Consider following circuit made of n resistors with r resistivity like as a mobious strip

I want to find a recurrence equation for equivalent resistor in terms of r and vs. In other words, An equation for equivalent resistor between Req(n+1) and Req(n)

And I want to find Thevenin circuit between A and B.

I think I should use source splitting for Vs. While I don't know how!?

enter image description here

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    \$\begingroup\$ Equivalent resistor...and what? \$\endgroup\$ – Bart Sep 27 '19 at 10:03
  • \$\begingroup\$ Sound like a school assignment. \$\endgroup\$ – Oldfart Sep 27 '19 at 10:04
  • \$\begingroup\$ @Oldfart Yes it is. But I don't have any idea to solve it. I don't want complete solution. I just want a hint. \$\endgroup\$ – Sania Sadian Sep 27 '19 at 10:08
  • \$\begingroup\$ @Bart thevenin equivalent circuit \$\endgroup\$ – Sania Sadian Sep 27 '19 at 10:08
  • \$\begingroup\$ Are all of the resistors equal? If so, what does symmetry tell you about the Thévenin voltage? \$\endgroup\$ – Dave Tweed Sep 27 '19 at 10:18

Here's a hint: Draw out the complete circuit for the N=1 case (5 resistors). Put the voltage source with its positive terminal at the top of the diagram and the negative terminal at the bottom. Does this circuit look at all familiar?


simulate this circuit – Schematic created using CircuitLab

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  • \$\begingroup\$ No. It doesn't look familiar. maybe I can't draw It well. Can you draw it? \$\endgroup\$ – Sania Sadian Sep 27 '19 at 12:29
  • \$\begingroup\$ Hint (and some history): It is Samuel Hunter Christie's 'diamond' method. \$\endgroup\$ – Huisman Sep 27 '19 at 13:04
  • \$\begingroup\$ for this shape, I will find equivalent resistance r/2. (all of 5 resistors have equal resistivity "r"). Is it true !? So I can find thevenin circuit by simplifying the resistors. I think for every n the thevenin voltage is the same!? \$\endgroup\$ – Sania Sadian Sep 27 '19 at 15:26
  • \$\begingroup\$ Yes, the resistance between A and B is r/2 for N=1. And yes, the Thévenin voltage is the same for all N. \$\endgroup\$ – Dave Tweed Sep 27 '19 at 19:12
  • \$\begingroup\$ Ok. Now I can find equivalent resistor. But I don't know how to connect Nth case to (N-1)th case for induction. And also Thevenin resistivity. \$\endgroup\$ – Sania Sadian Sep 29 '19 at 17:16

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