Question

Find the net resistance of this circuit?

Answer 1

`(1 + sqrt5)/2 R`

Explanation:

I am assuming that you want the resistance seen by the battery. Note that if you were to drop the first two resistors, the rest of the resistive network will be identical. So, if the equivalent resistance is `R_oo`, then we must have

`R_oo = R+R||R_oo`

so that

`R_oo = R+(R R_oo)/(R+R_oo)`

and so

`(R_oo - R)(R+R_oo)-R R_oo = 0`

or

`R_oo^2 -R R_oo -R^2 = 0`

Which can se solved to get

`R_oo = (1 + sqrt5)/2 R`

(where we ignore the negative root of the quadratic).