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Twelve indentical resistance each of ...


Twelve indentical resistance each of resistance R are joined to form a cube as shown in figure. Find resistance of the combination across AB.

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This circuit cannot be solved by considering series and parallel connections .
All three paths from A to B are identical . Let 3l current entered at end A and left at B. Current is distributed in all branches using symmetry .
If `V_(A) - V_(B) = V`, then `R_(AB) = (V)/(3l)" ".......(i)`
We have
`V_(A) - V_(B) = (V_(A) - V_(p)) + (V_(P) - V_(Q)) + (V_(Q) - V_(B))`
`rArr V = IR + (I)/(2) R + IR`
`rArr V = (5IR)/(2)`
`rArr (V)/(l) = (5R)/(2)`
`rArr R_(AB) = (V)/(3l) = (5R)/(6)`
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