Capacitance and Circuit Behavior Quiz

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Questions and Answers

What is the defining equation for capacitance in differential form?

  • $C = \frac{dQ}{dV}$
  • $dV = C dQ$
  • $C = \frac{dV}{dQ}$
  • $dQ = C dV$ (correct)

What does the capacitance, C, measure?

  • The amount of voltage stored in a capacitor
  • The resistance of the capacitor
  • The amount of current flowing through a capacitor
  • The ratio of charge to voltage (correct)

What is the unit of capacitance?

  • Ohm
  • Volt
  • Ampere
  • Farad (correct)

What is the value of capacitance in Farads if 1 As of charge increases the voltage by 1 V?

<p>1 F (C)</p> Signup and view all the answers

What is the relationship between the current and voltage of a capacitor for sinusoidal waveforms?

<p>Current leads voltage by 90 degrees. (C)</p> Signup and view all the answers

What is the defining equation for capacitance in integral form?

<p>$Q = C \int V dt$ (A)</p> Signup and view all the answers

What is characteristic of the current of a capacitor for periodical signals?

<p>It has a zero-mean average. (C)</p> Signup and view all the answers

What is the meaning of the phrase "capacitance has the characteristic to differentiate voltages or to integrate currents"?

<p>Capacitors can change the shape of voltage and current signals. (D)</p> Signup and view all the answers

What is the capacitance of the 2200μF/25V electrolytic capacitor?

<p>2200μF (D)</p> Signup and view all the answers

What is the stored energy of the 0.68μF/400V metallized PP film capacitor?

<p>54.4mJ (A)</p> Signup and view all the answers

Which of the two capacitor types is more efficient in energy storage for the same physical dimensions?

<p>Electrolytic capacitors (C)</p> Signup and view all the answers

What is the approximate relationship between stored energy and voltage for a given capacitor?

<p>Energy is proportional to the square of voltage (A)</p> Signup and view all the answers

Which components of the circuit are responsible for the voltage across the electrodes of a capacitor?

<p>The external circuit driving the capacitor (A)</p> Signup and view all the answers

Which of these dielectrics has the highest dielectric strength?

<p>PP (C)</p> Signup and view all the answers

Which of these ceramic capacitor classes has the highest permittivity?

<p>Class 3 (A)</p> Signup and view all the answers

Which of these dielectrics has the lowest dissipation factor at 10 kHz?

<p>PPS (D)</p> Signup and view all the answers

Which of these ceramic capacitor classes is typically used in snubber circuits?

<p>Class 1 (C)</p> Signup and view all the answers

Which of these ceramic capacitor classes is based on BaTiO3?

<p>Class 2 (B)</p> Signup and view all the answers

What is the formula for calculating the capacitance of a parallel-plate capacitor?

<p>C = ε0 * εr * A / d (C)</p> Signup and view all the answers

What is the Curie point?

<p>The temperature at which a ferroelectric material loses its ferroelectric properties (C)</p> Signup and view all the answers

What is the unit of measurement for permittivity (ε0)?

<p>Amperes per volt-meter (A/(Vm)) (D)</p> Signup and view all the answers

Which of these is NOT a type of ceramic capacitor?

<p>Electrolytic (A)</p> Signup and view all the answers

Which of the following factors contribute to the non-ideal characteristics of real capacitors?

<p>All of the above (D)</p> Signup and view all the answers

What is the meaning of the EIA-198 code X7R?

<p>-55°C to +125°C temperature range with +/- 15% capacitance change (B)</p> Signup and view all the answers

What are the three main components in the equivalent circuit of a real capacitor?

<p>Capacitance, Equivalent Series Resistance, Equivalent Series Inductance (B)</p> Signup and view all the answers

What is the typical capacitance range for ceramic capacitors?

<p>1 pF to 100 μF (A)</p> Signup and view all the answers

What is the significance of the dissipation factor (tan δ) in a real capacitor?

<p>It reflects the difference between the actual and ideal capacitor. (B)</p> Signup and view all the answers

Which of the following is NOT a non-ideal characteristic of a real capacitor?

<p>Infinite resistance between the electrodes (A)</p> Signup and view all the answers

Which of these is a characteristic of Class 2 ceramic capacitors?

<p>High temperature dependence (A)</p> Signup and view all the answers

What does the term 'LESL' represent in the equivalent circuit of a real capacitor?

<p>Equivalent Series Inductance (D)</p> Signup and view all the answers

What is the typical voltage range for ceramic capacitors?

<p>4 V to 50 kV (A)</p> Signup and view all the answers

What is the typical capacitance of a ceramic capacitor with the size notation 0603?

