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Capacitors

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The Electric Field The electric field strength at a point is the force acting on a unit positive charge at that point. Electric flux lines always extend from a positively charged body to a negatively charged body, always extend or terminate perpendicular to the charged surface, and never intersect. 4

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The Electric Field The electric field is represented by electric flux lines, which are drawn to indicate the strength of the electric field at any point around the charged body. The denser the lines of flux, the stronger the electric field. 3

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**Flux distribution from an isolated positive charge.**

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**Determining the force on a unit charge r meters from a charge Q of similar polarity.**

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**Electric flux distributions: (a) opposite charges (b) like charges**

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Basics of a Capacitor In its simplest form, a capacitor is an electrical device constructed of two parallel plates separated by an insulating material called the dielectric In the neutral state, both plates have an equal number of free electrons When a voltage source is connected to the capacitor, electrons are removed from one plate and an equal number are deposited on the other plate No electrons flow through the dielectric (insulator)

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The basic capacitor.

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**Symbols for the capacitor: (a) fixed; (b) variable.**

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Capacitance Capacitance is a measure of a capacitor’s ability to store charge on its plates. A capacitor has a capacitance of 1 farad (F) if 1 coulomb (C) of charge is deposited on the plates by a potential difference of 1 volt across its plates. The farad is named after Michael Faraday, a nineteenth century English chemist and physicist. 5

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**How a Capacitor Stores Energy**

A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates A capacitor obeys Coulomb’s law: A force exists between two point-source charges that is directly proportional to the product of the two charges and inversely proportional to the square of the distance between the charges

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**Illustration of a capacitor storing charge.**

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**The electric field stores energy in a capacitor**

The electric field stores energy in a capacitor. The beige area indicates the dielectric.

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**Lines of force are created by opposite charges.**

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**Electric flux distribution between the plates of a capacitor: (a) including fringing; (b) ideal.**

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Capacitance Fringing – At the edge of the capacitor plates the flux lines extend outside the common surface area of the plates. 7

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Basics of a Capacitor When the supply is removed from the capacitor, the capacitor retains the stored charge The amount of charge that a capacitor can store per volt across the plates is its capacitance (C) The unit of capacitance is the farad (F). One farad is the amount of capacitance when one coulomb of charge is stored with one volt across the plates Most capacitors in electronics work have capacitance values of F (10-6 F) or F (10-12 F)

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Capacitance The farad is generally too large a measure of capacitance for most practical applications, so the microfarad (106 ) or picofarad (1012 ) is more commonly used. Different capacitors for the same voltage across their plates will acquire greater or lesser amounts of charge on their plates, hence the capacitors have greater or lesser capacitance. 6

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**Dielectric – Insulator of the capacitor**

The purpose of the dielectric is to create an electric field to oppose the electric field setup by free charges on the parallel plates. Di for “opposing” and electric for “electric field” Dipoles – Formed within the insulator of a capacitor when the electrons of the insulating material are unable to leave the parent atom and travel to the positive plate of the capacitor 8

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Demonstrating the effect of inserting a dielectric between the plates of a capacitor: (a) air capacitor; (b) dielectric being inserted.

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Effect of a dielectric on the field distribution between the plates of a capacitor: (a) alignment of dipoles in the dielectric; (b) electric field components between the plates of a capacitor with a dielectric present.

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Capacitance With different dielectric materials between the same two parallel plates, different amounts of charge will deposit on the plates. Permittivity – The ratio of the flux density to the electric field intensity in the dielectric. A measure of how easily the dielectric will “permit” the establishment of flux lines within the dielectric. Relative permittivity – Often called the dielectric constant, it is the ratio of the permittivity of any dielectric to that of a vacuum. 9

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**Characteristics of a Capacitor**

Capacitance is directly proportional to the physical size of the plates as determined by the plate area Capacitance is inversely proportional to the distance between the plates The measure of a material’s ability to establish an electric field is called the dielectric constant () Capacitance is directly proportional to the dielectric constant

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**Capacitance is directly proportional to plate area (A).**

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**Capacitance is inversely proportional to the distance d between the plates.**

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**Three ways to increase the area of a capacitor: (a) rolling; (b) stacking; (c) insertion.**

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**Construction of a typical radial-lead mica capacitor.**

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**(a) Typical ceramic capacitors with radial leads. (b) Construction view.**

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Construction view of a typical ceramic chip capacitor used for surface mounting on printed circuit boards.

