# Chapter 15 Capacitance and RC Circuits © Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Objectives Define capacitance.

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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.

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

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance and the Capacitor (Cont.) Dielectrics Conductive plates

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Calculating Capacitance Measured in farads (F)farads (F) Determined by –Dielectric material –Area of plates –Distance between plates

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Calculating Capacitance (Cont.) Capacity increases with area of plates or dielectric constant Capacity decreases when distance between plates increases

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Types of Capacitors Fixed paper capacitors Rectangular oil filled capacitors Can type electrolytic capacitors Tubular electrolytic capacitors Ceramic capacitors

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Types of Capacitors (Cont.) Mica capacitors Variable capacitors –StatorsStators –RotorsRotors Trimmer capacitors –Adjusted with alignment toolsalignment tools Tantalum capacitors

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is capacitance? A property that opposes any change in voltage

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is a device that temporarily stores an electric charge? A capacitor

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is the insulation separating the two plates in a capacitor? Dielectric

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What are the three factors that determine capacitance? Material used as a dielectric, area of the plates, and distance between the plates

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response of the Capacitor Response of current and voltage immediately after change in applied voltage RC circuits

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response of the Capacitor (Cont.) Voltage builds up gradually with closed switch Current falls as capacitor charges Capacitor remains charged when switch opens

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response Example Short circuit in this RC circuit when switch closes

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Transient Response Example (Cont.) Discharge current rises to maximum and falls off

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. RC Time Constant (Cont.) At ignition, or firing voltage, lamp glows Repetitive cycle, causes neon to flash

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitors in Series (Cont.)

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitors in Parallel C T = C 1 + C 2 + C 3 … + C N

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What does transient response refer to? The response of current and voltage in a circuit immediately after a change in applied voltage

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is the amount of time needed for the capacitor to charge or discharge 63.2 percent? The time constant of the circuit

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance in AC Circuits Power in capacitive circuits Resistance and capacitance in AC circuits Parallel RC circuits

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance in AC Circuits (Cont.) AC voltage causes plates to charge and discharge repeatedly

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance in AC Circuits (Cont.) Current begins at maximum Current leads voltage by 90° in capacitive circuit

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance in AC Circuits (Cont.) Current depends on rate of capacitor’s charge and discharge As ac frequency increases, current increases Capacitive reactance

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance Example 10 µF capacitor 120-hertz frequency

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Capacitance Example (Cont.)

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Power in Capacitive Circuits Wattless power Apparent power = 100 V × 10 A = 1000 VA

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Resistance and Capacitance in AC Circuits Capacitive reactance causes phase displacement Total resistance is vector sum of X C and R Impedance

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Resistance and Capacitance Example Z = 500 Ω

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Resistance and Capacitance Example (Cont.) Angle between Z and R is phase displacement between current and voltage cos  = 0.6  = 53.1°

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RC Circuits No phase difference among voltages Phase difference among total and branch currents Current in phase with resistive branch’s voltage

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

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RC Circuit Example Capacitive reactance X C  80 Ω Branch currents

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Parallel RC Circuit Example (Cont.) Phase angle arctan 1.25 = 51.3° Total circuit current Impedance

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is capacitive reactance? The resistance resulting from capacitance

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is power called in a capacitive circuit? Wattless power

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Review What is the ratio of true power to apparent power in an ac circuit called? Power factor (PF)

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. For Discussion Research different types of capacitors, focusing on construction and various applications. Discuss the reasons a capacitor blocks dc while passing ac.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Alignment tool –A special fiber of plastic screwdriver used to adjust trimmer capacitors. Can type electrolytic capacitor –A capacitor that uses different methods of plate construction, such as aluminum, and a wet or dry electrolyte, such as borax or carbonate.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Capacitance –1. An inherent property of an electric circuit that opposes change in voltage. 2. A property of a circuit whereby energy may be stored in an electrostatic field. Capacitive reactance –Opposition to ac as a result of capacitance.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Capacitor –A device that possesses capacitance. A simple capacitor consists of two metal plates separated by an insulator. Ceramic capacitor –A small capacitor made of a special ceramic dielectric.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Dielectric –Insulating material between plates and capacitor. Dielectric constant –Numerical figure representing ability of a dielectric or insulator to support electric flux. Dry air is assigned number 1.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Farad (F) –Unit of measurement of capacitance. A capacitor has a capacitance of one farad when a charge of one coulomb raises its potential one volt. Fixed paper capacitor –A capacitor made of layers of tinfoil. The dielectric is made of waxed paper.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Mica capacitor –Capacitor made of metal foil plates separated by sheets of mica. RC circuit –A circuit that contains resistance and capacitance.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Rectangular oil filled capacitor –Hermetically sealed in a metal can and used in power supplies of radio transmitters and other electronic equipment. Rotor –Rotating part of an ac generator. Stator –Stationary coils of an ac generator.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Tantalum capacitor –Uses tantalum, instead of aluminum, for the electrode. Trimmer capacitor –A type of variable capacitor used where fine adjustments of capacitance are needed.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Tubular electrolytic capacitor –A small capacitor that has a metal case enclosed in an insulating tube. Variable capacitor –Capacitor with a capacitance that can be adjusted by turning a shaft.

© Goodheart-Willcox Co., Inc.Permission granted to reproduce for educational use only. Glossary Working voltage (WV) –Maximum voltage that can be steadily applied to a capacitor without arc-over.

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