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Figure shows an infinite ladder network ...

Figure shows an infinite ladder network of resistances. The equivalent resistance between points X and Y is

A

Ainfinite

B

`3Omega`

C

`8.62Omega`

D

`1.62Omega`

Text Solution

Verified by Experts

The correct Answer is:
D
Identify the repeating branch and replace it with single resistance having equivalent resistance as shown in below figure,

Now find equivalent resistance of the above network.
Let `R_(eq)` be the equivalent resistance of this network.
`impliesR_(eq)=1+(R_(eq)xx1)/(1+R_(eq))`
`impliesR+R^(2)=1+R+R`
`impliesR^(2)-R-1=0`
`impliesR=(1pmsqrt(1+4xx1))/(2xx1)`
`impliesR=(1pmsqrt5)/(2)`
`impliesR=1.62Omega`
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