CapacitanceInductanceSp03(1pp)

# CapacitanceInductanceSp03(1pp) - CAPACITANCE AND INDUCTANCE...

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CAPACITANCE AND INDUCTANCE Introduces two passive, energy storing devices: Capacitors and Inductors LEARNING GOALS CAPACITORS Store energy in their electric field (electrostatic energy) Model as circuit element INDUCTORS Store energy in their magnetic field Model as circuit element CAPACITOR AND INDUCTOR COMBINATIONS Series/parallel combinations of elements RC OP-AMP CIRCUITS Integration and differentiation circuits

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CAPACITORS First of the energy storage devices to be discussed Typical Capacitors Basic parallel-plates capacitor CIRCUIT REPRESENTATION NOTICE USE OF PASSIVE SIGN CONVENTION
Normal values of capacitance are small. Microfarads is common. For integrated circuits nano or pico farads are not unusual d A C ± ± 2 8 4 12 10 3141 . 6 10 016 . 1 10 85 . 8 55 m A A F ± ² ³ ± ± ² ± ± PLATE SIZE FOR EQUIVALENT AIR-GAP CAPACITOR gap in material of constant Dielectric ±

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Basic capacitance law ) ( C V f Q ± Linear capacitors obey Coulomb’s law C CV Q ± C is called the CAPACITANCE of the device and has units of voltage charge One Farad(F)is the capacitance of a device that can store one Coulomb of charge at one Volt. Volt Coulomb Farad ± EXAMPLE Voltage across a capacitor of 2 micro Farads holding 10mC of charge 5000 10 * 10 10 * 2 1 1 3 6 ± ± ± ± ± Q C V C V Capacitance in Farads, charge in Coulombs result in voltage in Volts Capacitors can be dangerous!!! Linear capacitor circuit representation
The capacitor is a passive element and follows the passive sign convention Capacitors only store and release ELECTROSTATIC energy. They do not “create” Linear capacitor circuit representation ) ( ) ( t dt dv C t i ± LEARNING BY DOING

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If the voltage varies the charge varies and there is a displacement current C C CV Q ± Capacitance Law One can also express the voltage across in terms of the current Q C t V C 1 ) ( ± ± ± ² ± t C dx x i C ) ( 1 Integral form of Capacitance law dt dV C dt dQ i C C ± ± … Or one can express the current through in terms of the voltage across Differential form of Capacitance law The mathematical implication of the integral form is . .. t t V t V C C ± ² ³ ´ ); ( ) ( Voltage across a capacitor MUST be continuous Implications of differential form?? 0 ± ² ± i Const V DC or steady state behavior A capacitor in steady state acts as an OPEN CIRCUIT
CAPACITOR AS CIRCUIT ELEMENT ± ² C v C i ) ( ) ( t dt dv C t i c C ± ± ± ² ± t C C dx x i C t v ) ( 1 ) ( ± ± ± ± ² ± ² ± ² t t t t 0 0 ±± ± ² ± ² 0 0 ) ( 1 ) ( 1 ) ( t t t C C C dx x i C dx x i C t v ± ± ² t t C C C dx x i C t v t v 0 ) ( 1 ) ( ) ( 0 The fact that the voltage is defined through an integral has important implications. .. R R R R Ri v v R i ± ± 1 Ohm’s Law ) ( O c t v elsewhere t i 0 ) ( ± CURRENT THE DETERMINE F C ± 5 ± ) ( ) ( t dt dv C t i ± mA s V F i 20 10 6 24 ] [ 10 5 3 6 ± ² ³ ´ µ · ¸ ¸ ¸ ± ± ± mA 60 ± LEARNING EXAMPLE

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CAPACITOR AS ENERGY STORAGE DEVICE ) ( ) ( ) ( t i t v t p C C C ± Instantaneous power ) ( ) ( t dt dv C t i c C ± dt dv t Cv t p c C C ) ( ) ( ± C t q dx x i C t v C t C C ) ( ) ( 1 ) ( ± ± ± ± ² ) ( ) ( 1 ) ( t dt dq t q C t p C C C ±
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CapacitanceInductanceSp03(1pp) - CAPACITANCE AND INDUCTANCE...

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