- Joined Mar 19, 2019
OK, but I'm not getting the 20(I -2) part. I guess it is the parallel resistors throwing me. I understand the I-2 but not multiplying the 2A by 20Ω part. It does prove out correct but the 20I-40 part is still not getting through my thick skull... I just don't see it.using KVL
120 = 12I + 20(I -2)
Remember, Ohm's Law doesn't allow you to grab just any voltage, current, and resistance and throw it at the equation.@crutschow et. al. I started with the Thevenin first. Note on this diagram the R3 current is 4A (book errata) although the question text says 2A. So, I worked it for 4A. All the way down to the point circled in the photo. The Vth is 75V but that leaves 45V of the 120Vs which is what is actually going across R3. So I'm not sure which is the correct method. Inserting R3 into the Thevenized circuit would mean that 75V/4A is 18.75Ω for R3. But subtracting the Rth from 18.75Ω gives me 11.25Ω for R3 which is correct and the same answer I would get from 45V/4A = 11.25Ω. The other scribbling is a few calculations ensuring everything in the circuit is copacetic.
View attachment 302810
Yet another approach you could take, which goes back even further, is to combine things using series/parallel resistance combinations until you get the equivalent total resistance.
This is pretty much what I do with LTS and did with this problem and knew what the R3 resistance was, just not how to calculate it. I let LTS do the calculating and just varied the R3 value until it fit but didn't know HOW it was calculating it. I think the KCL & KVL solution was what the book intended at this point as Thevenin & Norton are introduced a few chapters ahead. I thought about a Nodal approach but was thrown off by the parallel resistors. Thank you for the good input as usual!Yet another way to do it, which has utility in situations that don't lend themselves to solving things analytically or in which you are at an impasse and can't figure out how to do it analytically, is to do it iteratively.
Don't let the parallel resistors trip you up. Remember, Nodal analysis is nothing more than a systematic way of applying KCL to a circuit in such a way that KVL is intrinsically satisfied.I finally got the 20(I-4A) bit through my thick skull and...
View attachment 302893
I've been introduced to some very basic nodal analysis but mesh and superposition are yet to come.
This is pretty much what I do with LTS and did with this problem and knew what the R3 resistance was, just not how to calculate it. I let LTS do the calculating and just varied the R3 value until it fit but didn't know HOW it was calculating it. I think the KCL & KVL solution was what the book intended at this point as Thevenin & Norton are introduced a few chapters ahead. I thought about a Nodal approach but was thrown off by the parallel resistors. Thank you for the good input as usual!
I'm using his 13th Ed and Nodal along with Mesh are in Chap 8 now. I have done some very basic nodal analysis in other texts as well as Thevenin and Norton. I also use Microsoft Mathematics for more complex equations as I am prone to simple error which are disastrous to complex equations. If I can state the relationship in an equation MM will solve it and plot the equation. The plotting is something we had no experience with back in the 60s other than simple slopes and such without programming it in Fortran and keypunching the cards to hopefully compile, run, and print out on the mainframe that took up an entire floor of the main engineering building. Which often did not occur on the first attempt so the exercise could take days to complete. The first time I saw Visicalc running on an Apple IIE I thought I had died and gone to heaven. Instantaneous feeback without having to wait a day to see if the program even ran and gave you an answer.If nodal analysis leads to more complicated algebra, I have Maple to crank the algebra.
Exactly! Which is one reason I really like Boylestad over several other texts that I've studied. He not only is better organized and explicit in his explanations but makes you think and apply that knowledge by throwing a few curveballs at you in problems like this one. He is definitely making me work at it instead of simply repeating it verbatim.I think part of what is tripping you up is that these analysis techniques are geared towards solving for voltages and currents with the component values being givens.
Nice article. Thanks!LTS (or any Spice based simulator) uses iterative calculations
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