Need help in solving circuits using linearity property

Discussion in 'Homework Help' started by Azlaan, Nov 18, 2014.

  1. Azlaan

    Thread Starter New Member

    Nov 10, 2014
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    I am a little bit confused which method is easy to adopt to become expert in solving any type of circuit. First, I used Nodal Analysis then came to Mesh/Loop Analysis but finding currents after nodal voltages have been calculated is a bit more complex for me than calculating voltages after currents have been found using mesh analysis. I know both methods have their pros. & cons. like mesh analysis is difficult to apply if there is some non-planer circuits as compare to nodal analysis. But I myself worked hard in mesh analysis than nodal so that there could be a method in which I would get expertise. So first please suggest me, is my approach OK??.

    I was solving circuits using linearity property from the "fundamentals of Electrical circuits" by Charles Alexander 4th ed. the questions given in practice exercises looked piece of cake but the circuits in exercises got more complex so I got a solution manual and the author of solution manual used some shortcuts or whatever but I didn't get him. Please have a look on these pictures here, how he is using things to get answers and what he is assuming like in book mentioned that we assume some value and make calculations accordingly and then get our answers straight later. If anyone can explain the steps I'd be much Obliged.

    Is it a good approach to be carried on even for more complex circuits. ??
    https://www.dropbox.com/s/jupas85nb4wttep/1.png?dl=0
    https://www.dropbox.com/s/69rccev2na5xy7e/2.png?dl=0
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    As you indicated, all methods have pros and cons. That is why we don't have just one method available to us. Think of the toolbox of a good mechanic. They will have a number of different tools and most jobs could be performed using several of them. Their skill lies in knowing which tool to use for which job and how to use it effectively. Also, they won't have every tool in the world and there will be jobs for which they either don't have the best tool or might not even know about the best tool for that job, but they have skill with the tools they do have and therefore can still do the job with them. Circuit analysis and design is the same way -- learn how to skillfully use as many tools as you can and how to know when to use one tool over another and how to apply tools well even when the choice of that tool wasn't optimal. All of this involves lots of practice and experience. One of the best ways to get it is to analyze the same circuit using multiple approaches and ask your self which way was best for that circuit and what was it about that circuit that made some techniques easier than others.
     
  3. WBahn

    Moderator

    Mar 31, 2012
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    In the first one, he is simply using the kind of basic circuit analysis that you should have learned early on. Combining resistances and seeing that they work out to nice, neat values. Once he gets to a circuit that has the current source in parallel with two 8 Ω resistors, it is obvious that the current splits into two equal currents. But one of those this splits equally down the two 6 Ω paths, so each gets 1/4 of the total current and that current is what goes through the resistor for which the voltage is sought. This is a case where an ad-hoc approach is very effective because the component values work out nicely. But don't think that this only happens in textbook exercises. Remember, designers design circuits with one goal being for them to be easy to understand and analyze, so it is pretty common for "nice" values to exist in real world circuits.

    If the values weren't nice, or if you didn't recognize them as such, then this would be a case where mesh analysis would work well since you have three mesh equations but one of them is known by inspection, leaving you with just two unknowns.

    When solving a circuit, it is good to get in the habit of asking what you expect the answer to be. Try to get an estimate, even if you can only get it within an order of magnitude, but especially see if you can get the polarity of the answer. That will give you a sanity check to compare to your final result, which will let you catch quite a few mistakes. Also, in trying to get a sanity check answer, you often realize that you can get the exact answer by inspection. This circuit is one such example of that.

    In the second one, he used a wye-delta transform which made the circuit pretty trivial. I tend not to use these transforms too much, not because they aren't useful and a good tool, but because the kinds of circuits I work with seldom lend themselves to it. As a result, I'm sure that there are times that I could use such a transform very effectively but, instead, use other tools. That's a case of using a suboptimal tool but, if used effectively, still works just fine.

    In this case, I would tend to use nodal analysis because there are four nodes and you get to declare one of them to be 0V and another is trivially known, leaving you with just two unknowns. This is another case in which coming up with an estimate revealed the exact answer by inspection. When I asked myself what I expected the answer to be close to, I looked for a simplification to the circuit that would make it easy to get an answer and that was to remove the right hand resistor in the tee. Doing that, the answer would obviously be Vs/2. The next step was to ask whether I expected the actual answer to go up or go down when that resistor was reinserted at which point I realized that, without it, the voltage at the middle node would also be Vs/2 in which case their would be no voltage across the resistor and, hence, no current through it. That was not expected, but looking at the circuit just a bit more reveals that it is nothing more than a balanced Wheatstone bridge circuit with the resistor I mentally removed being the bridge resistance.
     
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  4. Azlaan

    Thread Starter New Member

    Nov 10, 2014
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    Thanks a lot sir
     
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