Answer1

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WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 1—What is resistance as seen between terminals A and B in the following infinite network?

Answer:

Let's call the value Rab. Also note that adding another pair of resistors to the left end won't change the final result, so the whole thing can be reduced to the following diagram:

In this network, Rab is equal to the total of 1 ohm in series with the parallel combination of Rab and 1 ohm, or

Rab = Rab × 1
Rab + 1 + 1

After simplification, we get a quadratic equation:

Rab² - Rab - 1 = 0

Solving this for Rab, we get

Rab = 1.6180339887... ohm

This happens to be the "Golden Ratio", which shows up in many areas of mathematics, art and biology.

Contributor: Naveen P N

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