Capacitance OBJECTIVES After

• • • • •

completing this chapter, the student

should be able to:

Explain the principles of capacitance. Identify the basic units of capacitance. Identify different types of capacitors. Determine total capacitance in series and parallel circuits. Explain RC time constants and how they relate to capacitance. See accompanying examples

CD for interactive

in MultiSim, Chapter

Capacitance allows for the storage of energy in an electrostatic field. Capacitance is present whenever two conductors are separated by an insulator. This chapter focuses on capacitance and its application to DC circuits. Capacitance is covered in more detail in Chapter 15.

presentations,

tutorials

and Capacitive

11.

FIGURE 11-1 A capacitor consists of two plates (conductors) separated by a dielectric (insulator or nonconductor). METAL PLATES

CAPACITANCE Capacitance is the ability of a device to store electrical energy in an electrostatic field. A capacitor is a device that possesses a specific amount of capacitance. A capacitor is made of two conductors separated by an insulator (Figure 11-1). The conductors are called plates and the insulator is called a dielectric. Figure 11-2 shows the symbols for capacitors. 116

When a DC voltage source is connected to a capacitor, a current flows until the capacitor is charged. The capacitor is charged with an excess of electrons on one plate (negative charge) and a deficiency of electrons on the other plate (positive charge). The dielectric prevents electrons from moving between the plates. Once the capacitor is charged, all current stops. The

CHAPTER

FIGURE 11-2 Schematic symbols for capacitors.

I(

11 CAPACITANCE

dinary use, so the microfarad (j.LF)and picofarad (pF) are used, The letter C stands for capacitance. 1 microfarad

FIXED CAPACITOR

1 picofarad

1

=

0.000,001 or

=

0.000,000,000,001 1

-------1,000,000,000,000

farad

1,000,000 or

farad

VARIABLE CAPACITOR

11-1 QUESTIONS capacitor's voltage is equal to the voltage of the voltage source. A charged capacitor can be removed from the voltage source and used as an energy source. However, as energy is removed from the capacitor, the voltage diminishes rapidly. In a DC circuit, a capacitor acts as an open circuit after its initial charge. An open circuit is a circuit with an infinite resistance.

CAUTION:

BECAUSE A CAPACITOR CAN BE REMOVED

FROM A VOLTAGE SOURCE AND HOLD THE POTENTIAL OF THE VOLTAGE SOURCE INDEFINITELY, TREAT ALL CAPACITORS AS THOUGH THEY WERE CHARGED. NEVER TOUCH BOTH LEADS OF A CAPACITOR WITH YOUR HAND UNTIL YOU HAVE DISCHARGED IT BY SHORTING BOTH LEADS TOGETHER. ~\ CAPACITor< li~ A CIRCUIT CAN HOLD A POTENTIAL I[~DEFINITELY IF IT DOES NOT HAVE A DISCHARGE PATH

The amount of energy stored in a capacitor is in proportion to the size of the capacitor. The capacitors used in classrooms are usually small and deliver only a small shock if discharged through the body. If a capacitor is large and charged with a high voltage, however, the shock can be fatal. Charged capacitors should be treated like any other voltage source. The basic unit of capacitance is the farad (F). A farad is the amount of capacitance that can store 1 coulomb (C) of charge when the capacitor is charged to 1 volt. The farad is too large for or-

1. What is capacitance? 2. Draw the symbol for capacitance. 3. What precautions should be observed when handling capacitors? 4. What is the unit for measuring capacitance? 5. What units are normally capacitors?

DI

associated

CAPACITORS

Four factors affect the capacitance They are: 1. 2. 3. 4.

with

of a capacitor.

Area of the plate Distance between the plates Type of dielectric material Temperature

A capacitor is either fixed or variable. A fixed capacitor has a definite value that cannot be changed. A variable capacitor is one whose capacitance can be changed either by varying the space between plates (trimmer capacitor) or by varying the amount of meshing between two sets of plates (tuning capacitor). Capacitance is directly proportional to the area of the plate. For example, doubling the plate area doubles the capacitance if all other factors remain the same.

SECTION

1 DC CIRCUITS

Capacitance is inversely proportional to the distance between the plates. In other words, as the plates move apart, the strength of the electric field between the plates decreases. The ability of a capacitor to store electrical energy depends on the electrostatic field between the plates and the distortion of the orbits of the electrons in the dielectric material. The degree of distortion depends on the nature of dielectric material and is indicated by its dielectric constant. A dielectric constant is a measure of the effectiveness of a material as an insulator. The constant compares the material's ability to distort and store energy in an electric field to the ability of air, which has a dielectric constant of 1. Paper has a dielectric constant of 2 to 3; mica has a dielectric constant of 5 to 6; and titanium has a dielectric constant of 90 to 170. The temperature of a capacitor is the least significant of the four factors. It need not be considered for most general-purpose applications. Capacitors come in many types and styles to meet the needs of the electronics industry. Electrolytic capacitors offer large capacitance for small size and weight (Figure 11-3). Electrolytic capacitors consist of two metal foils separated by fine gauze or other absorbent material that is saturated with a chemical paste called an electrolyte. The electrolyte is a good conductor and serves as part of the negative plate. The dielectric is formed by oxidation of the positive plate. The oxidized layer is thin and a good insulator. An electrolytic capacitor is polarized, having a positive and negative lead. Polarity must be observed when connecting an electrolytic capacitor in a circuit. Paper and plastic capacitors are constructed by a rolled foil technique (Figure 11-4). A paper dielectric has less resistance than a plastic film dielectric, and plastic film is now being used more as a result. The plastic film allows a metallized film to be deposited directly on it. This reduces the distance between plates and produces a smaller capacitor.

