R+\frac{R.R_{eq}}{R+R_{eq}}$

$R_{eq}=2R+\frac{R.R_{eq}}{R+R_{eq}}$

$Req(R+Req)=2R(R+Req)+R.Req$

$R{R}_{eq}+R_{eq}^2=2R+2R{R}_{eq}+R.R_{eq}$

$R_{eq}^2=2R^2+2R{R}_{eq}$

$R_{eq}^2=2R^2+2R{R}_{eq}$

$x^2-2Rx-2R^2=0$

$x=\frac{2R\pm \sqrt{4R62+8r^2}}{2}$

$=\frac{2R\pm \sqrt{12R^2}}{2}$

$R_{eq}=R\pm \sqrt{3}R$

$R_{eq}$ will never be negative,

Hence:

$R_{eq}=R(1+\sqrt{3})$

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