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Question

Find the effective resistance between A & B.


A
7R12
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B
R(1+3)2
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C
R(1+5)2
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D
R12
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Solution

The correct option is C R(1+5)2
Let the effective resistance between A & B be RE.

Since the network is infinite long, so removal of one group of resistance from the chain will not change the network.

Therefore, effective resistance between points C & D would also be RE.

The equivalent network will be as shown below.


The original infinite chain is equivalent to R in series with R & RE in parallel. So the effective resistance of infinite network will be

RE=R+RRER+RE

RER+R2E=R2+2RRE

R2ERRER2=0

RE=R±R241(R2)21

RE=R(1±5)2

Taking positive value, because resistance can't be negative.

RE=R(1+5)2

Hence, option (a) is correct.
Key Concept:
In an infinitely long network, addition or removal of one section from the chain still leaves the chain infinite (i.e. just about the same as before).

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