Capacitance - Capacitor Connections

Capacitance adds when capacitors are connected in parallel. It diminishes when capacitors are connected in series:

Recall that capacitance stores energy in the form of an electric field, as a function of the voltage applied to it. It we wish to increase capacitance by connecting multiple capacitors to each other, we need to do that in such a way that each capacitor receives the same (total) applied voltage so that each additional amount of capacitance included in the network will contribute a proportional amount of energy storage to the network. We know voltage is guaranteed to be equal only among parallelconnected components. If we were to connect multiple capacitors in series with one another, their individual voltages would be some fraction of the total voltage (series voltages always adding to equal the total voltage), thus diminishing the energy stored in each capacitor and similarly

 diminishing the total capacitance. Another way to comprehend why capacitance increases in parallel and diminishes in series is to consider a network of capacitors as one equivalent capacitor in terms of aggregate plate area and separation distance. Examining the directions of change to the corresponding variables in the permittivity/area/distance formula for capacitance, we see how parallel-connected capacitances must add while series-connected capacitances must diminish:

The relationship between voltage and current for a capacitor is as follows:

I = C dV/dt

As such, capacitors oppose changes in voltage over time by passing a current. This behavior makes capacitors useful for stabilizing voltage in DC circuits. One way to think of a capacitor in a DC circuit is as a temporary voltage source, always “wanting” to maintain voltage across its terminals as a function of the energy stored within its electric field. The amount of potential energy (Ep, in units of joules) stored by a capacitor may be determined by altering the voltage/current/capacitance equation to express power (P = IV) and then applying some calculus (recall that power is defined as the time-derivative of work or energy , P = dW/dt = dE/dt

In an AC circuit, the amount of capacitive reactance (XC) offered by a capacitor is inversely proportional to both capacitance and frequency:

XC = 1/2πfC

This means an AC signal finds it “easier” to pass through a capacitor (i.e. less ohms of reactance) at higher frequencies than at lower frequencies.