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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 (Chapter 5.1)• Inductor (Chapter 5.2)• Comparison of Capacitor and Inductor• Superposition for Dynamic Circuits
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
• Capacitor (Chapter 5.1)• Inductor (Chapter 5.2)• Comparison of Capacitor and Inductor• Superposition for Dynamic Circuits
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
• Capacitor (Chapter 5.1)• Inductor (Chapter 5.2)• Comparison of Capacitor and Inductor• Superposition for Dynamic Circuits
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
• Capacitor (Chapter 5.1)• Inductor (Chapter 5.2)• Comparison of Capacitor and Inductor• Superposition for Dynamic Circuits
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
• Linear System:• Property 2:
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
• Linear System:• Property 2:
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