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 RAB, or:
