# Capacitors

### Capacitors and Stored Energy

Capacitance is an ability of an electronic component to store energy in the form of an electrostatic charge (electric field). It is often described as a characteristic of a component that opposes any change in voltage.

Capacitor stores energy in an electric field between two parallel metal plates which are separated by an insulator (dielectric) such as air, glass, paper, mica, teflon, tantalum oxide or electrolyte.

Parallel plate capacitor: $C = \frac{A \cdot \varepsilon}{d} = \frac{\varepsilon_{0} \varepsilon_{r} \cdot A}{d}$ in Farads (F) where $\varepsilon_{0} = 8.85 \cdot 10^{-14}$ F / cm.

Dielectric permittivity εo is a measure of the easiness with which lines of electrical force are established within the material. In a sense, it is the electrical equivalent of magnetic permeability. Relative dielectric permittivity (dielectric constant) is equal to εr = ε/εo. Capacitance is proportional to the dielectric constant, εr of the insulator material.

Relative dielectric constants for selected materials are: air 1.0, diamond 5.5, mica 7.0, polyester 3.4, quartz 4.3, and water 78.5. To achieve small-volume capacitors, a very thin insulator having a high dielectric constant is desirable. Real capacitors have a maximum voltage rating at which the dielectric material breaks down.

Charge stored is proportional to an applied voltage: Q $\sim$ V or $Q = C \cdot V$ or $C = \frac{Q}{V}$ where the constant of proportionality is called the capacitance C.   Change in charge: $\frac{\Delta Q}{\Delta t} = C \cdot \frac{\Delta V}{\Delta t}$ which leads to $I = C \cdot \frac{\Delta V}{\Delta t}$ or in more general terms:

$I = C \cdot \frac{dV}{dt}$

### Characteristics of Capacitors

Characteristics of capacitors (opposite, dual, to an inductor):

• Voltage cannot change instantly (instantaneously) in a capacitor; it tries to keep voltage constant in a circuit
• Impedes flow of low-frequency signal (blocks DC) but easily conducts high frequency ac current. Capacitor provides both ac coupling and dc isolation.

Stores energy in an electric field: $E = \frac{1}{2} \cdot C \cdot V^{2}$

### Capacitive Time Constant

Time Constant: $\tau = RC$ expressed in seconds, where the resistance R is the Thevenin’s equivalent resistance of the circuit as seen from the terminals of the capacitor.

Many capacitors are constructed by rolling alternating layers of aluminum and dielectric. Some are made in a form of ceramic disks. Voltage can be applied in both directions (may be reversed) to capacitors constructed from mica, Teflon, mylar, polyethylene or ceramic disks. In electrolytic capacitors, one plate is metallic aluminum or tantalum and the dielectric is an oxide layer formed by chemical reaction with a solution called electrolyte. The result is a large-value capacitor with a small volume. Electrolytic capacitors are “polarized” and only one polarity of voltage is allowed. Application of opposite polarity voltage causes the electrolyte to chemically dissolve the dielectric and this leads to capacitor failure.

Real capacitors have some parasitic elements in the form of lead inductance and series resistance as well as a parallel conductance due to leakage through the dielectric.

This should give you a simple understanding of a capacitor, non-graphically.  The next lesson will discuss reactance as it applies to Inductors and Capacitors.  Wahoo! 🙂