One way to obtain a suitable set of equations is to apply the junction rule and the loop rule as many times as necessary to obtain a suitable number of equations.
1) Keep in mind that Kirchhoff's «laws» are not reliably true, the assertion is not really true.
2) Even if it were true, it would be uninformative, because it leans too heavily on the word "suitable" without explaining what's suitable and what's not.
3) It is not correct to suggest that the key concept is the number of equations. In real-world situations, blindly applying Kirchhoff's «laws» will result in an exponential number of equations, most of which are useless.
4) As mentioned in items #163 and #11, this is a brute-force approach that provides little insight as to what's going on. This interacts with point (3), because in the absence of insight it is difficult to prune the set of equations without doing an exponential amount of work.
Suggestions:
When teaching circuit analysis, start with series/parallel reduction.
At some later point, mention that it is possible _in principle_ to cobble up a set of equations by repeated application of Kirchhoff's «laws», but this is a brute-force method that generally provides little insight and might require exponentially much work.
In simple real-world cases, series/parallel reduction is easier and provides more insight.
For moderately-complicated linear circuits, linearity permits tremendous simplifications. As discussed in item #163, the wye circuit is an example.
In complicated real-world cases, a more sophisticated approach is needed, to prevent exponential explosion. The details are beyond the scope of this course.
There are selected cases where completely different methods are appropriate, e.g. the electrodynamics of continuous media. The details are beyond the scope of this course.
In section 31.7 on page 835 it asserts:
1) Keep in mind that Kirchhoff's «laws» are not reliably true, the assertion is not really true.
2) Even if it were true, it would be uninformative, because it leans too heavily on the word "suitable" without explaining what's suitable and what's not.
3) It is not correct to suggest that the key concept is the
number of equations. In real-world situations, blindly applying Kirchhoff's «laws» will result in an exponential number of equations, most of which are useless.4) As mentioned in items #163 and #11, this is a brute-force approach that provides little insight as to what's going on. This interacts with point (3), because in the absence of insight it is difficult to prune the set of equations without doing an exponential amount of work.
Suggestions: