# Why is it often assumed that parasitic (or "stray") capacitance is in parallel?

Consider a simple RC circuit operating in the DC regime. Depending on the specifics of the experimental setup, there can often be a significant amount of parasitic (or "stray") capacitance. In every undergraduate-level lab I've seen on the topic, the assumption usually needs to be made that the parasitic capacitance is in parallel with the "main" capacitor in the RC circuit.

I recognize that this makes the math easier, but I want to understand more fundamentally why this assumption can be made. (OR is it not a great assumption?)

I note in this question about the parasitic capacitance of an inductor, the answer given basically says, "if the capacitance were in series, the circuit would just act like an open circuit." I'm not sure I can wrap my head around whether this explanation helps in my case. In fact, an RC circuit is and open circuit, so I don't really understand why it would be a problem to place a second hypothetical capacitor in series.

What's the deal with this assumption? Is it a good/defensible assumption in many circumstances, or is it mostly done to make the math easy?

Here's an illustrative homework problem: suppose you have two very long, parallel conducting wires of radius $$a$$, whose centers are separated by a distance $$b>2a$$. What's the capacitance between these wires, per unit length? If you remember that the electric field for a wire holding charge $$q$$ goes like $$q/r$$, then you can tell that doing an integral $$V=\int\mathbf E\cdot \mathrm d\mathbf\ell$$ is going to give some constants and a $$\ln(b/a)$$ (unless it's $$\ln(a/b)$$, because of frowning about minus signs for three minutes). For a coaxial cable that's the whole solution, because you can use all of the nice radial-symmetry arguments; for parallel wires the integral is more complicated because they affect each other's charge distributions.

Now consider a circuit where your RC stuff is separated from your power supply by a cable:

power supply ------ cable ------- more cable ------- RC stuff


Well, you just computed the capacitance per unit length in that cable. The total capacitance in your circuit isn't only from the two conducting plates in your intended capacitor $$C$$: those plates are connected to the two conductors in the cable, which effectively increases the area of charged conducting surfaces that are close to each other.

If you did the integral in the first paragraph, you see that you can reduce the capacitance of the cable is the conductors are far apart and if the wires are really small, but you can't eliminate it completely. And since your cable will always have one wire connected to each plate of the capacitor you're driving intentionally, the cable capacitance always makes the circuit's total capacitance somewhat more than you expected. That's why we say that the stray capacitance is in parallel.

Sometimes it happens, in a real experiment, that a mouse (or another such agent of chaos) nibbles a tiny gap in one wire of a cable that you care about. That's a "stray" capacitance in series. Those change the behavior of a direct-current circuit dramatically, giving you the derivative of the signal you expect, but those kinds of accidental capacitors can be removed completely, while cable capacitance can be reduced but not eliminated.

• – rob
Nov 27 '19 at 5:46

A simple capacitor can look astonishingly like it's schematic symbol. But as long as there's a wire from one plate, through a resistor, and back to the other plate, any "series capacitance" is shorted out by the wire. The wire (and resistor) on the other hand, are electrostatically coupled to ground (and to everything else in the universe; eventually you might have to pay attention to that).

So it's not so much that the stray capacitance is assumed to be in parallel, it's that it's pretty much determined to be, if not proved, by the fact that there's a DC connection from each plate of the capacitor to the resistor (possibly through a battery or other power supply). Stray capacitance is, from an engineering standpoint, unwanted capacitance between the "hot" (signal or power) line and nearby ground. As such, it is always in parallel with the hot side of the circuit (RC or otherwise).

If it were in series with the hot line- which from a circuit modeling (i.e., physics) standpoint would be wrong- it would almost always completely block the passage of signals or power because stray capacitance is of order ~picofarads.