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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+2x2=0

x=31 or x=31

Since, value of resistance can't be negative.

RAC=31=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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