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

concepts/em/u11/e11-6-rc-circuits.tex

@@ -16,6 +16,8 @@ I(t) = \frac{\mathcal{E}}{R}\,e^{-t/RC}.
 \]
 Here $q(0) = 0$ and $I(0) = \mathcal{E}/R$. As $t \to \infty$, $q \to C\mathcal{E}$ and $I \to 0$.}
 
+\nt{The RC time constant $\tau=RC$ has units of seconds: $[\Omega]\cdot[\mathrm{F}]=[\mathrm{V/A}]\cdot[\mathrm{C/V}]=[\mathrm{C/A}]=[\mathrm{C/(C/s)}]=[\mathrm{s}]$. After one time constant during charging, the capacitor reaches $1-e^{-1}\approx 63.2\%$ of its final voltage. After five time constants, it reaches $99.3\%$, which is the practical definition of ``fully charged'' in circuit analysis.}
+
 \pf{Derivation of charging equations}{Apply Kirchhoff's voltage law around the loop. The potential drops across the resistor and capacitor sum to the battery emf:
 \[
 \mathcal{E} - IR - \frac{q}{C} = 0,