Calculate equivalent resistance

[Vibhor]

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

 

[haruspex]

Homework Statement

View attachment 211076

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

That all looks right to me.

 

[Vibhor]

That all looks right to me.

Thanks for confirming .

But official key states r/6 as the answer .

 

[haruspex]

Thanks for confirming .

But official key states r/6 as the answer .

That is clearly wrong. We could connect ABCDEF with a zero resistance, and the effective resistance from O to there would be r/6. There must be something to add to get to N.

 

[Vibhor]

That is clearly wrong. We could connect ABCDEF with a zero resistance, and the effective resistance from O to there would be r/6. There must be something to add to get to N.

Right .

Sorry , I had read answer of some other question in the key .

Answer key states answer as r/3 .Solution says there would be no current in AX , XN , AY, YN wires . Current would flow from O to A and from A to N . Resistance between O and N would be 2r . Hence equivalent resistance is r/3 .

 

[haruspex]

Solution says there would be no current in AX , XN , AY, YN wires .

Again, clearly false.