Capacitors can be connected in series to share charge value:

The “charge capacity rating” of any object to store energy by separating charge across a gap is its capacitance: C = Q/DV where Q is the magnitude of the net charge on either side of the separation (not the sum of the two sides, which is zero), and DV is the potential difference between those two sides. Units: “farads” 1 F = 1 C/V Any two electrodes form a capacitor. Only their geometry determines how much charge they can separate for a given size E-field (and thus a given voltage difference). Oregon State University PH 213, Class #14

Capacitors can be connected in series to share charge value: Or they can be connected in parallel to share voltage value: Oregon State University PH 213, Class #14

Rank in order, from largest to smallest, the equivalent capacitance (Ceq)a to (Ceq)d of circuits a to d. • (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c • (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a • (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d • (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c • (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b Oregon State University PH 213, Class #14

Capacitors are built to be UE-storage devices. So, how much energy can a given capacitor store? We know the amount of charge stored per volt of potential difference created: C = Q/DV = dq/dV But how do we add up the total energy required to force all that charge onto the same conductor? Each additional bit of charge faces a stronger E-field than the previous charge. Oregon State University PH 213, Class #14

Find the charge on, the potential difference across, and the energy stored in, each capacitor. Oregon State University PH 213, Class #14

Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are then separated by a distance d. (ISOLATED – not connected to a battery) Suppose the plates are pulled apart until they are separated by a distance D > d. The electrostatic energy stored in the capacitor is… 1. greater than 2. the same as 3. smaller than before the plates were pulled apart. (Follow up: What average force was required to pull apart the plates?) Oregon State University PH 213, Class #14

The energy density of a capacitor (indeed, any energy storage system) is of much practical interest. The energy is not “in the charge,” per se. It’s in the field formed by the presence of the charge—think of it something like a coiled spring. (If this weren’t the case—if the charge actually were to “contain” the energy—then there’s no way that an E-field could be a carrier of the energy without any charge present across empty space— EM radiation.) So, how many joules can we store per m3 of the E-field between the plates of a capacitor? (The same math results for any E-field, in fact.) Oregon State University PH 213, Class #14

Now, how do we get the electric potential energy out of a capacitor (or any device containing UE)? Consider a particle model of what happens when we offer a conductive path to the collection of (like) charge that has been forcibly crowded together on the plate of a capacitor… Oregon State University PH 213, Class #14

Capacitors can be connected in series to share charge value: