Question

The equivalent resistance in the infinite ladder network shown in the figure, is $R_e$.
$Thevalue{R}_e/Ris$

• A. 2.62

Answer 1

The correct option is A 2.62

For an infinite ladder network, if all the resistance are comprises of same value R, then

$\therefore R_{eq}=R+\frac{R.R_{eq}}{R+R_{eq}}$ .... (i)

After solving equation (i) we get,
$R_{eq}=\left(\frac{1+\sqrt{5}}{2}\right)R$ .... (ii)

From the given question, the circuit can be redraw as
$\therefore R_e=R+R_{eq}$ ... (iii)

From equation (ii) and (iii) we get,

$R_e=R+\left(\frac{1+\sqrt{5}}{2}\right)R=2.618R$ ... (iv)

$or\frac{R_e}{R}=2.618=2.62$