Capacitor confusion: basic pointers to salvage your sanity 

academics capacitors physics

You have recently started to learn about electrical circuits, and even though the occasional, particularly tricky circuit still proves challenging to solve, you feel like you “get” what batteries and resistors are and are starting to grasp fundamental concepts such as voltage and current. Forever dedicated to your torture, your physics teacher senses your comfort and doubles down by introducing capacitors, a new circuit element that supposedly relies on the same concepts but somehow feels far more confusing. 

Fret not. This sense of confusion is entirely normal, often rooted in poor explanations and will ultimately vanish. To get you started, here are a few pointers addressing some of its most common sources:  

1. Confusion around the definition

I feel like I have heard very different things be referred to as capacitors and I am confused as to what a capacitor is, exactly. 

Technically, any device which can be used to store electric energy by storing electric charge is a capacitor, and there are many ways of constructing such a device. The so-called parallel-plate capacitor, which consists of two parallel, conducting plates with an insulating gap in between, is by far the most common though, and is usually what is referred to when people use the word “capacitor”. This introduces a confusing ambiguity to the meaning of the word, but it shall not concern you in practice: Just think of parallel-plate capacitors by default. Any task that is concerned with a more exotic capacitor type, such as spherical or cylindrical capacitors, should say so very clearly. 

2. The "current-through-a-gap" confusion

So capacitors have an insulating gap and current does not flow through insulators. Yet, currents can supposedly flow through capacitors. How does this make sense?

The answer is that electrons arriving on one of the capacitor plates repel electrons on the other plate, causing the electrons on the latter to effectively continue the current flow. Therefore, we say that there is a current going “through” the capacitor, even though no electron physically moves across the insulating gap. 

Note that this only works because the gap is very small (meaning the repulsion across it is significant) and because the area of the capacitor plates is large enough to accumulate a significant amount of charge and thereby keep this effect going over a significant amount of time. When an insulating gap is created in a circuit by cutting a wire or opening a switch, for example, the resulting gap is much larger and the small wire-tip in question does not allow for the accumulation of an appreciable amount of charge, stopping any current flow virtually instantaneously. 

3. The "time-dependency" confusion 

So currents can flow through capacitors, effectively, similar to how they flow through resistors. Yet, we never worried about the currents through resistors changing over time, or about anything charging or discharging. Why are we doing so with capacitors?

This too has to do with the insulating gap. In resistors, charges can continue to flow indefinitely as long as a voltage gradient is applied, with an endless chain of electrons shuttling through one after the other. In capacitors, on the other hand, electrons cannot actually move across the gap, which forces them to accumulate or deplete over time and results in time-dependent behavior. Here is what happens in each scenario: 

In a charging resistor, a current can flow initially via the mechanism described above, but as more and more charges accumulate on the capacitor plate, additional incoming charges are more and more strongly repulsed by those already present. This “traffic jam” effect decreases the current over time until it becomes negligible. 

In a discharging capacitor, the reverse occurs: the many electrons gathered on the capacitor plate strongly repel each other, which initially results in a large current flow as the first electrons rush off the plate. Over time, fewer and fewer electrons remain, weakening the repulsion as the capacitor plate is getting depleted, and the resulting current vanishes.  

4. The "what-is-happening" confusion

Okay, I get it kind-of-sort-of, but that’s a lot to keep in mind and when I am confronted with a circuit that has a capacitor in it, I usually feel like I don’t know which scenario is occurring or how to even start thinking about what’s happening. Any advice?  

Yes. First, take a deep breath. Then look at what the capacitor in the circuit is connected to. If it is currently connected to a loop with a battery in it, it is likely being charged. If it is connected to a loop without a battery, it is likely discharging. Next, look out for certain language signals in the task: If you encounter terms such as “in equilibrium”, “after a long time” or “at t = infinity”, the task is likely concerned with the very end of a charging or discharging process, meaning that no current is flowing through the capacitor. If you encounter terms such as “right after the switch is flipped” or “at t = 0”, on the other hand, the task is likely concerned with the very beginning of a charging or discharging process, meaning the current flow through the capacitor is maximal. As with any physics task, it is also a good idea to write down relevant equations and all given quantities to get some inspiration whenever you are lost. 

And there you go. Capacitors are by no means trivial devices, and I would be lying if I said this should cover most of what you might be expected to know in the long run, but hopefully, these pointers helped clarify some basic things, made the whole topic feel a little bit less threatening or at least heightened your appreciation for how much you had understood already.

PS: If you had a hard time visualizing some of the above or would simply like to deepen your understanding further, I personally recommend this YouTube video I played no role in making. 

Robert holds a BSc in Physics from Jacobs University and a PhD in Physics from Harvard University. For his work as a Teaching Fellow at Harvard, Robert won the Harvard University Physics Department’s White Prize for excellence in teaching introductory physics


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