- #1
Vibhor
- 971
- 40
Homework Statement
Homework Equations
The Attempt at a Solution
In the attached image the outer circular wire is represented as N . We have to find the equivalent resistance between O and N . Consider a battery of voltage V between O and N . From O there are six similar paths OA ,OB,OC,OD,OE,OF . Now , All six points would be equipotential . Consider any point , say A . No current would flow between A and B . From A there are three paths AX, AN,AY . AX and AY are symmetric w.r.t to AN so current would flow from A to X and then from X to N . Similarly current would flow from A to Y to N . Current would flow directly from A to N .I have drawn the currents in attached image .
Resistance between A and N would be 2r || r || 2r = r/2 .Resistance between O and N via A would be r+r/2 = 3r/2 . Now there are six similar parallel paths from O to N .Hence equivalent resistance would be r/4 .
Is that correct ? Is the reasoning also valid ?
Many Thanks