Problem 2.9   Source:   Problem elaborated by the author of the site.

Calculate the equivalent resistance between the points a-b of the circuit shown in Figure 02-09.1.

Solution of the Problem 2.9

In the circuit above, the nodes are enumerated for clarity of solution. Notice that by the way 1-2-3 there are two resistors in series, one of 20 ohms and the other of 80 ohms . Thus, the equivalent resistance of this branch was called R ₁₂₃ = 80 + 20 = 100 ohms . In this way this resistance was in parallel with that which is between points 1-3. Therefore, the equivalent resistance of this branch, which was called R₁₃ will be:

It is easy to see that this resistance was in series with those between the a-1 points and b-3. So the value of the equivalent resistance by path a13b is equal to:

Of course this resistance is parallel to the resistor of 200 ohms which is between the point a-b, then:

That is, we can replace the entire circuit of the figure above with a single resistor of equal value 100 ohms.