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Question

# Find the equivalent resistance between A and B.

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

## The correct option is A 8r7Resistance 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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