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**Basic construction of axial-lead tubular plastic-film dielectric capacitors.**

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**(a) Several typical plastic-film capacitors**

(a) Several typical plastic-film capacitors. (b) Construction view of an axial-lead capacitor.

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Capacitance For every dielectric there is a potential that, if applied across the dielectric, will break the bonds within the dielectric and cause current to flow. The voltage required per unit length (electric field intensity) to establish conduction in a dielectric is an indication of its dielectric strength and is called the breakdown voltage 10

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Capacitors Working voltage – the voltage that can be applied across a capacitor for long periods of time with out breakdown Surge voltage – The maximum dc voltage that can be applied for a short period of time Leakage current – The current that results in the total discharge of a capacitor as the capacitor is disconnected from the charging network for a sufficient length of time. 15

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Types of Capacitors Fixed – mica, ceramic, electrolytic, tantalum and polyester-film Mica capacitor consists of mica sheets separated by sheets of metal foil. The plates are connected to two electrodes. The entire system is encased in a plastic insulating material. The mica capacitor exhibits excellent characteristics under stress of temperature variations and high voltage applications. 12

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**Electrolytic Capacitors**

Most commonly used in situations where capacitances of the order of one to several thousand microfarads are required. Primarily for use in dc networks because they have good insulating characteristics (high leakage current) between the plates in one direction but take on the characteristics of a conductor in the other direction. Basic construction consists of a roll of aluminum foil coated on one side with an aluminum oxide, the aluminum being the positive plate and the oxide the dielectric. A layer of paper or gauze saturated with an electrolyte is placed over the aluminum oxide on the positive plate. Another layer of aluminum without the oxide is then placed over this layer to assume the role of the negative plate. 14

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**Electrolytic Capacitors**

Two common types of electrolytic capacitors are Aluminum and Tantalum electrolytics The voltage polarity of these devices must be observed, as reversal of polarity will usually result in complete destruction of the capacitor

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**Electrolytic capacitors are polarized so that one plate is positive, and the other negative**

They come in capacitance values from 1F to 200,000 F, with voltage ratings to 350 V

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Demonstrating that, in general, for each type of construction, the size of a capacitor increases with the capacitance value: (a) electrolytic; (b) polyester-film; (c) tantalum.

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**Polyester-film Capacitors**

Basic construction consists of two metal foils separated by a strip of polyester material such as Mylar. The outside layer of polyester is applied to act as an insulating jacket. Each metal jacket is connected to a lead that extends either axially or radially from the capacitor. The rolled construction results in a large surface, and the use of the plastic dielectric results in a very thin layer between the conducting surfaces. The capacitor can be used for both dc and ac networks. 17

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(a) Film/foil polyester radial lead; (b) metalized polyester-film axial lead; (c) surface-mount polyester-film; (d) polypropylene-film, radial lead.

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**Capacitors Ceramic Capacitors**

Made in different shapes and sizes but the basic construction is the same A ceramic base is coated on both sides with a metal, such as copper or silver, to act as the two plates. The leads are then attached through electrodes to the plates. An insulating coating of ceramic or plastic is then applied over the plates and dielectric. Ceramic capacitors have very low leakage current and can be used in both dc and ac networks. 13

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Fixed Capacitors Ceramic dielectrics provide very high dielectric constants, and relatively large capacitance in a small physical size Capacitance ranges are from 1pF to 2.2F

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**Capacitors Variable Capacitors**

Most common are shown in the figure below. The dielectric for each is air. The capacitance is changed by turning the shaft at one end to vary the common area of the movable and fixed plates. The greater the common area the larger the capacitance. 18

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**Schematic symbol for a variable capacitor**

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**Variable capacitors: - air**

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**Variable capacitors: (b) air trimmer; (c) ceramic dielectric compression trimmer.**

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Trimmer capacitors.

