content(warnings): Add W17-W28, X8-X12, N7 — E&M misconceptions, cross-refs, notes

concepts/em/u11/e11-5-kirchhoff.tex

@@ -49,6 +49,8 @@ The assumed direction of each branch current must be declared before writing equ
 \end{enumerate}
 The number of independent equations needed equals the number of unknown branch currents.}
 
+Kirchhoff's rules generalize the equivalent-resistance method from Section 11.4. For single-battery circuits with pure series/parallel arrangements, equivalent resistance is faster. Kirchhoff's rules become necessary when multiple batteries or loops make reduction impossible.
+
 \ex{Illustrative example}{Consider a junction with three wires meeting. Current $I_1 = 3.0\,\mathrm{A}$ enters the junction and current $I_2 = 1.5\,\mathrm{A}$ leaves. The third branch carries current $I_3$. By the junction rule, $I_1 = I_2 + I_3$, so $I_3 = 1.5\,\mathrm{A}$ leaves the junction.}
 
 \nt{For circuits with a single battery and resistors in simple series or parallel, the equivalent-resistance method is faster. Kirchhoff's rules are needed whenever the circuit cannot be reduced to simple series/parallel combinations --- for instance, when there are two or more batteries arranged in different branches, forming multiple loops.}