Capacitor. 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.
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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.
i = dq/dt = C dv/dt
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
=360 (Dt / T) deg.
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.
How can an ac quantity be represented by a complex number?
Since Re and ejwtalways exist, for simplicity
Acos(wt+q) Aejq=Aq Phasor representation
Any sinusoidal signal may be mathematically represented in one of two ways: a time-domain form
v(t) = Acos(wt+q)
and a frequency-domain (or phasor) form
V(jw) = Aejq=Aq
In text book, bold uppercase quantity indicate phasor voltage or currents
Note the specific frequency w of the sinusoidal signal, since this is not explicit apparent in the phasor expression
Source vS(t) =Asinwt
vR and iR are in phase
Phasor representation: vS(t) =Asinwt = Acos(wt-90°)= A -90°=VS(jw)
IS(jw) =(A / R)-90°
Impendence: complex number of resistance Z=VS(jw)/ IS(jw)=R
Generalized Ohm’s law VS(jw) = Z IS(jw)
Everything we learnt before applies for phasors with generalized ohm’s law
VC(jw)= A -90°
Notice the impedance of a capacitance decreases with increasing frequency
Phasor: VL(jw)=A -90°
Opposite to ZC, ZL increases with frequency
R1=100 W, R2=75 W, C= 1mF, L=0.5 H, vS(t)=15cos(1500t) V.
Determine i1(t) and i2(t).
Step 1: vS(t)=15cos(1500t), w=1500 rad/s.
Step 2: VS(jw)=15 0
Step 3: ZR1=R1, ZR2=R2, ZC=1/jwC, ZL=jwL
Step 4: mesh equation