# Resistive Networks

### F. Poyo (yoshi.tamori@gmail.com)

Let us think about the following resistive network.
```
(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.)

# Question

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---+---...
|       |       |       |       |

...
```

```
(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?

# Solutions

Mathemusement

yoshi.tamori@gmail.com