# What’s goin’ on inside a capacitor?

Remember what I said about AC & DC last time? That’s gonna be helpful for us today as we’re gonna talk about an application of both – the capacitor, in which (at least to me) there’s a lot of stuff going on inside, other than just charging & discharging…

## Analogy with wires…

What people know is that a capacitor is a device that has certain amount of “capacity” to store energy electrostatically. Now, this statement doesn’t allow us to enjoy the taste insides of such a device (again, approximations suck). Sometimes, you may also hear that the capacitor stores charges. Does it do so? Nope..!!! It’s a common misconception. I don’t have to explain how this is a misconception. You’ll get it along the way eventually. I hope you remember the explanation I gave for current, using a battery, that a battery is a direct source which sucks electrons through one terminal and lets through the other.

Roughly, it’s just maintaining a potential difference which when setup, causes the free electrons to displace along a definite direction, and appear as if there were particles flowing at some uniform velocity (i.e) these particles at the drift speed, continue to flow as long as there’s a voltage. You pull the battery, and there’s no current.

Now, consider an open circuit like the one above. The common “electrical” explanation given, is that current doesn’t flow in an open circuit, which is true. But, not quite. There’s a transient current. Once the battery is connected, the free electrons in the orange wire acquire some energy (in metals, it’s easy to displace a free electron as it’s in the outermost energy level and also loosely bound to the atom) and they start moving towards the positive electrode, while those in the green thing move towards the end of the wire (away from the negative electrode), as a result of repulsion. There’s a constraint. “How far the free electron moves?” depends on the voltage source (the battery). The more the voltage, the more electrons get displaced and higher this transient current.

## Capacitor as a magnifier…

Now, you can see that there’s a voltage setup between both the ends of the wire. Intensifying this, is the work of a capacitor. You put chunks of metal at the end of the wires so that you can have more free electrons on the surface. There’s also this misconception that charges stick (like some tattoo) over the surface. An electron is a quantum particle. It can’t stay somewhere for a while. Moreover, in our case, it’s always perturbed by the atoms around. When we mean charges sticking to the surface (conductor or insulator), the electrons are redistributed around so that there’s a net potential over the surface. Anyways, now there are metal plates at the ends.

A metal plate, being a big mass of metal atoms (relatively giant compared to a thin wire) has a large number of free electrons with which we can play around a bit. In the presence of an applied electric field (battery), the metal plates get polarized. Displacement of electric charges inside the object is what we mean by “polarization” here. It happens in conductors, insulators, and even mirrors. Once the free electrons are displaced, there’s a net positive charge on one plate (due to deficit of free electrons), and a net negative charge on the other (due to excess free electrons). This charging (& discharging) of a capacitor is exponential in nature. Now, there’s another condition. These plates are very close to each other, that this potential difference is far enough to hold the net positive & negative charges together via electrostatic attraction. And, this design is quite critical. Too distant, and the charges can’t hold themselves, whereas too close, it exceeds the breakdown voltage (when ionization occurs) and the capacitor is permanently gone. “Poof”..!!!

In reality, a dielectric material (which can also be polarized) is used between the plates of a capacitor to increase the capacity (more charges can stick inside, for a given voltage), so that there’s no physical contact established between both the plates (preventing the charges from neutralizing themselves). Moreover, the material gets polarized and generates an electric field directly opposite to that of the plates. Now, the plates and dielectric hug together (i.e) the dielectric is pulled towards the plates.

## In AC & DC circuits

So, you’ve now seen that a capacitor doesn’t store charges. The electrons just get displaced so that there’s a net charge on the plates (i.e) if you think that a certain quantity of charges have left a plate, then there exists a same quantity of charges (opposite in nature) on the other plate.

As told previously, it’s not really true that flow of charges require a closed circuit. A difference in potential is far enough. You’ve also seen that a capacitor does get charged by direct current (though it’s transient). On the other hand, alternating current being just oscillation of charges back & forth (around 50-60 times a second, for domestic use), there’s no need for charges to flow in the circuit. In other words, the displaced charges settled by then, get reversed and the whole business happens again, which is why a capacitor can be charged continuously in AC, but dies out soon in DC. Electrically, it’s spoken out that a capacitor shows infinite resistance to DC which seems a plausible approximated statement.

But, always keep in mind that there’s a transient charging, at the moment you close the DC circuit. Now, what do you see above? It’s the phase diagram for a capacitor. The thicker line shows the AC sinusoidal voltage while the thinner line shows the instantaneous current, the result you get, after passing it through a capacitor. There’s a reduction in the peak value, because the capacitor offers some resistance (as every other electrical component does, unless they’re superconducting) and there’s also a phase shift in the wave. It shows that the voltage lags behind current by a phase angle $\pi/2$.

What’s that supposed to mean anyway? Remember that the current through a capacitor is the result of the change in voltage across the plates (i.e) current must flow to build up the charge on the plates and the voltage is directly proportional to the charge built-up on the plates. So, the instantaneous current is zero, whenever the instantaneous voltage reaches a peak (the point where & when the stuff is stopped from pulling out, and started pushing in). You have to visualize this for a minute. When the charges are set up on the plates, the current is zero because the charges don’t move at that moment, which doesn’t mean the voltage is zero because there’s exists a maximum electric field between both the plates when the charges are set up. As it drops down (when the charges start moving), the voltage gets reduced in its value and eventually reaches zero & it goes on…

Take the world in another point of view, this horror happens for about 50-60 times every second, for domestic frequency being 50-60 Hz. Remember when I said that the charging (& discharging) of a capacitor is exponential in nature? The rate at which the capacitor is being charged over a period of time (simply put, the instantaneous current), depends on the amount of charge present in the plates at that instant. Now, recall old-school, that for such a linear differential equation, the only solution that exists, is an exponential variation

In order to get a good understanding of all these horrific messes, I suggest you to read the hydraulic analogy (which is mostly helpful to the newcomers to the field)

### Why would it discharge then?

The same reason why a battery doesn’t keep the amount of electrostatic energy itself for its whole lifetime. Our world isn’t perfect. There are perturbations in this entropic universe. Any relatively small displacement of the free electrons can cause redistribution of charges leading to neutralization.

### How does it differ from a battery?

While there are a lot of differences like no chemical reaction is going on inside, it doesn’t split any atoms into mobile ions and electrons, etc., there’s a wonderful theme buried here. In any kind of power supply, you can’t obtain the whole bulk of power within a fraction of second. For example, take a battery. A capacitor connected in the circuit takes some time to charge, so does any other electrical component (only difference is that the capacitor gets charged exponentially, but that’s not necessary here). What I mean here? The battery is not giving up all its power instantaneously. But, a capacitor does..!!!

Say, you have a giant capacitor (a few microfarads) charged to some sufficient level. You close the circuit and BANG, it goes like hell..!!! The capacitor discharges immediately within a fraction of seconds. That’s the theme. It can give its stored energy all at once…