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

Question

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

Tardigrade Admin · Accepted Answer

Let equivalent resistance between A and B is R', so given circuit can be reduced as follows <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/276a87b5c49bb3cee7e0dec7bdb33d20-.png" /> R'=R+(2 R × R'/(2 R+R')) ⇒ R'2-R R'-2 R2=0 On solving the equation we get R=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

$\infty$

$R$

$2 R$

$3 R$

Let equivalent resistance between $A$ and $B$ is $R^{'}$ , so given circuit can be reduced as follows

$R^{'} = R + \frac{2 R \times R ^{'}}{( 2 R + R ^{'} )}$
$\Rightarrow R^{^{'} 2} - R R^{'} - 2 R^{2} = 0$
On solving the equation we get $R = 2 R$ .

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

Let equivalent resistance between A and B is R′, so given circuit can be reduced as follows R′=R+(2R+R′)2R×R′​ ⇒R′2−RR′−2R2=0 On solving the equation we get R=2R.

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

$\infty$

$R$

$2 R$

$3 R$

Let equivalent resistance between $A$ and $B$ is $R^{'}$ , so given circuit can be reduced as follows

$R^{'} = R + \frac{2 R \times R ^{'}}{( 2 R + R ^{'} )}$
$\Rightarrow R^{^{'} 2} - R R^{'} - 2 R^{2} = 0$
On solving the equation we get $R = 2 R$ .