<p>1 nF (A)</p> Signup and view all the answers

What is the relationship between the dissipation factor (tan δ) and the energy losses in a capacitor?

<p>Higher tan δ indicates higher energy losses (D)</p> Signup and view all the answers

What is the typical quality factor of a Class 1 ceramic capacitor?

<p>High (A)</p> Signup and view all the answers

What is the typical temperature coefficient of a Class 2 ceramic capacitor?

<p>Variable depending on the specific capacitor (B)</p> Signup and view all the answers

What happens to the capacitance of a ceramic capacitor when a DC bias voltage is applied?

<p>It decreases (D)</p> Signup and view all the answers

What is the typical useful life of a ceramic capacitor?

<p>5000 hours (D)</p> Signup and view all the answers

What is the definition of the dielectric material?

<p>A material that increases the ability of storing electric charges through a specific property that increases capacity. (B), A material that can be polarized and is used to form capacitors. (C), A material that increases the ability of storing electric charges and therefore increases the capacity. (D)</p> Signup and view all the answers

What is the relationship between the electric displacement field (D), the electric field strength (E), and the polarization density (P)?

<p>D = E + P (D)</p> Signup and view all the answers

Which of these are the mentioned types of capacitors?

<p>Film capacitors, ceramic capacitors, electrolytic capacitors, and supercapacitors (C)</p> Signup and view all the answers

Which of these correctly represents the types of film capacitors?

<p>Metallized paper, metallized plastic film, and plastic film/foil (D)</p> Signup and view all the answers

Which of these are the types of electrolytic capacitors listed in the text?

<p>Aluminum electrolytic capacitors and tantalum electrolytic capacitors (C)</p> Signup and view all the answers

What is the definition of tan δ in relation to capacitors?

<p>It is the ratio of the imaginary part to the real part of the impedance. (E), It is the ratio of power loss to the reactive power. (F)</p> Signup and view all the answers

What is the relationship between the dielectric constant (χ) and the electric susceptibility (ε)?

<p>χ = ε - 1 (C)</p> Signup and view all the answers

Which of the following are the main reasons for the non-linear behaviour of capacitors? (Select all that apply.)

<p>Frequency-dependent properties of the dielectric material. (B), The capacitance value depends on the voltage applied. (C), Non-uniform distribution of the electric field within the capacitor. (D), Non-linear relationship between electric field and polarization. (E)</p> Signup and view all the answers

What are the typical applications of capacitors in switched-mode power supplies? (Select all that apply)

<p>Reactive current compensation (C), Voltage smoothing (E), Energy storage (F), Filtering (G)</p> Signup and view all the answers

What are the key characteristics of a class 1 ceramic capacitor? (Select all that apply)

<p>High stability (A), Low dissipation factor (B), Low dielectric constant (C)</p> Signup and view all the answers

Based on the provided information, which type of polarization best describes the mechanism behind the increased electric field in a dielectric material with air inclusions?

<p>Inner breakdown (D)</p> Signup and view all the answers

Which material has the highest relative permittivity based on the provided table?

<p>Ceramic (SrBi)TiO3 (B)</p> Signup and view all the answers

What is the dielectric dissipation factor of polypropylene?

<p>3 x 10-4 (B)</p> Signup and view all the answers

Which of the following is a potential cause of thermal breakdown in a dielectric?

<p>Inhomogeneities causing uneven current distribution (B)</p> Signup and view all the answers

What is the primary difference between avalanche breakdown and thermal breakdown in dielectrics?

<p>Avalanche breakdown is caused by electron collisions, whereas thermal breakdown is caused by heat generation. (D)</p> Signup and view all the answers

Which of the following materials has the lowest dielectric dissipation factor?

<p>Polypropylene (A)</p> Signup and view all the answers

Which of the following describes the complex relative permittivity?

<p>A combination of the dielectric's ability to store and dissipate electrical energy. (D)</p> Signup and view all the answers

What is the relationship between the dielectric dissipation factor and the dielectric loss factor?

<p>The dielectric dissipation factor is the tangent of the loss angle (tan δ), while the dielectric loss factor is represented as tan δ itself. (C)</p> Signup and view all the answers

Flashcards

Ideal Capacitance

A theoretical measure of a capacitor's ability to store charge without losses.

Stored Energy in Capacitors

The amount of energy a capacitor can hold, determined by capacitance and voltage.

Electrolytic Capacitor

A type of capacitor known for high capacitance and energy storage but limited voltage ratings.

Metallized PP Film Capacitor

A capacitor that uses a polymer film as a dielectric, offering stable capacitance but lower energy storage.