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**Oil-filled, metallic oval case snubber capacitor (the snubber removes unwanted voltage spikes).**

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Capacitor Labeling Capacitors use several standard labeling methods; we will consider a small ceramic capacitor: values marked as .001 or .01 have units of microfarads values marked as 50 or 330 have units of picofarads a value of 103 or 104 would be 10x103 (10,000 pF) or 10x104 (100,000 pF) respectively The units may be on the capacitor as pF or F (F may be written a MF or MFD)

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**Various marking schemes for small capacitors.**

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**Various marking schemes for small capacitors**

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**Capacitors Measuring and testing**

The digital reading capacitance meter shown will allow you to simply place the capacitor between the provided clips with the proper polarity and the meter will display the level of capacitance. Insert Fig 10.20 19

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**A typical LCR meter (Photography courtesy of B&K Precision Corp.)**

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**Checking the dielectric of an electrolytic capacitor.**

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**Checking a capacitor with an analog ohmmeter**

Checking a capacitor with an analog ohmmeter. This check shows a good capacitor.

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Capacitors in Series Capacitors, like resistors, can be placed in series and in parallel. When placed in series, the charge is the same on each capacitor. 26

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Series capacitors.

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Series Capacitors When capacitors are connected in series, the total capacitance is less than the smallest capacitance value since the effective plate separation increases 1/CT = 1/C1 + 1/C2 + 1/C3 + … + 1/Cn

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**Capacitors in series produce a total capacitance that is less than the smallest value.**

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**General circuit with n capacitors in series.**

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**Capacitors in Parallel**

Placing capacitors in parallel the voltage across each capacitor is the same. The total charge is the sum of that on each capacitor. 27

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Parallel Capacitors The total parallel capacitance is the sum of all capacitors in parallel CT = C1 + C2 + C3 + … + Cn

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Parallel capacitors.

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**Capacitors in parallel produce a total capacitance that is the sum of the individual capacitances.**

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**General circuit with n capacitors in parallel.**

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Stray Capacitance Stray capacitances exist not through design but simply because two conducting surfaces are relatively close to each other. Two conducting wires in the same network will have a capacitive effect between them. 29

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Series / Parallel

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**Equivalent circuit for a nonideal capacitor.**

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**Capacitors in DC Circuits**

A capacitor will charge up when it is connected to a dc voltage source When a capacitor is fully charged, there is no current There is no current through the dielectric of the capacitor because the dielectric is an insulating material A capacitor blocks constant dc

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**Transients in Capacitive Networks: Charging Phase**

The placement of charge on the plates of a capacitor does not occur instantaneously. Transient Period – A period of time where the voltage or current changes from one steady-state level to another. The current ( ic ) through a capacitive network is essentially zero after five time constants of the capacitor charging phase. 20

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**Fundamental charging circuit.**

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**Basic R-C charging network.**

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Charging a capacitor.

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**Discharging a capacitor.**

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**Current and voltage in a charging and discharging a capacitor.**

Thomas L. Floyd Electronics Fundamentals, 6e Electric Circuit Fundamentals, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.

