capacitor load
DESCRIPTION
Capacitor Load. The capacitive reactance of a capacitor. Generalized Ohm’s law:. Notice I c and V C are amplitudes. ICE. Inductive Load. The Inductive reactance of a inductive. Generalized Ohm’s law:. Notice I L and V L are amplitudes. ELI. I. e. i. v R. V R. w t- f. V L. v C. - PowerPoint PPT PresentationTRANSCRIPT
Capacitor Load
tCVdt
dqi
Cvq
tVv
CC
CC
CC
cos
sin
90sin90sin1
tIt
C
Vi C
CC
The capacitive reactance of a capacitor CXC
1
C
CC X
VI Generalized Ohm’s law: Notice Ic and VC are amplitudes
ICE
Inductive Load
tL
Vdt
L
Vi
dt
diLv
tVv
LLL
LL
LL
cossin
sin
90sin90sin tItL
Vi L
LL
The Inductive reactance of a inductive LX L
L
LL X
VI Generalized Ohm’s law: Notice IL and VL are amplitudes
ELI
The series RLC circuittdm sin
1. Same current through R, L, C
tIi dsin
Same frequency as in the source
t-
Ii2. Consider VR, VC, VL
tIRiRV dR sinVR
vR
C
IIXVtv
dCCdC
,
2sinVC
VC
vCLIIXVtv dLLdL
,
2sinVL
VL
LCR vvv
The series RLC circuit: Continuous
LCR vvv
This relation has to be maintained as phosors are rotating
Values at t.
CLRm VVV
General rules: 1. KVL and KCL still hold, but
values at the same t have to be used, i.e. vertical components in phasor diagram.
2. Vectors operation for Amplitude
vV
The series RLC circuit: Continuous
CLRm VVV
22
22
22
1R
CLI
RXXI
VVV
CL
RCLm
R
XX
RCL
CL
1
tan
ZRCLI mm
221
Z is the impedance of the circuit
=I(XL-XC)
=IR
=IZ
Examples33-43P. A coil of inductance 88 mH and unknown resistance and a 0.94 F are connected in series with an alternating emf of frequency 930 Hz. If the phase constant between the applied voltage and current is 75, what is the resistance of the coil.
f=930 Hzd=2f
=I(XL-XC)
=IR
=IZ
=I(XL-XC)
=IR
=IZRLC Resonance
R
XX
RCL
CL
1
tan
XL>XC: inductive loading
XC>XL: Capacitive loading
XL=XC: Resonance
RLC Resonance: Cont
R
XX
RCL
CL
1
tan 221 RCL
I m
LC
CL
XX
d
dd
CL
1
1
RI mmax
=I(XL-XC)
=IR
=IZConditions at Resonance
22
22
1 RCL
RXXI
m
CL
m
• I is a maximum
• Z is at minimum; Z=R; Z is purely resistive• XL=XC; inductive reactance cancels capacitive reactance; net reactance is zero• The phase angle is zero; the current is perfectly in phase with applied emf; the tangent of the phase angle is zero.• The driven frequency is identical to the natural frequency.
• The power factor is unity