Once again, one reply
was all it took to get the right answer. I posted the circuit in Figure 1 just
over a week ago after my second EE Fundamentals entry on the differences
between series and parallel connections. The question asked you to find the
total power dissipation in the circuit. You needed to apply concepts from all
the previous EE Fundamentals segments to solve the problem.

**The correct answer: 3.6 watts.**

**Figure 1. Quiz circuit from the last EE Fundamentals Post**

Similar to my first quiz, the easiest way to solve this
problem is to reduce the circuit to its simplest equivalent model. Step 1 is to
look into the circuit from the perspective of the source, which is a voltage
source in this case. Looking into the circuit from the left, we note that the
source sees two 10 ohm resistors in series with a 20 ohm resistor on the far
side. Adding up these values according to the rules of series connections we
find that these three resistors can be reduced to a 40 ohm resistor. We now
have a circuit that looks like Figure 2 below.

**Figure 2. The circuit from Figure 1 after reducing the far right side**

We want to keep reducing the circuit from right to left.
After combing the first three resistors, we now have two 40 ohm resistors in
parallel with each other. When two resistors of the same value are in parallel
with each other, their equivalent resistance is half their nominal value. In
this example, that means we can model them with a 20 ohm resistor like in
Figure 3. If these resistances were different values, you would need to use the
parallel resistance rules from my first series-parallel post.

**Figure 3. Equivalent circuit after series and parallel resistance reductions**

At this point, it looks just like what we started with in
Figure 1 before reducing the circuit. I would hope that by now you could finish
this up since you just do the same thing over and over until there is only one
resistance left. When you are finished, you should end up with the circuit in
Figure 4.

**Figure 4. Final equivalent model of the circuit in Figure 1**

Cool. So we found the equivalent circuit….but that wasn’t
the question I asked. To find the power dissipation you will have to make use
of the hints I gave you in the quiz question. The power loss in a circuit is
found by summing the power losses of all its elements. Power dissipation in a
circuit element is equal to the voltage across the element multiplied by the
current through the element. If we look at our circuit, we only have one
element to worry about assuming the wires connecting the resistor to the source
are ideal conductors.

So here is what we know:

- Supply Voltage: 12 volts
- Equivalent circuit resistance: 40 ohms
- Power Loss = V * I in the resistor

To get the current, use ohms law (I = V/R) and divide the
voltage across the resistor by its resistance. You should find that the current
is equal to 300 milliamps. Therefore,

Power
= V*I = 12 volts * 0.3 amps =

**3.6 watts**.
It is possible to go branch by branch and sum the various
voltages, currents, and power losses, but that should not change the answer.
Equivalent circuit models like the one we used in Figure 4 are great for
looking at this type of circuit because they break it down to its simplest form
while keeping the analysis completely valid. Next time, we solve RC circuits.

## 1 comments:

Next time, we eat RC circuits.

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