Trouble understanding KVL for discharging RC circuit
I think I may have answered it myself.
The issue relates to the fact that dq / dt refers to the current through the resistor (a positive quantity) and therefore dq refers to the differential charge related to the resistor, whereas I am &quot;mixing&quot; my charges when also referring to charge on the capacitor in the same equation (q and dq to not refer to the same charges in the same system).
If I want the quantity dq / dt to refer to the current through the capacitor, which is a negative quantity when it is discharging due to the passive sign convention, (so that I do not &quot;mix&quot; my q's) then I need to apply a negative sign in front of it, since dq / dt for the capacitor itself is also negative and the negative's &quot;cancel&quot; to yield the correct KVL equation