Infinite Ladder Resistance Network- Classic Problem

Q. An infinite ladder is constructed with 1Ω and 2Ω resistors as shown in the figure below. Find the effective resistance between points A & B.

The Solution-

Notice that the entire resistor network is made up of one simple repeating unit i.e -
As the question states this unit repeats itself infinite number of times.

Firstly lets say that the total effective resistance offered by infinite repeating units is R.

Now, we can redraw a simpler diagram by replacing the infinite repeating units by a single resistor, R-
But, what if we separate out (or add) one more of the repeating units to the original circuit? It will not change the total resistance of the circuit.
(infinite units + 1 unit= infinite units)

Alright! Let's calculate the total resistance in the above circuit.
Rtotal  is nothing but the effective resistance, R.

Therefore, the total resistance between points A & B is 2 Ohms!

After all, resistance is futile 😊

Do leave a comment if this article helped you understand resistor networks better :)

Comments

1. Excellent answer

2. After many ,,(actually infinite) searches I found the correct procedure thanks!

3. Top class answer