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Question

Find the equivalent resistance between A and B.

A
2r3
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B
r
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C
r2
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D
r3
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Solution

The correct option is A 2r3
Given circuit is symmetrical about the line 123 and it is perpendicular to AB.


So, due to the perpendicular axis symmetry, point 1, 2 and 3 are equipotential. So resistors between them can be removed since current will not flow through them.

Now, the resistors between A1 and 1B are in series. Their equivalent resistance will be r+r=2r. Similarly resistors A2, 2B and A3, 3B have equivalent resistance 2r.

Now all three are in parallel combination. Their equivalent resistance will be, RAB=2r3

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