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Physics 121: Electricity &
Magnetism – Lecture 13
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
LC Oscillations
q2
UE 
2C
April 18, 2007
UB 
1 2
Li
2

1
LC
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LC Oscillations (cont.)
d 2q 1
L 2  q0
dt
C
d 2q
dq 1
L 2 R  q0
dt
dt C
q  Q cos t   
q  Qe Rt / 2 L cos t   
Damped Oscillation
q2 Q2
UE 

cos 2 t   
2C 2C
dq
i
 Q sin t   
dt
April 18, 2007
q2 Q2
UB 

sin 2 t   
2C 2C
Center for Solar-Terrestrial Research
Alternating Current/Forced
Oscillations
AC: alternating current
DC: direct current
d: driving angular frequency
Whatever the natural angular
frequency  of a circuit may be,
forced oscillations of charge,
current, and potential difference
in a circuit always occur at the
driving frequency d.
April 18, 2007
Center for Solar-Terrestrial Research
Resistive, Capacitive, & Inductive Load
VR  I R R
XC 
1
d C
VC  I C X C
X L  d L
VL  I L X L
Resistor
April 18, 2007
Capacitor
Inductor
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Series RLC Circuit
April 18, 2007
Center for Solar-Terrestrial Research
Series RLC Circuit (cont.)
Impedance
Z  R   X L  XC 
2
m
m
Current
amplitude
I
Phase constant
X L  XC
tan  
R
Resonance
April 18, 2007
Z

d   
2
R  d L  1/ d C  
2
1
LC
Center for Solar-Terrestrial Research
2
Power in Alternating–Current Circuits
RMS current
RMS voltage
I rms
I

2
Vrms
V

2

RMS EMF
 rms 
Average power
2
Pavg  I rms
R
2
Pavg   rms I rms cos 
April 18, 2007
Center for Solar-Terrestrial Research
Transformers
Transformation of voltage
Ns
Vs  Vp
Np
Transformation of currents
Is  I p
Np
Ns
Load resistance
Step–up transformer
Step–down transformer
April 18, 2007
2
 Np 
Req  
 R
 Ns 
Center for Solar-Terrestrial Research