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An infinite ladder network is constructe...

An infinite ladder network is constructed with `1Omega `and `2Omega` resistors as shown. Find the equivalent resistance points `A` and `B`.

A

`1Omega`

B

`2Omega`

C

`3Omega`

D

`4Omega`

Text Solution

Verified by Experts

The correct Answer is:
B
The equivalent circuit is

`R_("eq")=(2xxR_("eq"))/((2+R_("eq")))=(2+3R_("eq"))/(2+R_("eq")) i.e. R_("eq")^(2)-R_("eq")-1=0``Rightarrow R_("eq")=(1)/(2)[1pmsqrt(1+8)=2Omega`
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