PHY 2049: Physics II
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Tutoring Center is open in room NPB 1215,
M-F 12:00AM -4:00PM. It is free.
The following hitt numbers need to register.
Please do so ASAP.
402407
405767
416479
402614
406876
417029
432808
411209
420713
432798
Ch. 31 Electromagnetic Oscillations
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RC, RL, LC circuits
Driven damped Oscillations
Resonance
Series RLC circuits
Power
Transformer
Last time
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LC circuit
Analogous to a
pendulum
L m
q x
C 1/k
Be careful with ωt in
radians (not degrees)
2
L
d q
dt
2

q
0
C
q  q o sin  o t
U 
1
2
Li 
2
1 q
o 
2
2 C

qo
2
2C
1
LC
Alternating Currents
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A resistance
V o sin  t  IR  0
I 
V
R
sin  t  I R sin(  t   )
 0
The current and voltage are in phase
Capacitor: AC response
q  CV o sin  t
i (t ) 
dq
dt

V0
  CV o cos  t  I C sin(  t  90 )
sin(  t  90 )
XC
XC 
1
C
The current leads the voltage
Inductor: AC response
vL  L
di
dt
i (t )  
 V o sin  t
Vo
L
cos  t 
Vo
sin(  t  90 )
XL
X L  L
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The current lags the voltage
HITT
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A capacitor in an LC oscillator has a maximum
potential difference of 15V and a maximum
energy of 360 μJ. At a certain instant the
energy in the capacitor is 40 μJ. At that
instant what is the potential difference across
the capacitor?
A. zero
E. 20V
B. 5V
C. 10V
D. 15V
A different problem
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An LC circuit has a capacitance of 30 μF and
an inductance of 15mH. At time t = 0 the
charge on the capacitor is 10 μC and the
current is 20mA. The maximum charge on
the capacitor is:
A. 8.9 μC
B. 10 μC
C. 12 μC
D. 17 μC
E. 24 μC
Yet different
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A 45-mH inductor is connected to a source of
sinusoidal emf with a frequency of 400 Hz and a
maximum emf of 20V. The maximum current is:
A. 0
B. 0.18A
C. 1.1A
D. 360A
E. 2300A
ans: B
RLC circuit
2
L
d q
dt
2
q  Qe

'2
R
dq

dt
- Rt/2L
 V o cos  t
C
cos(  t   )
 (
2
q
'
R
2L
)
2
RLC circuit
e  v L  vC  v R
e I
R  X L  X C 
2
2
 IZ
tan  
XL  XC
R
Inductive
Capacitive
In resonance
e = E sin ωt i = io sin (ωt –φ)
Capacitor current leads
Power = I2R
= ermsirmscosφ (cos φ =R/Z)
Resonance
Transformers