Capacitors as Circuit Elements The most common use of capacitors is in electric circuits. They are used primarily as a means of storing charge, which can later be released to continue providing energy to the circuit. A capacitor becomes charged when attached to the terminals of a power supply. Charge flows out of the power supply and into the plates of the capacitor where it remains until the power supply is removed. When the power supply is removed the charge is free to leave the plates of the capacitor and released back into the circuit. This is a simple capacitive circuit connected to a power supply (battery). The capacitance of the capacitor is set by the physical geometry of the element This is the potential difference between the terminals of the battery, and hence the potential difference applied across the entire circuit. The plates of the capacitor will have the same potential as the terminal it is connected to. Each plate of the capacitor will have the same magnitude of charge, but one plate will be positively charged and the other negatively charged. The amount of charge on the plates of the capacitor can be determined from the capacitance and the potential difference using Q = C  V.

Circuits using capacitors often use multiple capacitors. Capacitors can be connected in two different configurations. Series Connection Parallel Connection These two plates are electrically connected they must have the same amount of charge, but opposite sign. The right plate of each capacitor is electrically connected, and must have the same electric potential as the plate of the power supply they are connected to. Same electric potential The electric potential difference across each of the capacitors is the same.

How then could we describe the charge on each capacitor for the two possible combinations? Series: All the plates on the capacitors must have the same amount of charge. Parallel: The total charge supplied by the power supply is distributed between the two capacitors. What is the potential difference across each of the capacitors for the two possible combinations? Series: The total potential difference is distributed across both of the capacitors. Parallel: The total potential difference must be the same across each of the capacitors.

What is the total capacitance of each circuit combination? Series: Parallel: In General: Series: Parallel:

The charge in a capacitor is stored on opposite plates of the capacitor. You could imagine that if you started with an uncharged plate and tried to pull the negative charges from the plate an place them on a second plate some distance away you would have to do work on the charges. Since you had to do work against an electric field to separate the charges it requires that electric potential energy is stored in each of the charges. This suggests that a capacitor not only stores charge, but energy as well. We can look at the amount of energy stored in a capacitor by imagining that we move charges across the separation gap in the capacitor. Charges do not actually move between the plates through the gap! The electric potential difference between the plates of the capacitor is a function of the amount of charge on the plates!

The energy stored in a capacitor is considered stored in the electric field that permeates the region between the plates of the capacitor. This makes it more convenient to discuss the energy stored per unit volume between the plates. This is called Energy Density. Energy Density – Energy stored per unit volume. Volume contained between the plates u – Energy Density [J/m 3 ] U – potential energy [J] V – Volume [m 3 ] E – Electric Field Strength [N/C]