Question

# Each resistor shown in the figure is an infinite network of resistance 1 Ω. The effective resistance between points A and B is (√3=1.73)

A
Less than 1 Ω
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B
1 Ω
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C
3 Ω
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D
More than 1 Ω but less than 3 Ω
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Solution

## The correct option is D More than 1 Ω but less than 3 Ω We can see that, section FACE is similar to section HBDG. For section FACE, let us assume equivalent resistance between A and C is x. Since, section FACE is an infinite ladder network, so we may consider the given circuit of FACE as From diagram, effective resistance between A and C is given by RAC=(x+2)×1x+2+1=x+2x+3 ⇒x+2x+3=x [∵RAC=x] ⇒x+2=x2+3x ⇒x2+2x−2=0 ⇒x=√3−1 or x=−√3−1 Since, value of resistance can't be negative. ∴RAC=√3−1=0.73 Ω Further, from symmetry, circuit become ∴RAB=0.73+1+0.73=2.46 Ω Hence, option (c) is correct. Why this question ?Key Idea-This question help studentsto understand that how we can combinetwo or more infinite resistor series andfind the equivalent resistance.

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