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Chapter 31:
Simple AC circuits
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V
I R
Resistor circuits
•
Notation: Use lowercase for
instantaneous values, Uppercase
for peak values
v
R
=
ε
= V
R
sin ωt
i
R
= v
R
/R = I
R
sin ωt
•
In an AC circuit, resistor voltage
and current oscillate
in phase
.
ε=ε
m
sinωt
Capacitor circuits
v
C
=
ε
= V
C
sin ωt
i = dq/dt
and q = Cv
C
:
i
C
= ωCV
C
cos ωt
which we write as:
i
C
= ωCV
C
sin (ωt + π/2)
The current
leads
voltage by π/2 rads
ICE
ε=ε
m
sinωt
Current reaches peak value I
C
the instant the capacitor is fully discharged and v
C
=0.
The current is zero the instant the capacitor is fully charged.
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View Full Document Capacitive Reactance – Relationship between peak
current and voltage in a capacitor
•
I
C
= ωCV
C
, although they
don’t happen at the same
time.
•
Define the
capacitive
reactance
X
C
= 1/ ωC, then:
•
I
C
= V
C
/X
C
•
This is analogous to Ohm’s
Law for DC.
•
at very high frequencies, X
C
approaches 0 and the
capacitor acts like a wire.
Units of X
C
:
Consider this circuit. The
frequency of the AC source is
adjusted, while its voltage
amplitude is kept constant.
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This note was uploaded on 02/05/2011 for the course PHYS 220B taught by Professor Preminger during the Fall '10 term at CSU Northridge.
 Fall '10
 Preminger
 Current

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