Question

the resistance between P and Q in the following infinite ladder network of resistance is

Answer 1

Answer:

Correct option is

A

1Ω

Let the equivalent resistance of the combination is R.

So the infinite network can be changed into given network int the image. 

⟹R=R+22R+1

⟹3R+2=R2+2R

⟹R2−R−2=0

⟹R=2Ω                          (∵−ve value can be neglected)

Now, the two resistance of 2Ω each are in parallel to each other and the combination is in series with a combination of 1Ω.

Req=1Ω+2+22×2Ω

Req=1+1⟹2Ω

Required equivalent resistance between point A and B is 2 Ω