(A)
+---R---o---R---+
| | |
R R R
| | |
+---R---o---R---+
(B)
The equivalent resistance of the above resistive circuit (thus, the resistance observed between terminals (A) and (B)) is
3
Re = --- R
5
The following one
+---R---+---R---+---R---+---R---+
| | | | |
R R R R R
| | | | |
+---R---+---R--(A)--R---+---R---+
| | | | |
R R R R R
| | | | |
+---R---+---R--(B)--R---+---R---+
| | | | |
R R R R R
| | | | |
+---R---+---R---+---R---+---R---+
has
49
Re = ---- R.
93
It may have mistake. (Sorry about that in the case.)
The question is to solve the equivalent resistance between (A) and (B) for the following infinitely extended circuit.
...
| | | | |
...---+---R---+---R---+---R---+---R---+---...
| | | | |
R R R R R
| | | | |
...---+---R---+---R--(A)--R---+---R---+---...
| | | | |
R R R R R
| | | | |
...---+---R---+---R--(B)--R---+---R---+---...
| | | | |
R R R R R
| | | | |
...---+---R---+---R---+---R---+---R---+---...
| | | | |
...
It is good idea to think about the following resistive ladder.
(A)o---R---+---R---+---R--- ...
| |
R R ..... (repeat infinitely)
| |
(B)o-------+-------+------- ...
Someone may have a hunch that the equivalent resistance of
the above resistive ladder be an irrational number.
Do you believe that? Then what about the first network
in question?