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Question

Find the equivalent resistance between A and B.

A
2r5
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B
2r7
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C
8r5
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D
8r7
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Solution

The correct option is D 8r7
Resistance between A and B can be divided into two equal resistance having value r/2. We can observe that the circuit is symmetrical about the line DF and this is perpendicular to AB.

So, due to the perpendicular axis symmetry, point D and F are equipotential. These two points can be joined. The circuit can be redrawn as:

Resistance between C and D are in parallel. Their equivalent resistance is
r×r/2r+r/2=r3.

Resistances (AC and CD) and (DE and EB) are in series. Their equivalent resistance is
r+r/3=4r3.

Now both the resistance between (A and D) and (D and B) are in parallel. Their equivalent resistance is
r×4r/3r+4r/3=4r/7.

Both the resistances are in series. Their eequivalent is,
RAB=4r7+4r7=8r7

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