Problem + Hard. 2.1
Source: Problem 2.45-b , page 64,
SADIKU, Matthew N. O. , ALEXANDER, Charles K. -
Book: Fundamentals of Electric Circuits - McGraw Hill - 5th edition - 2013.
Calculate the equivalent resistance at terminals a - b of the circuit below.
Solution of the Problem + Hard 2.1
Notice in the circuit that the points c and d are
connected by a wire, that is, a short circuit.
Therefore, point c and point d are the same.
Then we can draw a new diagram as shown below.
Now we can
clearly see that the 12 ohm resistor is in parallel
with the 60 ohm resistor. Using the equation below, which allows
calculate the parallel of two resistors and, substituting for numerical values,
we find an equivalent resistance of 10 ohms.
It is easy to see that this equivalent resistance that we calculated is
in series with the 20 ohms resistor, which
adds up to 30 ohms. Therefore,
we now have two 30 ohms resistors in parallel.
This set of resistors, highlighted in yellow in the figure on the side,
reduces to a single resistor of value equal to 15 ohms (parallel of the two
30 ohms resistors), as seen in the circuit below.
Well, we managed to reduce the circuit considerably. Let's solve
the circuit highlighted in green in the figure on the side.
We have to calculate the series of the 15 ohms and 10 ohms resistors, which
totals 25 ohms. And finally we have a parallel of two resistors
values equal to 25 ohms. Therefore, an equivalent resistance results
of the block highlighted in green with a value equal to 12.5 ohms.
Therefore, we reduce the whole circuit into a much simpler circuit.
as we can see in the figure on the side.
To calculate
the total resistance just add all the values
resistors that are in series.