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Introduction to Energy Storage Elements: The Capacitor

Introduction to Energy Storage Elements: The Capacitor. Review. So far, we have talked about two kinds of circuit elements: Sources (independent and dependent)- active, can provide power to the circuit. Resistors-passive, can only dissipate power. Energy Storage Elements.

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Introduction to Energy Storage Elements: The Capacitor

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  1. Introduction to Energy Storage Elements:The Capacitor Lecture 10

  2. Review • So far, we have talked about two kinds of circuit elements: • Sources (independent and dependent)- active, can provide power to the circuit. • Resistors-passive, can only dissipate power. Lecture 10

  3. Energy Storage Elements • Capacitors store energy in an electric field. • Inductors store energy in a magnetic field. • Capacitors and inductors are passive elements: • Can store energy supplied by circuit • Can return stored energy to circuit • Cannot supply more energy to circuit than is stored. Lecture 10

  4. Energy Storage is Fun! • Voltages and currents in a circuit without energy storage elements are linear combinations of source voltages and currents. • Voltages and currents in a circuit with energy storage elements are solutions to linear, constant coefficient differential equations! Lecture 10

  5. Even More Fun! • Practicing engineers almost never solve the differential equations directly. They also almost never use the techniques in Chapter 6. • Instead, they use: • LaPlace transforms (covered in EEE 302) • AC steady-state analysis • These techniques convert the solution of differential equations into algebraic problems-circuit analysis (eg the voltage divider) can be applied directly. Lecture 10

  6. Power Generation and Distribution • Energy storage elements model electrical loads: • Capacitors model computers and other electronics (power supplies). • Inductors model motors. Lecture 10

  7. Signal ProcessingCommunicationInstrumentation • Capacitors and inductors are used to build filters and amplifiers with desired frequency responses: • RF and IF amplifiers in a superhetrodyne receiver. • Instrumentation amplifiers. Lecture 10

  8. Signal ProcessingCommunicationInstrumentation • Capacitors are used in A/D converters (PCM encoders) to hold a sampled signal until it can be converted into bits. Lecture 10

  9. Solid StateDigital Design • Integrated circuits have layers of conductors (metal, silicon with impurities) with insulators (glass) between. This is a capacitor! • This capacitance is one of the limiting factors in processor speeds. • This capacitance is used to create RAM’s. Lecture 10

  10. Electromagnetics • For high frequency signals, inductance and capacitance are more significant effects than resistance. Lecture 10

  11. Capacitance • Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator). • Charge on the two conductors creates an electric field that stores energy. • The voltage difference between the two conductors is proportional to the charge: q = C v Lecture 10

  12. Capacitance • The proportionality constant C is called capacitance. • Units of Farads (F) - C/V Lecture 10

  13. The rest of the circuit + i(t) v(t) - Capacitor Lecture 10

  14. Capacitor Voltage Lecture 10

  15. Energy Stored Lecture 10

  16. i(t) 1A 2s -1A t 1s Example i(t) The rest of the circuit + 0.2F v(t) - Lecture 10

  17. Find v(t)Find wc(t) Lecture 10

  18. v(t) 5V 2s 1s t Solution wc(t) 2.5J 2s 1s t Lecture 10

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