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RC Time Constant The voltage across a capacitor cannot change instantaneously because a finite time is required to move charge from one point to another (limited by circuit resistance) The time constant of a series RC circuit is a time interval that equals the product of the resistance and the capacitance = RC

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Initial Conditions The voltage across a capacitor at the instant of the start of the charging phase is called the initial value. Once the voltage is applied the transient phase will commence until a leveling off occurs after five time constants called steady-state as shown in the figure. 22

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**C during the charging phase.**

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**Plotting the equation C = E(1 – e–t/) versus time (t).**

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**FIG. 10.30 Plotting the equation iC = E/R x (e–t/) versus time (t).**

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**FIG. 10.28 Universal time constant chart.**

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**Charging and Discharging**

The charging curve is an increasing exponential The discharging curve is a decreasing exponential

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Transient time It takes 5 time constants to change the voltage by 99% (charging or discharging), this is called the transient time

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The Current Ic Current ic associated with the capacitance C is related to the voltage across the capacitor by Where dvc / dt is a measure of the change in vc in a vanishingly small period of time. The function dvc / dt is called the derivative of the voltage vc with respect to time t. 25

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**Energy Stored by a Capacitor**

The ideal capacitor does not dissipate any energy supplied to it. It stores the energy in the form of an electric field between the conducting surfaces. The power curve can be obtained by finding the product of the voltage and current at selected instants of time and connecting the points obtained. WC is the area under the curve. 28

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**Capacitors in ac Circuits**

The instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor This rate of change is a maximum positive when the rising sine wave crosses zero This rate of change is a maximum negative when the falling sine wave crosses zero The rate of change is zero at the maximum and minimum of the sine wave

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**The current in a capacitive circuit varies directly with the frequency of the source voltage**

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**Capacitive Reactance, XC**

Capacitive reactance (XC) is the opposition to sinusoidal current, expressed in ohms The rate of change of voltage is directly related to frequency As the frequency increases, the rate of change of voltage increases, and thus current ( i ) increases An increase in i means that there is less opposition to current (XC is less) XC is inversely proportional to i and to frequency

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**Capacitive Reactance, XC**

The relationship between capacitive reactance, capacitance and frequency is: XC = 1/(2 f C) where: XC is in ohms () f is in hertz (Hz) C is in farads (F)

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**FIGURE 9-39 Rate of change of a sine wave increases when frequency increases.**

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**Analysis of Capacitive ac Circuit**

The current leads the voltage by 90 in a purely capacitive ac circuit

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Power in a Capacitor Energy is stored by the capacitor during a portion of the voltage cycle; then the stored energy is returned to the source during another portion of the cycle Instantaneous power (p) is the product of v and i True power (Ptrue) is zero, since no energy is consumed by the capacitor The rate at which a capacitor stores or returns energy is called reactive power (Pr); units: (VAR)

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**Power curve for a capacitor.**

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FIGURE 9-73

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**Capacitor Applications**

Capacitors are used for filtering in power supplies Since capacitors do not pass dc, they are used for dc blocking and ac coupling For power line decoupling, capacitors are connected between the dc supply and ground, to suppress unwanted voltage spikes that occur on the dc supply voltage due to fast switching Capacitors are used to bypass an ac voltage around a resistor without affecting the dc resistance

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**Basic operation of a power supply filter capacitor**

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**FIGURE 9-51 An application of a capacitor used to block dc and couple ac in an amplifier.**

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**Example of the operation of a bypass capacitor**

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**Capacitively coupled amplifier**

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Summary A capacitor is composed of two parallel conducting plates separated by a dielectric insulator Energy is stored by a capacitor in the electric field between the plates Capacitance is measured in units of farads (F)

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Summary Capacitance is directly proportional to the plate area and inversely proportional to the plate separation Dielectric constant is an indication of the ability of a material to establish an electric field Dielectric strength is one factor that determines the breakdown voltage of a capacitor A capacitor blocks constant dc

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Summary The time constant for a series RC circuit is the series resistance times the capacitance In an RC circuit, the voltage and current in a charging or discharging capacitor make a 63% change during each time-constant interval 5 time constants are required for a capacitor to fully charge or to discharge fully. This is called the transient time Charging and discharging are exponential curves

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**Summary Current leads voltage by 90 in a capacitor**

Capacitive reactance is the opposition to ac, expressed in ohms XC is inversely proportional to frequency and capacitance value The true power in a capacitor is zero; that is, there is no energy loss in an ideal capacitor most capacitors have some small energy loss due to leakage resistance

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