Question

The equivalent resistance between the terminals P and Q of infinite network as shown in the figure is

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

Answer 1

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

Let the total Resistance be X

then we can write circuit as drawn

$R_{eff}=X$

$X=2R+\frac{RX}{R+X}$

$(R+X)X=2R^2+2RX+RX$

$RX+X^2=2R^2+2RX+RX$

$X^2-2RX-2R^2=0$

$X=\frac{2R\pm \sqrt{4R^2+8R^2}}{2}$

$X=\frac{2R+2R\sqrt{3}}{2}$

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