

Capacitor and Current
Name: Hadia
Status: student
Grade: 912
Country: Pakistan
Date: Spring 2012
Question:
How exactly can current pass through a capacitor? Be it A.C or D.C. Even if we consider the general logic that current 'flows through' a capacitor as it charges and discharges via A.C, then in what does the discharged current flow. If it flows through, shouldn't power be dissipated. And if it flows back and what is the use of a capacitor? Even if you say, it flows through, how would you explain it in terms of individual charges?
Replies:
Hadia,
Your question is a natural one because it appears that current flows “through” a capacitor. Indeed, we treat capacitors as though they are resistors in which individual electrons enter on one terminal and exit through the other. A capacitor operates differently. The word “capacitor” implies a device that has “capacity,” or a device that has the capability to store a certain amount of charge, somewhat like a “charge bucket.” In fact, the formula for capacitance, Q=CV, implies just this storage: The charge stored by a capacitor (Q measured in Coulombs) is given by its capacitance (C measured in Farads) multiplied by the voltage applied to the capacitor (V measured in Volts). Current does not flow through the capacitor as much as into the plates of the capacitor, i.e., into its “charge bucket.”
Let us consider a simple circuit to explain this phenomenon. Take a battery and a capacitor and connect the capacitor to the positive and negative terminals of the battery. Initially, assume the capacitor is uncharged. The charge bucket of the capacitor is empty (Q=0) and the voltage across its terminals is zero (V=Q/C with Q=0 so that V=0). The battery does have a voltage across it, and it can provide charges to the capacitor. When we connect the battery, charges will flow until the voltages across the battery and the capacitor are the same (the net charge carried by the capacitor will be given by Q=CV). The question is, how does charge flow in this case?
In a wire, electrons flow as charges (as you know, these charges are negative). The positive terminal of the battery will attract the electrons from the capacitor plate connected to it. Electrons flow from one side of the capacitor to the battery. These charges came from the plate itself. Electrons will flow until the capacitor no longer sees a positive voltage from the battery. When we remove electrons from the capacitor plate, a net positive charge is left on the plate, and it will exactly match the battery voltage. Now, the opposite happens on the other side of the capacitor. Electrons will flow from the battery into the other side of the capacitor until the voltage difference between the battery and the capacitor are equal. The result is that we have electron flow out of one side of the capacitor and electron flow into the other side; however, we did not force electrons across the plates and through the capacitor. We can look at it using our bucket analogy. We remove electrons from one side of the capacitor (call it the “top bucket”) place them into the other side (call it the “bottom bucket”). The battery does the work of emptying and filling the two buckets. Now we have electrons missing from the top bucket and placed into the bottom. At the bottom, it is easy to see that the plate has negative charge now since it has more electrons than before; the top bucket has fewer electrons (by the same number) and these “empty spots” creates a net positive charge. These charges are separated in the capacitor, and the result is that there is a voltage across the plates.
We can reverse the situation: flip the battery and the opposite situation exists. Electrons from the bottom plate will be removed and placed on the top. The movement of charges is the definition of current, and we have put current into the capacitor and taken it out. In neither case did the current flow through the capacitor. In the ideal capacitor, we would remove the same net charge as we put in, and there is no loss. In reality, the charges would flow in wires which have resistance and would create loss. Also, capacitors are not perfect, and they leak. The ideal capacitor only stores charge, however, and does not have loss.
This last sentence explains the utility of capacitors. They store charge (and energy). Contrary to what you might think, they are extremely useful. Consider what a battery does: it stores charge. Why is it useful? You carry it around and draw energy from it when you need to power your electronics. Consider one use for capacitors, as filters. Sometimes we need a voltage to stay steady, and we will use a capacitor to keep it steady. When the voltage rises, the capacitor draws current and stores it. The voltage does not rise as much as it would otherwise because the capacitor acts as a load. When the voltage falls, the capacitor provides current, much like a battery would. The voltage does not fall as much as without the capacitor as extra energy is supplied by the capacitor. The net result is a smoother, or filtered voltage. Other uses exist for capacitors, and I would encourage you to discover just how useful (and prevalent) they are in electronics.
Kyle Bunch
Hadia,
Current flows into one side of the capacitor, adding charge to one plate. The same amount of current flows out the other side, removing charge from the other plate. The charge on the plate remains balanced, and the current in one side balances with the current out the other side. Current does not physically cross from one plate to the other.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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Update: June 2012

