chapter 15 capacitance and rc circuits © goodheart-willcox co., inc.permission granted to reproduce...

Chapter 15

Capacitance and RC Circuits

© Goodheart-Willcox Co., Inc. Permission granted to reproduce for educational use only.

Objectives

• Define capacitance and capacitor.

• Identify the many different types of capacitors.

• Describe the transient response of a capacitor.


Objectives

• Explain how a capacitor behaves in a dc circuit.

• Discuss the effect of capacitance on an ac circuit.

• Describe the results of combining capacitance and resistance in a circuit.


Capacitance and the Capacitor


Capacitance and the Capacitor (Cont.)

• Dielectrics• Conductive plates


Capacitance and the Capacitor (Cont.)

• Electrons from negative terminal of source flow to one plate of capacitor

• Capacitor blocks direct current

• Dielectric constants• Working voltage (WV)


Calculating Capacitance

• Measured in farads (F)

• Determined by – Dielectric material– Area of plates– Distance between plates

E

QC


Calculating Capacitance (Cont.)

• Capacity increases with area of plates or dielectric constant

• Capacity decreases when distance between plates increases

d

n–KAC

1)( 0.225


Types of Capacitors

• Fixed paper capacitors

• Rectangular oil filled capacitors

• Can type electrolytic capacitors

• Tubular electrolytic capacitors

• Ceramic capacitors


Types of Capacitors (Cont.)

• Mica capacitors

• Variable capacitors– Stators– Rotors

• Trimmer capacitors– Adjusted with alignment tools

• Tantalum capacitors


Review

What is capacitance?

A property that opposes any change in voltage


Review

What is a device that temporarily stores an electric charge?

A capacitor


Review

What is the insulation separating the two plates in a capacitor?

Dielectric


Review

What are the three factors that determine capacitance?

Material used as a dielectric, area of the plates, and distance between the plates


Transient Response of the Capacitor

• Response of current and voltage immediately after change in applied voltage

• RC circuits


Transient Response of the Capacitor (Cont.)

• Voltage builds up gradually with closed switch

• Current falls as capacitor charges

• Capacitor remains charged when switch opens


Transient Response Example

• Short circuit in this RC circuit when switch closes


Transient Response Example (Cont.)

• Discharge current rises to maximum and falls off


RC Time Constant

• Time between charge and discharge of voltage and current in RC circuit

• Time constant = R × C• Five time constant periods needed for complete charge or

discharge


RC Time Constant (Cont.)

• At ignition, or firing voltage, lamp glows

• Repetitive cycle, causes neon to flash


Capacitors in Series

21

21T CC

CCC


Capacitors in Series (Cont.)

N321T CCCCC

1

1

1

1

1


Capacitors in Parallel

• CT = C1 + C2 + C3 … + CN


Review

What does transient response refer to?

The response of current and voltage in a circuit immediately after a change in applied voltage


Review

What is the amount of time needed for the capacitor to charge or discharge 63.2 percent?

The time constant of the circuit


Capacitance in AC Circuits

• Power in capacitive circuits

• Resistance and capacitance in AC circuits

• Parallel RC circuits


Capacitance in AC Circuits (Cont.)

• AC voltage causes plates to charge and discharge repeatedly



• Current begins at maximum

• Current leads voltage by 90° in capacitive circuit



• Current depends on rate of capacitor’s charge and discharge

• As ac frequency increases, current increases

• Capacitive reactance

fCX C 2

1


Capacitance Example

• 10 µF capacitor

• 120-hertz frequency

fCX C 2

1


Capacitance Example (Cont.)

F) 10 (10 Hz) (120 6.28

1

6-CX

132.7 0.007536

1 CX


Power in Capacitive Circuits

• Wattless power• Apparent power = 100 V × 10 A = 1000 VA

powerApparent

power True cos (PF)factor Power


Resistance and Capacitance in AC Circuits

• Capacitive reactance causes phase displacement

• Total resistance is vector sum of XC and R

• Impedance22 CXRZ


Resistance and Capacitance Example

Z = 500 Ω

22 ) (400 ) (300 Z


Resistance and Capacitance Example (Cont.)

• Angle between Z and R is phase displacement between current and voltage

cos = 0.6 = 53.1°

Z

R PF cos

500

300 cos


Resistance and Capacitance Example (Cont.)

• Apparent power = I × E– Apparent power = 0.2 A × 100 V

Apparent power = 20 VA

• True power = I × E × cos – True power = 0.2 A × 100 V × cos 53.1°

True power = 12 W


Parallel RC Circuits

• No phase difference among voltages

• Phase difference among total and branch currents

• Current in phase with resistive branch’s voltage


Parallel RC Circuit Formulas

T

S

I

EZ

22 CRT III

R

C

I

I arctan


Parallel RC Circuit Example

• Capacitive reactance

XC 80 Ω

• Branch currents

F) 10 (2 Hz) 10 (1

0.159

6-3 CX

A 0.2 100

V 20

RI

A 0.25 80

V 20

CI


Parallel RC Circuit Example (Cont.)

• Phase angle

arctan 1.25 = 51.3°

• Total circuit current

• Impedance

A 0.2

A 0.25arctan

A 0.32 A) (0.25 A) (0.2 22 IT

62.5 A 0.32

V 20 Z


Review

What is capacitive reactance?

The resistance resulting from capacitance


Review

What is power called in a capacitive circuit?

Wattless power


Review

What is the ratio of true power to apparent power in an ac circuit called?

Power factor (PF)


For Discussion

• Research different types of capacitors, focusing on construction and various applications.

• Discuss the reasons a capacitor blocks dc while passing ac.

chapter 15 capacitance and rc circuits © goodheart-willcox co., inc.permission granted to reproduce...

Documents

educational use

circuit slide

dielectric slide

discharge slide

closes slide

capacitorcapacitor slide

applied voltage slide

voltage wv slide