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Capacitance Calculation Formula

The equation used to calculate capacitance involves charge quantity and voltage across electrodes.

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Capacitance

Measure of a capacitor's ability to store electric charge at a given voltage.

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Units of Capacitance

Capacitance is measured in Farads (F), where 1 F = 1 As/V.

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Ideal Capacitor

An ideal capacitor perfectly differentiates voltage or integrates current based on impressed values.

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Current-Voltage Relationship

The current in a capacitor leads its voltage by 90 degrees in sinusoidal waveforms.

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Zero-Mean Current

For periodic signals, the average current through a capacitor is zero.

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Capacitor Symbol

A graphical representation used to denote a capacitor in circuit diagrams.

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Calculating Capacitance

Capacitance can be calculated using the equation C = Q/V where Q is charge and V is voltage.

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Types of Capacitors

Capacitors are classified based on their construction and application types.

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Parallel-plate capacitor

A capacitor consisting of two parallel conductive plates separated by a distance.

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Capacitance formula

C = ε × (A/d) where C is capacitance, A is the area, and d is the distance between plates.

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Vacuum permittivity (ε0)

The ability of a vacuum to permit electric field lines, valued at 8.8542 pF/m.

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Equivalent series resistance (RESR)

The resistance that appears in series with an ideal capacitor, affecting its performance.

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Dissipation factor (tan δ)

A ratio comparing active and reactive power in a capacitor, indicating efficiency.

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Insulating resistance (Riso)

The resistance between capacitor electrodes that prevents current leakage.

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Capacitor spacing (d)

Distance between the plates in a parallel-plate capacitor, influencing capacitance.

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tan δ Definition

The ratio of power loss to reactive power in capacitors.

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ESC

Equivalent series capacitance in a capacitor's circuit.

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ESR

Equivalent series resistance indicating energy loss in capacitors.

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Linear Capacitors

Capacitors with constant capacitance, such as film and ceramic types.

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Non-Linear Capacitors

Capacitors whose capacitance changes with voltage or frequency.

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Electric Energy Storage

The function of capacitors to hold electric energy.

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Voltage Smoothing

Using capacitors to reduce voltage fluctuations in circuits.

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Reactive Current Compensation

Using capacitors to counter reactive power in circuits.

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Ceramic Capacitors

A type of non-polarized capacitor using ceramic as dielectric.

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Dielectric Properties

Material qualities that enhance a capacitor's charge storage capacity.

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Electric Polarization

The separation of positive and negative charges in a material under an electric field.

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Complex Relative Permittivity

A measure of how a dielectric material responds to an electric field, including its storage and loss of energy.

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Dielectric Dissipation Factor

A measure of energy loss in a dielectric material, represented as tan δ.

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Avalanche Breakdown

A process where free electrons accelerate and generate more free electrons, leading to a current surge.

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Thermal Breakdown

Breakdown caused by uneven current densities that increase temperature, leading to further current increase.

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Inner Breakdown

A breakdown occurring at air inclusions in the dielectric material, where electric fields intensify.

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Relative Permittivity of Water

A measure showing water's capacity to permit electric fields, valued at 81.

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Dielectric Materials Comparison

Materials are rated by their relative permittivity and dissipation factors; ceramics have high values.

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Dielectric Strength

The maximum electric field a dielectric can withstand without breakdown, measured in V/μm.

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Dissipation Factor

A measure of energy loss in a dielectric material when subjected to an alternating electric field.

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Relative Permittivity

A measure of a material's ability to store electrical energy in an electric field, often referred to as dielectric constant.

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Capacitance in Ceramic Capacitors

Ceramic capacitors typically range from 1 pF to 100 μF, depending on their design and application.

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Class 1 Ceramic Capacitors

Characterized by low permittivity and high stability, suitable for precision applications.

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Class 2 Ceramic Capacitors

Have higher permittivity and acceptable temperature dependence, with non-linear behavior.

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Ageing in Ceramic Capacitors

Refers to the gradual change in capacitance and characteristics due to factors like temperature and voltage over time.

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Temperature Coefficients

Measurements that indicate how the capacitance of a capacitor changes with temperature.

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Piezoelectric Effect in Ceramic Capacitors

The generation of electrical noise when mechanical pressure is applied to a ceramic capacitor.

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Multi-Layer Ceramic Capacitor (MLCC)

A type of ceramic capacitor that consists of multiple layers of dielectric and electrodes, enhancing capacitance without increasing size.

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Voltage Derating

The practice of using a capacitor at a voltage lower than its maximum rated voltage to extend its useful life and reliability.

