Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | whitcomb-jagger |
View: | 30 times |
Download: | 1 times |
Capacitor
d
A
V
qC
:capacitora of dimension physical theon dependsonly eCapacitanc
A circuit element that stores electric energy and electric charges
A capacitor always consists of two separated metals, one stores +q, and the other stores –q. A common
capacitor is made of two parallel metal plates.
Capacitance is defined as: C=q/V (F); Farad=Colomb/volt
Once the geometry of a capacitor is determined, the capacitance (C) is fixed (constant) and is independent of voltage V. If the voltage is increased, the charge will increase to keep q/V constant
Application: sensor (touch screen, key board), flasher, defibrillator, rectifier, random access memory RAM, etc.
Capacitor: cont.
• Because of insulating dielectric materials between the plates, i=0 in DC circuit, i.e. the braches with Cs can be replaced with open circuit.
• However, there are charges on the plates, and thus voltage across the capacitor according to q=Cv.
• i-v relationship:
i = dq/dt = C dv/dt
• Solving differential equation needs an initial condition
• Energy stored in a capacitor: WC =1/2 CvC(t)2
Capacitors in
V=V1=V2=V3
q=q1+q2+q3
321321 CCC
V
qqq
V
qCeq
parallel series
V=V1+V2+V3
q=q1=q2=q3
321
321
111
1
CCC
q
VVV
q
V
Ceq
Inductor
i-v relationship: vL(t)= LdiL/dt
L: inductance, henry (H)Energy stored in inductors
WL = ½ LiL2(t)
In DC circuit, can be replaced with short circuit
Sinusoidal waves
• Why sinusoids: fundamental waves, ex. A square can be constructed using sinusoids with different frequencies (Fourier transform).
• x(t)=Acos(t+)• f=1/T cycles/s, 1/s, or Hz =2f rad/s 2t / rad
=360 t / deg.
Average and RMS quantities in AC Circuit
01
0
T
dttxT
tx
It is convenient to use root-mean-square or rms quantities to indicate relative strength of ac signals rather than the magnitude of the ac signal.
rmsrmsavermsrms VIPV
VI
I ,2
,2
T
rms dttxT
x0
21
Complex number review
A
Ae
jA
ba
bj
ba
abajba
j
sincos
2222
22
Euler’s indentity
ab
11
2
1
2
1
2
1
11212121
22221111
21
21
21 ,
A
Ae
A
A
c
c
AAeAAcc
AeAcAeAc
j
j
jj
Phasor
How can an ac quantity be represented by a complex number?Acos(t+)=Re(Aej(t+))=Re(Aejtej )
Since Re and ejt always exist, for simplicity
Acos(t+) AejPhasor representation
Any sinusoidal signal may be mathematically represented in one of two ways: a time-domain form
v(t) = Acos(t+)
and a frequency-domain (or phasor) formV(j) = Aej
In text book, bold uppercase quantity indicate phasor voltage or currents
Note the specific frequency of the sinusoidal signal, since this is not explicit apparent in the phasor expression