Question

The effective resistance of the infinite resistance
ladder circuit between terminals A and B as shown
in the figure is
​

Answer 1

Answer:

$(1) (2+2\sqrt{2}) \Omega$

Explanation:

1) Let the equivalent resistance of the given Ladder circuit about A and B, be 'x'.

Note : In every forward branch of the ladder network ,, next resistance becomes the twice the previous.

2) Now, as shown in figure if equivalent resistance of given ladder network is 'x' . Then , equivalent resistance across the next branch is '2x'.

That is,

'2x' and '4' are in parallel, and '2' is in series with the required .

$x=\frac{2x*4}{2x+4}+2\\ \\=>(x-2)=\frac{4x}{x+2}\\ \\=> (x-2)(x+2)=4x\\ \\=>x^2-4=4x\\ \\=>x^2-4x-4=0\\ \\=>x=\frac{4+4\sqrt{2}}{2}=(2+2\sqrt{2}) \Omega$

Hence, Equivalent resistance of the given ladder network is

$\boxed{(2+2\sqrt{2}) \Omega}$