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

Chapter 15

Capacitance and RC Circuits

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Objectives

• Define capacitance and capacitor.

• Identify the many different types of capacitors.

• Describe the transient response of a capacitor.

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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.

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Capacitance and the Capacitor

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Capacitance and the Capacitor (Cont.)

• Dielectrics• Conductive plates

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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)

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Calculating Capacitance

• Measured in farads (F)

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

E

QC

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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

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Types of Capacitors

• Fixed paper capacitors

• Rectangular oil filled capacitors

• Can type electrolytic capacitors

• Tubular electrolytic capacitors

• Ceramic capacitors

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Types of Capacitors (Cont.)

• Mica capacitors

• Variable capacitors– Stators– Rotors

• Trimmer capacitors– Adjusted with alignment tools

• Tantalum capacitors

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Review

What is capacitance?

A property that opposes any change in voltage

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Review

What is a device that temporarily stores an electric charge?

A capacitor

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Review

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

Dielectric

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Review

What are the three factors that determine capacitance?

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

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Transient Response of the Capacitor

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

• RC circuits

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Transient Response of the Capacitor (Cont.)

• Voltage builds up gradually with closed switch

• Current falls as capacitor charges

• Capacitor remains charged when switch opens

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Transient Response Example

• Short circuit in this RC circuit when switch closes

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Transient Response Example (Cont.)

• Discharge current rises to maximum and falls off

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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

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RC Time Constant (Cont.)

• At ignition, or firing voltage, lamp glows

• Repetitive cycle, causes neon to flash

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Capacitors in Series

21

21T CC

CCC

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Capacitors in Series (Cont.)

N321T CCCCC

1

1

1

1

1

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Capacitors in Parallel

• CT = C1 + C2 + C3 … + CN

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Review

What does transient response refer to?

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

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Review

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

The time constant of the circuit

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Capacitance in AC Circuits

• Power in capacitive circuits

• Resistance and capacitance in AC circuits

• Parallel RC circuits

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Capacitance in AC Circuits (Cont.)

• AC voltage causes plates to charge and discharge repeatedly

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Capacitance in AC Circuits (Cont.)

• Current begins at maximum

• Current leads voltage by 90° in capacitive circuit

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Capacitance in AC Circuits (Cont.)

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

• As ac frequency increases, current increases

• Capacitive reactance

fCX C 2

1

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Capacitance Example

• 10 µF capacitor

• 120-hertz frequency

fCX C 2

1

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Capacitance Example (Cont.)

F) 10 (10 Hz) (120 6.28

1

6-CX

132.7 0.007536

1 CX

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Power in Capacitive Circuits

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

powerApparent

power True cos (PF)factor Power

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Resistance and Capacitance in AC Circuits

• Capacitive reactance causes phase displacement

• Total resistance is vector sum of XC and R

• Impedance22 CXRZ

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Resistance and Capacitance Example

Z = 500 Ω

22 ) (400 ) (300 Z

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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

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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

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Parallel RC Circuits

• No phase difference among voltages

• Phase difference among total and branch currents

• Current in phase with resistive branch’s voltage

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Parallel RC Circuit Formulas

T

S

I

EZ

22 CRT III

R

C

I

I arctan

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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

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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

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Review

What is capacitive reactance?

The resistance resulting from capacitance

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Review

What is power called in a capacitive circuit?

Wattless power

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Review

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

Power factor (PF)

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For Discussion

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

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