Capacitors: Understanding Electrical Energy Storage

Posted on Jan 9, 2025 in Electromechanical Engineering

Capacitors

In electricity and electronics, a capacitor is a device that stores electrical energy, a passive component. It consists of a pair of conductive surfaces positioned to influence each other totally (that is, all electric field lines that start from one go to the other). These surfaces are usually in the form of tables, fields, or plates, separated by a dielectric material (used in a capacitor to reduce the electric field because it acts as an insulator) or by a vacuum. Following a difference of potential (d.d.p.), they acquire a certain electric charge, one positive and the other negative (the total charge storage being zero).

The charge stored in one of the plates is proportional to the difference in potential between that plate and the other, the constant of proportionality being called capacity or capacitance. In the International System of Units, it is measured in Farads (F), where 1 Farad is the capacity of a capacitor in which, subject to a d.d.p. of 1 volt across its plates, they acquire an electric charge of one coulomb.

The capacity of one Farad is much larger than that of most capacitors, so in practice, the capacity is usually indicated in micro- (µF = 10-6), nano- (nF = 10-9), or pico- (pF = 10-12) Farads. Capacitors made from supercapacitors (EDLC) are an exception. They are made of activated charcoal to achieve a large relative area and have molecular separation between the “plates”. Thus, capacities are achieved in the hundreds or thousands of Farads. One of these capacitors is incorporated into the Seiko Kinetic Watch with a capacity of 1/3 Farad, making the battery unnecessary. They are also being used in prototype electric cars.

The value of the capacity of a capacitor is defined by the following formula:

C = \ frac (Q_1-V_2) (v_1) = \ frac (V_2 Q_2-v_1) ()

where:

  • C: Capacity
  • Q1: Electric charge stored in plate 1.
  • V1 – V2: Potential difference between plate 1 and 2.

Note that in the definition of capacity, it is deemed irrelevant whether the plate’s charge is positive or negative since:

Q_2 = C (V_2-v_1) =-C (v_1-V_2) =-Q_1 \

but by convention, the charge of the positive plate is usually considered.

As for the constructive side, the shape of the plates or armors, as well as the nature of the dielectric material, are highly variable. There are capacitors formed by plates, usually aluminum, separated by air, ceramics, mica, polyester, paper, or with a layer of aluminum oxide obtained by electrolysis.

The Ideal Capacitor

The ideal capacitor (Figure 2) can be defined from the following differential equation:

i (t) = C (du (t) \ over dt) \;

where C is the capacity, u(t) is the function of the potential difference applied to its terminals, and i(t) is the resulting current flowing.

Direct Current Behavior

A real capacitor in direct current (DC) behaves almost as an ideal capacitor, that is, as an open circuit. This is in a steady state, as during the transient state (that is, when connecting or disconnecting a capacitor from a circuit), transient electrical events occur that affect the d.d.p. at their terminals (see RL and RC series circuits).

Alternating Current Performance

In alternating current (AC), an ideal capacitor offers a resistance to the passage of current called capacitive reactance, XC, whose value is given by the inverse of the product of the pulse (\ Quad \ omega = 2 \ pi f ) by the capacity, C:

X_C = (1 \ over \ omega C j) \;