Lecture 10 Capacitor and Inductor Hung-yi Lee. Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition.

Lecture 10Capacitor and Inductor

Hung-yi Lee

Outline

• Capacitor (Chapter 5.1)• Inductor (Chapter 5.2)• Comparison of Capacitor and Inductor• Superposition for Dynamic Circuits

Outline


Capacitor – i-v characteristics

If v is constant i=0

Open circuit

Dynamic dt

tdvCti

)()(

diC

tvt

1)(

)(tv

)(ti

reference current should flow from “+” to “-”

diC

tvt

t0

10

Capacitor – i-v characteristics

dt

tdvCti

)()(

tv

Continuity - Capacitor

• The voltage of capacitor should be continuous

dt

tdvCti

)()(

Infinite current

Current changes

Capacitor – Power and Energy

tdttptE

dt

tdvtCvtitvtp c

ccc

)()()()()(

Instantaneous consumed power of a capacitor:

Total energy consumed:

)(2

1 2 tCvc

t

cc dt

dt

tdvtCv )(tp

)(E t

)(tvc

)(tic

Depend on voltage at t

The energy stored

Capacitor - Application

• Automated external defibrillators (AED)

Capacitor - Application

• Automated external defibrillators (AED)

5000V

22 50002

1)(

2

1E CtCvc 0)(

2

1E 2 tCvc

5000)( tvc0)( tvc

Capacitor - Series

Nvvvv 21

dt

dvC

dt

dvC

dt

dvCi N

N 22

11

iCCC N

111

21

dt

dv

dt

dv

dt

dvdt

vvvd

dt

dv

N

N

21

21

dt

dvCi seri

Cser

1

N

ser

CCC

C111

1

21

Capacitor - Parallel

dt

dvC

dt

dvCCC

dt

dvC

dt

dvC

dt

dvC

iiii

par

N

N

N

21

21

21

Cpar=C1+C2+ +C‥ ‥ ‥ N

Outline


Inductor – i-v characteristics

dt

tdiLtv

)()(

dvtidvtit

t

t

0L

1

L

1)( 0

If i=constant v=0

short circuit

Dynamic

)(tv)(ti

reference current should flow from “+” to “-”

Inductor – i-v characteristics

dt

tditv

)(L)(

ti

Continuity - Inductor

• The current of inductor should be continuous

Infinite Voltage

Voltagechanges

dt

tdiLtv

)()(

Shock by Inductor

http://www.allaboutcircuits.com/worksheets/ind.html

Inductor – Power and Stored Energy• Instantaneous consumed power of an inductor

• Total Energy consumed

)()(

)()()( tt

ttt LL

LL idt

diLivp

tdttptE

)(L2

1 2L ti

t

LL dttidt

tdiL

Depend on current at t

The energy stored

Inductor - Series

dt

diL

dt

diLLL

dt

diL

dt

diL

dt

diL

vvvv

ser

N

N

N

21

21

21

Lser=L1+L2+ +L‥ ‥ ‥ N

Inductor - Parallel

N

par

LLL111

1L

21

Niiii 21

dt

diL

dt

diL

dt

diLv N

N 22

11

dt

di

dt

di

dt

didt

iiid

dt

di

N

N

21

21

vL

vLLL

par

N

1

111

21

dt

diLv par

Outline


Summary - i-v characteristics

dt

tdvCti

)()(

dt

tdiLtv

)()(

愛愛C V V L

Summary - Series and Parallel

dt

tdvCti

)()(

dt

tdiLtv

)()( tRitv )(

Series

Parallel

i-v

Resistor Capacitor Inductor

is RR

ip R

1

R

1 ip CC

is C

1

C

1 is LL

ip L

1

L

1

Outline


Review

i

ii xay This equation only for circuits with sources and resistors.

• y: any current or voltage for an element• xi: current of current sources or voltage of voltage sources

Proportionality Principle, Superposition Principle

Can be used in any circuit in this course

Linearity

• A circuit is a multiple-input multiple-output (MIMO) system• Input: current of current sources or voltage of voltage

sources• Output: the current or voltage for the elements

v i +

-

Circuit(System)

input output

Linearity

• All linear circuits are linear system• Linear Circuit:• Sources• Linear Elements:• Resistor, Capacitor, Inductor

All circuits in this course are linear circuits.

R

vi

Linearity

• Linear System:• Property 1:

Input: g1(t), g2(t), g3(t), ……output: h1(t), h2(t), h3(t), ……

Input: Kg1(t), Kg2(t), Kg3(t), ……output: Kh1(t), Kh2(t), Kh3(t), ……

Proportionality Principle

Linearity


Input: a1(t), a2(t), a3(t), ……output: x1(t), x2(t), x3(t), ……

Input: a1(t)+ b1(t), a2(t)+ b2(t), a3(t)+ b3(t), ……output: x1(t)+y1(t), x2(t)+y2(t), x3(t)+y3(t), ……

Superposition Principle

Input: b1(t), b2(t), b3(t), ……output: y1(t), y2(t), y3(t), ……

Linearity


Input: a1(t), a2(t), a3(t), ……output: x1(t), x2(t), x3(t), ……

Input: a1(t)+ b1(t), a2(t)+ b2(t), a3(t)+ b3(t), ……output: x1(t)+y1(t), x2(t)+y2(t), x3(t)+y3(t), ……

Superposition Principle

Input: b1(t), b2(t), b3(t), ……output: y1(t), y2(t), y3(t), ……

t 1g0

tv

t 2g ti

0

Linearity

t t t 21 ggg

ti

tv t g

Superposition Principle can be applied on all circuits in this course (Textbook: Chapter 6.5).

Announcement

• 10/22 ( 三 ) 第一次小考• Ch1. Circuit Variables and Laws (1.4, 1.5) • Ch2. Properties of Resistive Circuits (2.3, 2.4, 2.5) • Ch3. Applications of Resistive Circuits (3.2) • Ch4. Systematic Analysis Methods (4.1, 4.2, 4.3, 4.4)

• 助教時間：週一到週四 PM6:30~8:30• 助教 : 黃盈庭 [email protected]• 時間 : 週三 PM6:30~8:30• 地點 : 電二 146

Thank you!

Appendix

Capacitor – Series (2)

If v is constant i=0

Open circuit

What are v1, v2 ……?

Capacitor Application

• How Capacitive Liquid Level Sensors Work• https://www.youtube.com/watch?v=0du-QU1Q0T4

Acknowledgement

• 感謝林楷恩 (b02)• 指出投影片中 Equation 的錯誤

Lecture 10 Capacitor and Inductor Hung-yi Lee. Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition.

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