21.2 Ac circuits

1
21.2 Ac circuits

• Resistors, capacitors, inductors in
• ac circuits
• Reactance

2
In an ac circuit current and voltages are
sinusoidal. The phase relation between the
current and voltage is different for resistors,
capacitors and inductors. The maximum voltage
across the capacitor and inductor are
proportional to the current. The constant
of proportionality is a property called the
reactance.
3
Capacitor in an ac circuit
current reverses
I
I
?v
?Vc
t
Voltage lags current
IImax sin2pft
?Vc
4
Capacitative Reactance, Xc
?VC XC I
Recall
Dimensional analysis
R
C
has units of ohms
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Capacitive Reactance, Xc
?VC XC I
The capacitive reactance impedes the current.
Recall
XC is higher at low frequency. The capacitor
block current at long time, low frequency.
because charge accumulates. At high frequency
less charge accumulates. Therefore, less
reactance at high frequency
R
C
6
f0 DC
XC ?
infinity
I0
fhigh
I high
XC ?
low
7
A 10 microfarad capacitor is in an ac circuit
with a voltage source with maximum RMS voltage
of 10 V. a) Find the current for a frequency of
100 Hz. b) Find the current for a frequency
of 1000 Hz.
a)
The frequency is 10 x higher, the current is 10 x
higher I10x6.3x10-26.3x10-1A
b)
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Inductor in an ac circuit
I
?VL
?v
t
Voltage lead current
?VL
max
min
0
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Inductive reactance, XL
?VLXL I

Dimensional analysis
R
L
XL has units of ohms
10
Inductive reactance, XL
?VLXL I

An inductor has higher back emf when ?I/?t is
greater, i.e. at high frequency. Inductive
reactance higher at high frequency.
At low frequency, DC, the current is not blocked,
i.e. low reactance at low frequency.
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f0
I high
XL ?
0
f high
XL ?
high
I low
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• A inductor with L 10-5 H is driven by a 10 V ac
  source.
• Find the current at f100 Hz.
• Find the current at f1000Hz

a)
the frequency is 10x greater the current is
inversely proportional to f the current is 10x
less I1.6x103/101.6x102A
b)
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Application. High pass and low pass filters.
tweeter high f
amplifier
woofer low f
pass high frequency/block low frequency
Capacitor
stereo speakers
pass low frequency/block high frequency
Inductor
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log-log plot of X vs f
1000
L
X
100
C
10
10
100
1000
f