FIGURE 11-3 Electrolytic capacitors.

RADIAL CAPACITOR

LEAD

AXIAL CAPACITOR LEADS

The ceramic disk capacitor is popular because it is inexpensive to produce (Figure 11-5). It is used for capacitors of 0.1 microfarad and smaller. The ceramic material is the dielectric. This is a tough, reliable, general-purpose capacitor. Variable capacitors also come in all sizes and shapes (Figure 11-6). Types include padders, trimmers, and tuning capacitors. Padder and trimmer capacitors must be adjusted by a technician. Tuning capacitors can be adjusted by the user.

CHAPTER 11 CAPACITANCE

FIGURE 11-4

FIGURE 11-6

Paper and plastic capacitors.

Variable capacitors.

FIGURE 11-5 1

1

1

1

CT

C1

C2

C3

-=-+-+-

Ceramic disk capacitors.

1

... +-

Cn

When capacitors of different values are connected in series, the smaller capacitors charge up to the highest voltage. Placing capacitors in parallel effectively adds to the plate area. This makes the total capacitance equal to the sum of the individual capacitances: CT

=C1 +C2 +C3

...

+Cn

Capacitorsin parallel all charge to the same voltage.

11-2

QUESTIONS

1. What four factors affect capacitance? Like resistors and inductors, capacitors can be connected in series, parallel, and series-parallel combinations. Placing capacitors in series effectively increases the thickness of the dielectric. This decreases the total capacitance, because capacitance is inversely proportional to the distance between the plates. The total capacitance of capacitors in series is calculated like the total resistance of parallel resistors:

2. What are the advantages of electrolytic capacitors? 3. What are other names for variable capacitors? 4. What is the formula for total capacitance in series circuits? 5. What is the formula for total capacitance in parallel circuits?

SECTION 1 DC CIRCUITS

Circuit used to determine RC time constant.

An RC time constant reflects the relationship between time, resistance, and capacitance. An RC circuit is shown in Figure 11-7. The time it takes a capacitor to charge and discharge is directly proportional to the amount of the resistance and capacitance. The time constant reflects the time required for a capacitor to charge up to 63.2% of the applied voltage or to discharge down to 36.8%. The time constant is expressed as: t

-

FIGURE 11-7

RC TIME CONSTANTS

CHARGE

;/

DISCHARGE

E-==T+

:::::_ C 1

= RC

shows the time constants needed to charge and discharge a capacitor. Note that it takes approximately five time constants to fully charge or discharge a capacitor.

where: t = time in seconds R = resistance in ohms C = capacitance in farads What is the time constant of a 1microfarad capacitor and a I-megohm resistor?

11-3

Given:

1. What is a time constant for a capacitor?

EXAMPLE:

C = 1

Solution: t = RC

j-LF

R = 1 Mil

t

=

2. How is the time constant determined for a capacitor? 3. Flow many time constants are required to fully charge or discharge a capacitor?

= (1,000,000)(0.000001) t = 1 second t

?

QUESTIONS

The time constant is not the time required to charge or discharge a capacitor fully. Figure 11-8 FIGURE 11-8 Chart of time constants required to charge and discharge a capacitor. 100

w

----1-r--.---.--.-~

-----

-I

DISCHARGE

CJ

~ :..J 0

80

> :2

::::l :2

60

x

« :2 LL

40

0 IZ

w

20

o a:

w 0..

0

2

345

o

1

TIME CONSTANTS

2

3

4

5

CHAPTER 11

4. A l-microfarad and a O.I-microfarad capacitor are connected in series. What is the total capacitance for the circuit? 5. A 0.0 15-microfarad capacitor is charged to 25 volts. What is the voltage 25 milliseconds after placing a 2-megohm resistor across its terminals?

SUMMARY • Capacitance is the ability to store electrical energy in an electrostatic field. • A capacitor consists of two conductors separated by an insulator. • The symbol for a fixed capacitor is:

• The symbol for a variable capacitor is:

CAPACITANCE

• The unit of capacitance is the farad (F). • Because the farad is large, microfarads (J-LF) and picofarads (PF) are more often used. • The letter C represents capacitance. • Capacitance is affected by: 1. Area of the capacitor plates 2. Distance between the plates 3. Types of dielectric materials 4. Temperature • Capacitor types include: electrolytic, paper, plastic, ceramic, and variable. • The formula for total capacitance in a series circuit is: 1

1

CT

C1

III

-=-+-+-

C2

C3

... +-

c,

• The formula for total capacitance in a parallel circuit is: CT =C1 +C2 +C3 ••• +Cn • The formula for the RC circuit time constant is: t = RC • It takes five time constants to fully charge and discharge a capacitor.

CHAPTER

11 SELF-TEST

"

1. Where is the charge stored in a capacitor? 2. Four capacitors are connected in series, 1.5 f..LF, 0.05 J-LF, 2000 pF, and 25 pE What is the total capacitance of the circuit? 3. Four capacitors are connected in parallel, 1.5 f..LF, 0.05 f..LF, 2000 pF, and 25 pE What is the total capacitance of the circuit?