Chapter 10: Capacitors

• Introduction

• Electric field

• Capacitance

• Dielectric strength

• Leakage current

• Various types of capacitors

• Capacitors in series and parallel

• Energy stored by a capacitor

• Stray capacitances

• Transient analysis (Next class)

Introduction

• A capacitor is a device that stores electrostatic potential energy, i.e. it is a energy storage device.

• May either produce or absorb energy.

• Mainly acts as a filter which blocks the DC but allows AC.

• Charging or discharging will take time unlike resistors

Basic Construction

• The capacitor is constructed with the dielectric sandwiched between the two conducting plates.

• Each plate is capable of being charged with electrical current and has the ability to hold the charge. The difference in the charge levels of the conductive plates allows an electric field to exist in the dielectric which acts an insulator or separator.

• Dielectrics are materials that do not conduct electricity.

• Example of dielectric materials: air, paper, plastic, ceramic etc.

• Capacitance (ability to hold electrical charges) usually measured in farads or microfarads.

Capacitance of a dielectric-filled parallel plate capacitor is

Dielectric Strength• Dielectric Strength is a measure of the electrical strength of a material to act as

an insulator.

• It is defined as the maximum voltage required to produce a dielectric breakdown through the material and is expressed as Volts per unit thickness (Volts/meter).

• The higher the dielectric strength of a material the better its quality as an insulator.

• The corresponding voltage is known as breakdown voltage.

Leakage current

• In reality dielectrics are not perfect insulators

• When a voltage is applied across a capacitor, a leakage current is established between the plates

• Becomes important when capacitors remain in a charged state for long periods of time and establishes a discharge current through the resistor

• Electrolytic capacitors have high leakage currents

Image courtesy: Wikipedia

Various Types of Capacitors

• Fixed capacitors

Maintain a constant and unchanging value of capacitance, its ability to hold an electrical charge.

Examples: Electrolytic, film, polyester, foil, polypropylene, teflon

• Variable capacitors

Value of capacitance can be adjusted or varied. E.g. ceramic trimmer capacitor.

(Image Courtesy: http://www.learnabout-electronics.org/ac_theory/Fig2_1_3.swf)

Capacitors in Series and Parallel

• Exactly opposite of the phenomenon exhibited by resistors.

• When capacitors are connected in series, the total capacitance is less than any one of the series capacitors' individual capacitances. (Capacitances diminish in series.)

• When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitors' capacitances.(Capacitances add in parallel.)

• The energy stored in a capacitor is given by-

Energy Stored by a Capacitor

Stray Capacitances

• Stray capacitance is the capacitance that occurs due to electric stray fields. • Arises when two conducting surfaces are relatively close to one another

• May lead to serious errors in system design if they are not considered carefully.

• It is undesired as it slows down voltage changes, hence speed.

• Undesirable capacitance between circuit wires, between wires and the chassis, or between components and the chassis of electronic equipment. (McGraw-Hill Dictionary of Scientific & Technical Terms)

Transient Analysis

This is the equation that defines the behaviour of a capacitor (one may compare it to the Ohm’s law for resistors).

Are capacitors linear?

• Charging Phase• Time constant• Discharge Phase

Charging Phase

The placement of charge on the plates of a capacitor does not occur instantaneously. Instead, it occurs over a period of time determined by the components of the network.

This period of time during which charge is being deposited on the plates is called the transient period—a period of time where the voltage or current changes from one steady-state level to another.

Transient voltage/current

The factor tau, called the time constant of the network (unit time)

How long will it take to totally discharge the capacitor?

Discharging Phase

For a fixed-resistance network, the effect of increasing the capacitance is clearly demonstrated in Fig. The larger the capacitance, and hence the time constant, the longer it takes the capacitor to charge up—there is more charge to be stored.

Theory review for solving problems