Transcript Document
Lecture 12 Electromagnetic Oscillations and
Alternating Current Chp. 33
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Cartoon -. Opening Demo - Warm-up problem
Physlet
Topics
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LC Circuit Qualitatively
Electrical and Magnetic energy oscillations
Alternating current
\Pure R and L, circuti
Series RLC circuit
Power and Transfomers
Demos
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LR circuit
Series LRC circuit
Axis of rotation
Coil of wire
m B nˆdA
B dA
B cos dA
nˆ
B
d
d(BAcos )
d cos
d
BA
BAsin
dt
dt
dt
dt
d
BA sin but t so
dt
BA sint
m sint
2pf and f= 60 Hz
Where is the rotational angular
frequency of the generator
phase
m sin(t )
Instantaneousvoltage
Amplitude
time
Angular frequency
m
Phasor diagram
t
Phase constat
v R Ri
vR vL
i I sin(t)
m sint
2pf
di
I cos(t)
dt
f 1000 Hz
di
v L L LI cos(t)
dt
v L LI cos( t)
I
R R
V
L = 4.22mH
I
X L L
V
L
VR=RI
VL= XLIL or VL= (L)I since I=IL
Impedance Z: New quantity for AC circuits.
This is analogous to resistance in DC circuits
Z R2 (L)2
I
I
m
Z
m
R (L)
2
X L L
2
RL Circuit Example
Suppose m = 100 volts, f=1000 Hz, R=10 Ohms, L=4.22 mH,
Find XL, Z, I, VR, and Vl.
X L L 6.28 1000 0.00422 H 26.5
Z R2 (L)2
Z 102 (26.5)2 28.3
m
100
I
3.53A
Z 28.3
VR RI 10 3.53 35.3v
VL X L I 26.5 3.53 93.5v
Power in AC circuits
P i 2 R (I sin(t)) 2 R
Instantaneous power doesn’t mean anything
Need to average over time or one period of the sine wave
Pavg
2p
1
2p
Rd (I sin())
2
0
Note
Irms
2
Pavg Irms
R
I
2
2p
1
2p
1
I 2
RI sin d RI ( ) R
2
2
0
2
2
2
Averaging over a sine curve
Calculate Power lost in resistor from example
2
Pavg Irms
R
Irms
I
3.53A
2.50 A
2 1.414
Pavg (2.50A)210 62.5Watts
To calculate power produced by the generator you
need to take account of the phase difference between
the voltage and the current. In general you can write:
Pavg rms Irms cos
For an inductor P = 0 because the phase difference between
current through the inductor and voltage across the inductor is
90 degrees
Series LRC circuit
VR
v R vC v L
VC
m sint
i I sin(t )
I
R (XL XC )
2
m
R (X L XC )
2
Z R 2 (L
2
m
XC=1/(C)
2
VL XL=L
Z
1
L
C
tan
R
1 2
)
C
ELI the ICE man
Resonance
X L XC
1
L
C
1
LC
Series LRC demo
10 uF
4.25 mH
1
1
6.28 LC 6.28 4.25 103 H 106 F
f 2442Hz
f
Series LCR circuit