Inductance and Capacitance
INEL 4075 –Chapter 7
Dr. Sandra Cruz-Pol
Professor
Electrical & Computer Engineering
UPRM
Capacitors
Capacitors store electrons in form
of separated charge or E field.
http://www.kpsec.freeuk.com/components/led.htm
Electromagnetica Aplicada
Capacitance, in Farads [F]
• The capacitance is
εA
C =
d
q = Cv
• The charge
i = C
dv
dt
• The current in a capacitort
v =
1
C
∫ i dτ
−∞
• The voltage, cannot change
instantaneously
Capacitors
• Energy stored in capacitor
t
w (t ) =
∫
vi d τ
−∞
w (t ) =
C
tot
p
=
1
Cv
2
2
(t )
N
∑
n =1
C
1
n
C
tot
s
• Parallel and Series capacitors
Electromagnetica Aplicada
=
N
∑
n =1
1
C n
Electric Circuit
Discharging a capacitor
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Charge/discharge Capacitor
Piezoelectric
material
Chip – (integrated circuits)
The 555 timer regulator pin layout (from http://www.doctronics.co.uk/555.htm)
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1k
C1
C2
C3
C4
C5
C6
C7
C (µ
µF) Frequency
(Hz)
.100
111
.068
170
.047
230
.033
348
.022
490
.015
718
.010
1,173
What is a circuit Board?Nodes?
Electromagnetica Aplicada
Myth: Why is the Ocean Blue?
FALSE: The ocean is blue
because the sky reflection
on its surface.
TRUE: Water is blue.
frequency spectra
But you need a huge
amount of it to really see
its color.
Look at a swimming pool
as it gets deeper; even on
cloudy days.
http://ece.uprm.edu/~pol/OceanBlue.html
Myth #2
• FALSE: Thomas Edison, greatest contributor to Electricity and
systems used today.
• TRUE: Nikola Tesla – greatest contributor to Electricity.
Invented ac motor,
perfected dc motor,
invented radio transmission, (wireless)
designed Niagara Falls generator,
distribution systems,
fluorescence lamps,
remote control, wireless,
logic circuits,
3 phasic and many others.
Electromagnetica Aplicada
Inductors
Symbol
Inductors
• Energy storage – inductors store energy
in the form of a magnetic field
• Series and parallel inductance
• Initial conditions of switch circuits
solenoid
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• The
inductance is
Inductance,
2
in µHenries
[H]
oN A
L=
l + .45d
• The voltage in an inductor
v=L
di
dt
v=N
dφ
dt
t
1
• The current, cannotichange
=
v dτ + i (to )
instantaneously
Lt
∫
o
• Energy storedInductors
in inductor
t
w (t ) =
∫
vi d τ
−∞
w =
1
Li
2
2
N
• Series
and
Parallel inductors
1
tot
Ls
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=
∑
n =1
C
n
L
tot
p
=
N
∑
n =1
1
C n
Electro-magnet
***Warning!! It can get HOT.
Where to find this material?
• http://ece.uprm.edu/~pol/cursos
Electromagnetica Aplicada