What are Capacitors?

Capacitors are passive two-terminal energy storage elements composed of two conductors separated by an insulating (dielectric) material. The most basic parallel-plate capacitor is a device consisting of two parallel conducting plates of area A separated by a distance d.

How do Capacitors Work?

Consider the basic circuit shown below consisting of a voltage source connected to a capacitor controlled by a switch.

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When the switch closes, the voltage source becomes electrically connected to the capacitor. Naturally, electrons begin to flow from the negative terminal of the voltage source to the lower plate as shown below. Electrons residing above along the upper plate are then repulsed towards the positive terminal of the voltage source. As the electrons continue along this behaviour, the lower plate will be associated with an increasingly negative charge. Similarly, the upper plate will have an increasingly positive charge of the same magnitude.

The resulting effect of this phenomenon is the formation of a potential difference across the two plates. This is characterized by an electric field which stores electrical energy. It must also be noted that the voltage across capacitors may not change in a discontinuous fashion, that is, the function describing the voltage across a capacitor with respect to time is continuous. The current "across" capacitors however, can change instantaneously. In DC steady state, capacitors act ideally as open circuits.

Capacitor Theory

Charge on a Capacitor

For a fully charged capacitor in steady state, we have the following expression:

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Here, we note:

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Units of Capacitance

The unit of capacitance is farads (F).

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A 1F capacitor stores 1C of charge with a 1V potential applied to it.

Capacitance of Two Parallel Plates

The capacitance of a parallel plate capacitor is:

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Here, we note:

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Capacitor Current

The current "across" a capacitor is given by:

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Capacitor Voltage

The voltage across a capacitor is given by:

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Note that t_0 is an initial time where the voltage across the capacitor is known, and tau is merely a variable of integration representing time.

Capacitor Power

The instantaneous power of a capacitor is given by:

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Capacitor Energy

The energy of a capacitor is given by

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where:

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As with the other pages here, I’ll just link to pages that already explain this instead of writing everything out again - as the pages I have linked explain everything way better than I could.

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