An Infinite ladder network of resistance is constructed with 1 Ω and 2 Ω resistances as shown in the figure. The 6 V battery between A and B has negligible resistance. The effective resistance between A and B is:

Question

An Infinite ladder network of resistance is constructed with 1 Ω and 2 Ω resistances as shown in the figure. The 6 V battery between A and B has negligible resistance. The effective resistance between A and B is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-hmq5sj4z3ytbzcxi.jpg" /> (A) 1 Ω (B) 2 Ω (C) 3 Ω (D) 5/8 Ω

Tardigrade Admin · Accepted Answer

x=(2 x/x + 2)+1 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-hmq5sj4z3ytb1ixa.jpg" /> x2+2x=2x+x+2 x2-x-2=0 (.x-2.)(.x+1.)=0 x=2 Ω

Q. An Infinite ladder network of resistance is constructed with $1 Ω$ and $2 Ω$ resistances as shown in the figure. The $6 V$ battery between $A$ and $B$ has negligible resistance. The effective resistance between $A$ and $B$ is :

$1 Ω$

$2 Ω$

$3 Ω$

$5/8 Ω$

$x = \frac{2 x}{x + 2} + 1$

$x^{2} + 2 x = 2 x + x + 2$
$x^{2} - x - 2 = 0$
$(x - 2) (x + 1) = 0$
$x = 2 Ω$

Q. An Infinite ladder network of resistance is constructed with 1Ω and 2Ω resistances as shown in the figure. The 6V battery between A and B has negligible resistance. The effective resistance between A and B is :

1Ω

2Ω

3Ω

5/8Ω