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
B
2 Ω
C
3 Ω
D
4 Ω

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)(X−1) ⇒2X=2X+X2−X−2 ⇒X2−X−2=0 ⇒X2−2X+X−2=0 ⇒(X+1)(X−2)=0 ∴X=2 Ω Hence, the correct answer is (B).Physics

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