Download RLC Circuits

RLC Circuits
Ohm for AC
 An AC circuit is made up with
V0 sin t
VR  IR
R
VC  IX C
C
X C  1 C
•
•
•
•
Power source
Resistors
Capacitor
Inductors
 Kirchhoff’s laws apply just like
DC.
• Special case for phase
VL  IX L
L
components.
X L  L
Series RLC
 A series RLC circuit can be
made from each component.
i
R
v
L
• One loop
• Same current everywhere
 Reactances are used for the
capacitors and inductors.
C
 The combination of
resistances and reactances in
a circuit is called impedance.
Vector Map
 Phase shifts are present in AC
circuits.
• +90° for inductors
• -90° for capacitors
VL=IXL
VR=IR
 These can be treated as if on
the y-axis.
• 2 D vector
• Phasor diagram
VC=IXC
Vector Sum
 The current is the same in the loop.
• Phasor diagram for impedance
 A vector sum gives the total impedance.
XL
XC
XL
Z
R
R
XC
Vector Sum
 The total impedance is the
magnitude of Z.
XC
XL
Z
f
 The phase between the current
and voltage is the angle f
between Z and the x-axis.
R
Z  R2  X L  X C 
2
1 

2
Z  R   L 

C 

2
X L  XC
tan f 
R
1


L


C
f  arctan 
R









Phase Changes
 The phase shift is different in each component.
Power Factor
 Power loss in an AC circuit
depends on the instantaneous
voltage and current.
• Applies to impedance
p  vi  i 2 Z cos f
 The cosine of the phase angle
is the power factor.
2
Prms  Vrms I rms  I rms
Z cos f
P
I 0 Z cos f
2
0
t
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