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Electric Field Strength

The intensity of the electric field at a point in space, contributing to how forces are exerted on charges.

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Temperature Range of Capacitors

The range of temperatures within which a capacitor can operate effectively without damage.

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Ceramic Capacitor Applications

Used in snubber circuits, output capacitors, and DC link applications due to their high current capability.

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Ripple Current Rating

The maximum AC current a capacitor can handle without overheating or degrading over time.

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Study Notes

Passive Components: Capacitors

  • Capacitors are technical implementations of capacitance (C), a measure of the capacity to store electric charge (Q) at a given voltage (V).
  • The symbol for capacitance is C.
  • The unit for capacitance is 1 Farad (1 F).
  • 1 F is a charge of 1 Coulomb (1 C) if the voltage increases by 1 Volt (1 V).
  • Mathematically, capacitance is expressed as C = Q/V, where Q is the electric charge stored and V is the voltage.

Ideal Capacitance

  • Defining equation (differential form): ic(t) = C * (dvc(t)/dt).
  • Defining equation (integral form): vc(t) = (1/C) * ∫-∞t ic(Ï„) dÏ„ = vc(t0) + (1/C) * ∫t0t ic(Ï„) dÏ„.
  • Capacitance has the characteristic to differentiate voltages or to integrate currents, depending on the impressed value.

Calculation of Capacitances

  • General equation C = Q/V = ∫S D • dà / ∫C E · dl.
  • The numerator represents the charge (Coulomb's Law).
  • The denominator represents the voltage across the electrodes.
  • Parallel-plate capacitor equation: C= εrε0 * (A/d), where εr is the relative permittivity, ε0 is the vacuum permittivity, A is the area of the plates, and d is the separation between the plates.
  • Double wire circuit equation: C = (π·ε0·l)/ln((d)/(2r) -1), where ε0 is the vacuum permittivity, l is the length, d is the conductor spacing, and r is the conductor radius.

Real Capacitor

  • Real capacitors have non-ideal characteristics.
  • Conductors for carrying current have finite conductances.
  • Current-carrying conductors generate magnetic fields.
  • Leakage currents exist, resulting in finite resistance between electrodes.
  • Equivalent circuit: Includes capacitance (C), equivalent series resistance (ESR), equivalent series inductance (ESL), and insulating resistance (Riso).

Classification of Technologies

  • Linear constant capacitors, film capacitors, paper capacitors, ceramic capacitors, electrolytic capacitors, adjustable capacitors, and non-linear capacitors.

Classification of Applications

  • Electric energy storage.
  • Voltage smoothing.
  • Carrying dynamic currents (AC currents).
  • Filtering (active, passive, AC/DC, EMC).
  • Reactive current compensation.
  • Snubber circuits.
  • Forming resonance circuits.
  • Frequency-dependent impedance.

Ceramic Capacitors

  • Dielectrics are oxides.
  • Available in two main classes.
  • Generally have small capacitances (from 1 pF to 100 µF).
  • Available for voltages between 4 V and 50 kV.
  • Capacitance depends on voltage, temperature, and frequency.
  • Have low equivalent series resistance (ESR) and low equivalent series inductance (ESL).

Film Capacitors

  • Self-healing effects.
  • Available up to 1000 V and 100 µF.
  • Different construction structures.
  • Dielectrics based on plastic or paper.
  • Metal foil electrodes.
  • Plastic film.
  • Metal contact layer.
  • Terminating wire.

Electrolytic Capacitors

  • Available up to 600 V and approximately 1 F.
  • Aluminum, tantalum, or niobium anodes.
  • Available in SMD, through-hole technologies.
  • Have small size at high capacitances.
  • Polarized; operate with DC voltage.

Tantalum Electrolytic Capacitors

  • Relatively expensive.
  • Available up to 125 V and approximately 1.5 mF.
  • Tantalum anodes and tantalum oxide dielectrics.
  • High relative permittivity (εr = 26).
  • Extremely high capacitance at low volumes.

Polymer Capacitors

  • Available up to 250 V and approximately 4.7 mF.
  • High temperature stability.
  • Good behavior at low temperatures.
  • Very low equivalent series resistances (ESR).
  • High ripple current capability.
  • High capacitance at low volumes.

Double Layer Capacitors

  • Relatively expensive.
  • Available up to 2.8 V and 5000 F.
  • Tantalum anodes and tantalum oxide dielectric.
  • High relative permittivity (εr = 26).
  • Extremely high capacitance at low volumes.

AC Filter

  • Components that filter AC components.

Snubber Circuits

  • Circuits that protect electronic components.

EMC Filters

  • Filters that suppress noise.

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