Chapter 3: Capacitors and Inductors

Van Su Luong

http://phenikaa-uni.edu.vn

Contents

• Capacitors and Capacitance

• Typical Capacitors and Coding

• Parallel and Series Capacitances

• Capacitive Circuits

• Inductors and Inductance

• Types of Inductors

• Parallel and Series Inductances

• Inductive Circuits

Capacitors and Capacitance

• Capacitor:

A capacitor is a passive element that stores energy in its electric field

It consists of two conducting plates separated by an insulator (ordielectric)

The plates are typically aluminum foil

The dielectric is often air, ceramic, paper, plastic, or mica

The measure of how much charge is stored is the capacitance C.

The farad (F) is the basic unit of capacitance.

• Most capacitors have values less than 1 F:

➢1 μF (microfarad) = 1 × 10-6 F

➢1 nF (nanofarad) = 1 × 10-9 F

➢1 pF (picofarad) = 1 × 10-12 F

• Capacitor:

When a voltage source v is connected to the capacitor,the source deposits a positive charge q on one plate anda negative charge –q on the other.

The charges will be equal in magnitude

The amount of charge is proportional to the voltage:

𝑞 = 𝐶𝑣

Capacitance is determined by the geometry of thecapacitor:

Proportional to the area of the plates (A)

Inversely proportional to the space between them (d)

• Capacitor:

Ideal capacitors all have these characteristics:

➢When the voltage is not changing, the current through the cap is zero.

➢ This means that with DC applied to the terminals no current will flow.

➢ Except, the voltage on the capacitor’s plates can’t change instantaneously.

➢ An abrupt change in voltage would require an infinite current!

➢ This means if the voltage on the cap does not equal the applied voltage,charge will flow and the voltage will finally reach the applied voltage.

A real capacitor has a parallel-model leakage resistance, leading to aslow loss of the stored energy internally

This resistance is typically very high, on the order of 100 MΩ and thuscan be ignored for many circuit applications.

Types of Capacitors

• Dielectric Constant:

Plastic

Ceramic

Types of Capacitors

• Typical Capacitors:

Mica: Typically used for small capacitance values of 10 to 5000 pF.

Paper: Typically used for medium capacitance values of 0.001 to 1.0 μF.

Film: Very temperature-stable. Frequently used in circuits where thischaracteristic is a necessity, such as radio frequency oscillators andtimer circuits.

Ceramic: Available in a wide range of values because Kε can betailored to provide almost any desired value of capacitance. Often usedfor temperature compensation (to increase or decrease capacitancewith a rise in temperature).

Surface-mount: Also called chip capacitors. Like chip resistors, chipcapacitors have their end electrodes soldered directly to the coppertraces of the printed-circuit board.

Types of Capacitors

• Typical Capacitors:

Variable capacitors:

Fixed metal plates form the stator.

Movable plates on the shaft form the rotor.

Air is the dielectric.

Capacitance is varied by rotating the shaft to make the rotor platesmesh with the stator plates.

Common applications include the tuning capacitor in radio receivers.

Leakage Current:

A disadvantage of electrolytic is their relatively high leakage current,caused by the fact that the oxide film is not a perfect insulator.

Capacitor Coding

• Film-Type Capacitors:

Capacitor Coding

• Ceramic Disk Capacitors:

Capacitor Coding

• Chip Capacitors:

Capacitor Coding

Current Voltage Relationship

• Formula:

Parallel Capacitors

• Applying KCL:

Thus, parallel capacitors combine as the sum of all capacitance

Series Capacitors

• Applying KVL:

Thus, series combination of capacitors resembles the parallel combination of resistors.

Applications for Capacitors

• Capacitors have a wide range of applications, some of which are:

Blocking DC

Passing AC

Shift phase

Store energy

Suppress noise

Start motors

AC in a Capacitive Circuit

• Capacitive reactance: is the opposition a capacitoroffers to the flow of sinusoidal current

AC in a Capacitive Circuit

• Applications:

Inductors and Inductance

• Inductor:

An inductor is a passive element that storesenergy in its magnetic field

They have applications in power supplies,transformers, radios, TVs, radars, andelectric motors.

Any conductor has inductance, but the effectis typically enhanced by coiling the wire up.

• Inductor:

If a current is passed through aninductor, the voltage across it isdirectly proportional to the time rateof change in current

Where, L, is the unit of inductance,measured in Henries, H.

On Henry is 1 volt-second perampere.

• Properties of Inductors:

If the current through an inductor is constant, the voltage across it iszero

Thus an inductor acts like a short for DC

The current through an inductor cannot change instantaneously

If this did happen, the voltage across the inductor would be infinity!

This is an important consideration if an inductor is to be turned offabruptly; it will produce a high voltage

In reality, inductors do have internal resistance due to the wiring usedto make them.

A real inductor thus has a winding resistance in series with it.

• Practical inductor values are in these ranges:

➢1 H to 10 H (for iron-core inductors)

➢1 mH (millihenry) = 1 × 10-3 H

➢1 mH (microhenry) = 1 × 10-6 H

• Mutual inductance (LM) occurs when current flowing throughone conductor creates a magnetic field which induces a voltage ina nearby conductor.

• Transformers

Types of Inductors

• Practical inductor values are in these ranges:

➢ Air-core coils

➢ Laminated core

➢ Powdered iron core

➢ Ferrite core

Current Voltage Relationship

• Formula:

Series Inductors

• Applying KVL:

• Thus,

Parallel Inductors

• Applying KCL:

• Thus,

AC in a Inductive Circuit

• Inductive reactance:

Summary of Capacitors and Inductors

• Important characteristics of the basic elements:

Transient Circuits

• RC Circuit:

• Time constant:

Transient Circuits

• RL Circuit:

• Time constant:

Steady-State Circuits

• RLC Circuits:

Steady-State Circuits

• RLC Circuits:

Applications

• Resonance:

• Filters:

Chapter 3. Questions and Exercices

• BTVN:

Problems in Chapter 16-26:

Mitchel E. Schultz, Grob’s Basic Electronics 12th Ed., Mc Graw-Hill Education (2015).

Chapter 3: Capacitors and Inductors

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