Problema 2.19   Source:   Adapted of the Exercicie 2.31 - page 65 - THOMAS, Roland E. & ROSA, Albert J. & TOUSSAINT, Gregory J. - Book: The Analysis and Design of Linear Circuits - 6ª edição - Ed. John Wiley & Sons, Inc. - 2009.

In the circuit shown in the Figure 02-19.1, find the equivalent resistance between the following terminals:

a) A-B

b) A-C

a) B-D

Solution of the Problem 2.19

Item a

Note that the resistors of 30 and 10 ohms that are connected to point 1 do not interfere with the calculation because the other side of these resistors is in a open circuit. Thus, the resistors of 40 and 80 ohms that are connected to point 1 are in a serial connection. Thus, a single resistor of value 120 ohms results. And this is parallel the resistor of 40 ohms that interconnects the points A-2. This parallel results in a resistor of value 30 ohms . And this resistor is in series with the 60 ohms resistor that is connected between the B-2 points. Performing the sum, we will find:

Item b

In this case, the resistors of 60 and 10 ohms that are connected to point A and point D respectively , are the ones that do not interfere with the calculation, because the other side of these resistors is in an open circuit. Thus, the resistors of 40 and 80 ohms that are connected between points A-2-1 are in a serial connection. Thus, a single resistor of value 120 ohms results. And this is parallel to the resistor of 40 ohms that interconnects the points A-1. This parallel results in a value resistor 30 ohms. And this resistor is in series with the 30 ohms resistor that is connected between the 1-C points. Performing the sum, we will find:

Item c

For the calculation of equivalent resistance between BD points, the only resistor that does not interfere with the calculation is the 30 ohms resistor that is connected to 1-C points. So the two resistors of 40 ohms that interconnect the points 1-A-2 are in series, resulting in a single resistor of 80 ohms. And this resistor is in parallel with the 80 ohms resistor that is connected between points 1-2, resulting in an equivalent 40 ohms resistor. And this resistor is in series with the resistors of 60 ohms and 10 ohms. Performing the sum, we will find: