An infinite ladder network is arranged with resistances R and 2R as shown. The effective resistance between terminals A and B is

Question

An infinite ladder network is arranged with resistances R and 2R as shown. The effective resistance between terminals A and B is (A)  ∞  (B)  R  (C)  2R  (D)  3R

Tardigrade Admin · Accepted Answer

: Let the total resistance of the infinite ladder network be Z. Subtract first step from the infinite network. The total resistance of the remaining ladder still remains to be Z.

∴

Resistance between C and

D = \frac{2 R \times Z}{2 R + Z}

Total resistance between A and

B = R + \frac{2 RZ}{2 R + Z}

∴

Z = R + \frac{2 RZ}{2 R + Z}

Or

(2 RZ + Z^{2})

= (2 R^{2} + 2 Z) + 2 RZ

or

Z^{2} - RZ - 2 R^{2} = 0

or

(Z - 2 R) (Z + R) = 0

or

Z - 2 R = 0;

or

Z = 2 R

Q. An infinite ladder network is arranged with resistances $R$ and $2 R$ as shown. The effective resistance between terminals A and B is

$\infty$

$R$

$2 R$

$3 R$

Q. An infinite ladder network is arranged with resistances R and 2R as shown. The effective resistance between terminals A and B is

∞

R

2R

3R

Q. An infinite ladder network is arranged with resistances $R$ and $2 R$ as shown. The effective resistance between terminals A and B is

$\infty$

$R$

$2 R$

$3 R$