Alternating Current

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Alternating Current
Voltage Source v(t) V cos ?t Current Source
i(t) I cos ?t
Phasors a graphical method for (combinations) of
trigonometric functions
2
Full Wave Rectifier
G
Irav (2/??? I
i
t
3
RMS values
i2(t)
Root-Mean-Square
i(t)
4
?
Current is in phase with Voltage
I
VIR
??t
i(t)I cos ??t
v(t)V cos ??t
5
?
L
i(t) Icos(?t)
?
?
I
VIXL
??t
Current lags Voltage Voltage leads Current
i(t)I cos ??t
v(t)V cos (??t90)
6
?
I
??t
VIXL
i(t)I cos ??t
v(t)V cos ??t
Current leads Voltage Voltage lags Current
7
?
8
L-R-C Circuit
i I cos(?t)
vL(t)IXLcos(?t????)
L
i(t)Icos(?t) v(t)Vcos(?t??) IXLcos(?t????)
IRcos(?t) IXCcos(?t?????)
R
vR(t)IRcos(?t)
vC(t)IXCcos(?t?????)
C
9
v(t)Vcos(?t??) IXLcos(?t????) IRcos(?t)
IXCcos(?t?????)
Z2 R2 X2 R2 (XL?XC)2 tan(??) X/R
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LRC series circuit example
12
Power
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Series Resonance
log(?)
I V/Z
log(?)
14
I
?o
?
HW add Q, ?? calculations to all rlc series HW
problems
15
LRC series circuit example (more)
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LRC series circuit example (and more)
17
Parallel L-R-C Circuit
iL(t) ILcos(?t-90 )
iC(t) ICcos(?t ?????)
iR(t) IRcos(?t)
C
R
L
v(t) Vcos(?t)
i I cos(?tf) IL cos(?t-90 ) IR cos(?t)
IC cos(?t?????)
V/XLcos(?t-90 ) V/R cos(?t) V/XC
cos(?t?????)
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IL
i I cos(?tf) IL cos(?t-90 ) IR cos(?t)
IC cos(?t?????)
IC
IC- IL
V
IV/Z
?
IR
IC
I2 IR2 (IC?IL)2 tan(??) (IC?IL)/IR
IL
IV/Z
IC- IL
?
V
IR
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LRC parallel circuit example
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Parallel Resonance
log(?)
log(?)
22
?
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Transformers Ferromagnetic Materials Strengthen
Flux
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Transformers
B
N1 V1, I1 Primary
N2 V2, I2 Secondary
N2 gtN1 gt V2 gt V1 Step-Up Transformer N2 ltN1 gt
V2 lt V1 Step-Down Transformer
25
A coffee maker from Europe is designed to operate
on a 240-V line (rms) to obtain 960W of power.
(a) Determine what characteristics are needed
by a transformer so that the proper delivery
voltage be obtained from the US standard voltage
of 120 V (rms)? (b) What current is drawn at the
secondary? (c) What is the resistance of the
coffee maker? (d) What current is drawn from the
120 V outlet by the primary? (e) What is the
power delivered by the 120 V source?