Problem 2.10   Source:   Problem elaborated by the author of the site.

Calculate the equivalent resistance between the points A-B of the circuit shown in Figure 02-10.1.

Solution of the Problem 2.10

In the circuit above the nodes were enumerated for a better understanding of the solution. Between the points 2 and 3 there are two resistors in parallel: one of 80 ohms and one of 20 ohms. Thus, the equivalent resistance due to the parallel of these two resistors is equal to R₂₃ = 16 ohms. Note that this equivalent resistance was in series with the other resistors that are connected to points 1-4. Thus, the equivalent resistance presented by this branch, which was called R'₁₄, is R'₁₄ = 14 + 16 + 40 = 70 ohms.

You can now work with the lower branch between 5 and 6 . Note that the situation is the same as before. There are two resistors in parallel, resulting R₅₆ = 15 ohms . Hence, it results in an equivalent resistance between points 1 and 4 of value equal to R''₁₄ = 30 ohms.

It is easy to see that these two sets of resistors stayed in parallel. So:

Note that there is a resistance of 10 ohms connected between points A and 1 as well as one of 9 ohms linked between points B and 4 . Therefore, calculating the series of these three resistors is the value of R_AB, or: