Problem 2.20   Source:   Problem elaborated by the author of the site.

Calculate the equivalent resistance between the a-b points of the circuit shown in Figure 02-20.1.

Solution of the Problem 2.20

In the circuit above we number the nodes to better understand the solution. See that among points 2-3 we have two resistors in series. One of 2 ohms and one of 22 ohms. Thus the equivalent resistance due to the series of these two resistors is equal to: R'₂₃ = 2 + 22 = 24 ohms . Note that this equivalent resistance paralleled the other resistor, which we will call R''₂₃ = 12 ohms . Below is the equation that allows us to calculate the value of the equivalent resistance. of a parallel circuit formed by two resistors.

Replacing the numerical values we find:

As we can see in the Figure 02-20.2, we can simplify the branch between the points 2-3. Now notice that the situation is the same as before. We have two resistors in series R₂₃₄ = 8 + 22 = 30 ohms and is parallel to R'₂₄ = 30 ohms . Hence the parallel results in an equivalent resistance between points 2-4 with a value of R₂₄ = 15 ohms .

In the Figure 02-20.3, we can see how the circuit looked after the simplifications. See that among points 1-2 we have two resistors in parallel. Solving we found R₁₂ = 10 ohms. And this resistor is in series with the resistor between points 2-4. So, summing the two together we find R₁₂₄ = 25 ohms. But let's not forget that we also have the resistor R'₁₄ =75 ohms between the points 1-4.

So these two resistors are in parallel. Resolving this parallel we find the final value of R₁₄ or R₁₄ = 18.75 ohms.

Now, in the Figure 02-20.4, we see the circuit very reduced. Once again we have two resistors in series, that together we found R₁₄₅ = 18.75 + 6.25 = 25 ohms. And this resistor is in parallel with the resistor R'₁₅ = 100 ohms which is connected between points 1-5 . Then we must find the parallel between them. After the calculations we find the final value of R₁₅ or R₁₅ = 20 ohms.

After all the simplifications, in the Figure 02-20.5, we have the final circuit that will allow us to calculate the value of R_ab . We easily realize that all resistors are in series facilitating the calculation of the resistance that is "seen" through the terminals a-b. Below is the final calculation.

This means that the entire initial circuit can be replaced by a single resistor of value equal to 50 ohms.