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?

1 F (C) Signup and view all the answers

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

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

What is the defining equation for capacitance in integral form?

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

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

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

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

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

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

2200μF (D) Signup and view all the answers

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

54.4mJ (A) Signup and view all the answers

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

Electrolytic capacitors (C) Signup and view all the answers

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

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

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

The external circuit driving the capacitor (A) Signup and view all the answers

Which of these dielectrics has the highest dielectric strength?

PP (C) Signup and view all the answers

Which of these ceramic capacitor classes has the highest permittivity?

Class 3 (A) Signup and view all the answers

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

PPS (D) Signup and view all the answers

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

Class 1 (C) Signup and view all the answers

Which of these ceramic capacitor classes is based on BaTiO3?

Class 2 (B) Signup and view all the answers

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

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

What is the Curie point?

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

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

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

Which of these is NOT a type of ceramic capacitor?

Electrolytic (A) Signup and view all the answers

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

All of the above (D) Signup and view all the answers

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

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

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

Capacitance, Equivalent Series Resistance, Equivalent Series Inductance (B) Signup and view all the answers

What is the typical capacitance range for ceramic capacitors?

1 pF to 100 μF (A) Signup and view all the answers

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

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

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

Infinite resistance between the electrodes (A) Signup and view all the answers

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

High temperature dependence (A) Signup and view all the answers

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

Equivalent Series Inductance (D) Signup and view all the answers

What is the typical voltage range for ceramic capacitors?

4 V to 50 kV (A) Signup and view all the answers

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

1 nF (A) Signup and view all the answers

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

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

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

High (A) Signup and view all the answers

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

Variable depending on the specific capacitor (B) Signup and view all the answers

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

It decreases (D) Signup and view all the answers

What is the typical useful life of a ceramic capacitor?

5000 hours (D) Signup and view all the answers

What is the definition of the dielectric material?

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) 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)?

D = E + P (D) Signup and view all the answers

Which of these are the mentioned types of capacitors?

Film capacitors, ceramic capacitors, electrolytic capacitors, and supercapacitors (C) Signup and view all the answers

Which of these correctly represents the types of film capacitors?

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

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

Aluminum electrolytic capacitors and tantalum electrolytic capacitors (C) Signup and view all the answers

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

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) Signup and view all the answers

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

χ = ε - 1 (C) 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.)

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) Signup and view all the answers

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

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

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

High stability (A), Low dissipation factor (B), Low dielectric constant (C) 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?

Inner breakdown (D) Signup and view all the answers

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

Ceramic (SrBi)TiO3 (B) Signup and view all the answers

What is the dielectric dissipation factor of polypropylene?

3 x 10-4 (B) Signup and view all the answers

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

Inhomogeneities causing uneven current distribution (B) Signup and view all the answers

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

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

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

Polypropylene (A) Signup and view all the answers

Which of the following describes the complex relative permittivity?

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

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

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) Signup and view all the answers

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 * (dv_c(t)/dt).
Defining equation (integral form): vc(t) = (1/C) * ∫_-∞^t ic(τ) dτ = vc(t₀) + (1/C) * ∫_t₀^t ic(τ) dτ.
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 • dÃ / ∫_C E · dl.
The numerator represents the charge (Coulomb's Law).
The denominator represents the voltage across the electrodes.
Parallel-plate capacitor equation: C= ε_rε₀ * (A/d), where ε_r 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 (R_iso).

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 (ε_r = 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 (ε_r = 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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Description

Test your knowledge on the principles of capacitance, including its defining equations, measurements in Farads, and relationships with current and voltage. This quiz covers various aspects of capacitors, including energy storage efficiency and characteristics in sinusoidal waveforms.