At the top of the image you posted it says:
MrAl says "That diagram is not correct with respect to how it shows the currents i1 and i2. " There's nothing wrong with how the currents are shown; they're mesh currents. It's perfectly ok to show mesh currents as unknowns in a network problem.
Hello,
There's nothing wrong with the currents if we were doing anything other than nodal analysis, but also
that can not be the currents they wanted to see solved for because i1 and i2 exactly as drawn will not
come out to 2.22 amps and 470ma as the answers tell us. The only way to get those values is to
assume that the currents are as shown in Figure 3. What i meant was that they must have used another
drawing to show the student and didnt bother to redraw where the currents to be solved for actually
would be found.
Hello again,
Ok, but he was asking for nodal not mesh analysis right? That means the way those currents are drawn dont make sense.
Im sure what happened here was the original problem was using mesh analysis, then the student was asked to do the
circuit using nodal analysis later.
i dont know why you all guys did a long
just mark the unknown node as V1,
then we have
(V1-3)/10 + (V1-10)/14 + (V1-0)/8 = 0
so V1= 3.42V
so i1= (10-V1)/14 = 0.47A
(10-3)/4 = i1-i2
so i2= -1.28
Because the OP asked for an explanation of the nodal method of solution.
Actually, i2= (10-V1)/14 = 0.47A
Then if (10-3)/4 = i1-i2 we have i1 = 2.22A
Hello again,
Another interesting fact here is that nodal analysis is more general than mesh analysis, in that mesh analysis does not work for every circuit we can find whereas nodal does.
Hello again,
mesh analysis does not work for every circuit we can find whereas nodal does.
I much prefer nodal analysis, but there are circuits that classical nodal analysis can't directly deal with, such as those involving transformers. A number of tricks have been used in the past to get around this limitation, but when Ruehli, et al, invented MNA (modified nodal analysis) in 1975, all limitations to the classical nodal method were eliminated.
When you say mesh analysis doesn't work for every circuit, you are probably alluding to the fact that non-planar networks are generally unsolvable with mesh analysis. But that limitation is readily removed by just going to loop analysis, which uses KVL in the same manner as mesh analysis.
i don't agree with it, we can use any of the method for all circuit we can find, but some can be easily solved by nodal method and some are by mesh
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