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Question

An infinite ladder network is constructed with 1 Ω and 2 Ω resistors as shown. The effective resistance between A and B is



A
1 Ω
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B
2 Ω 
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C
3 Ω 
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D
4 Ω 
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Solution

The correct option is B 2 Ω 
Let the equivalent resistance between A and B be X. If we retain the basic repetitive unit then the remiaing circuit is identical to the total circuit and hence will also posses a resistance X.

RAB=X=2X2+X+1

2X=(2+X)(X1)

2X=2X+X2X2

X2X2=0

X22X+X2=0

(X+1)(X2)=0

X=2 Ω

Hence, the correct answer is (B).

Physics

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