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Capacitor Basics

Tenth Part of DC Electricity for Industrial Instrumentation

Any two electrical conductors separated by an insulating medium possess the characteristic called capacitance: the ability to store energy in the form of an electric field. Capacitance is symbolized by the capital letter C and is measured in the unit of the Farad (F). The relationship between capacitance, stored electric charge (Q), and voltage (V ) is as follows:

Q = CV

For example, a capacitance having a value of 33 microfarads charged to a voltage of 5 volts would store an electric charge of 165 microcoulombs.

Capacitance is a non-dissipative quantity. Unlike resistance, a pure capacitance does not dissipate energy in the form of heat; rather, it stores and releases energy from and to the rest of the circuit.

Capacitors are devices expressly designed and manufactured to possess capacitance. They are constructed of a “sandwich” of conductive plates separated by an insulating dielectric. Capacitors have voltage ratings as well as capacitance ratings. Here are some schematic symbols for capacitors:

 

Capacitors_Fig_042.JPG

 

A capacitor’s capacitance is related to the electric permittivity of the dielectric material (symbolized by the Greek letter “epsilon,” ε), the cross-sectional area of the overlapping plates (A), and the distance separating the plates (d):

C = εA / d

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

Cparallel = C1 + C2 ・ ・ ・Cn

Cseries = 1 / ((1 / C1) + (1 / C2) + ・ ・ ・(1 / Cn))

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 creating 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 at the same value.

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 ):

I = C ( dV / dt )

P = IV = CV ( dV / dt )

dEp / dt = CV ( dV / dt )

(dEp / dt) / dt = CV dV

(dEp / dt) / dt = CV dV


dEp = C dV

Ep = (1/2 ) CV2

 

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.

 

Click here to go to the contents page of Basic DC Electricity for Industrial Instrumentation

Click here to go back reading on the DC Electromagnetism - Ninth Part of DC electricity for Industrial Instrumentation

Click here to continue reading on the Inductors - Eleventh Part of DC electricity for Industrial Instrumentation

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