AC Circuits Summary
Average values (r
oot
m
ean
s
quare
)
avg for sin
2
or cos
2
= 1/2
Transformers:
Energy conservation
Power:
Ohm’s Law
: V = I Z Z = impedence, combined resistance and reactance.
Reactance
,
ω dependent
:
Capacitors
Inductors:
Phase difference means combination requires PythagoreanTheorem:
in Ohms
Phase difference also means that the amplitude of
the power is less than the
(voltage amplitude) ∙ (current amplitude);
Filters
:
Low Pass
High Pass
V
C
high at low ω
(RC
> 1/ω to
charge)
V
L
high at high ω
(V ~ ΔI/Δt ~ ω)
Oscillator
Approach 1
: Remember the spring and mass oscillator.
When the mass is at the maximum or minimum spring extension, the stored
potential energy in the spring is a maximum and the mass is momentarily at
rest.
When the mass passes through the equilibr
ium position, the velocity is at
maximum and the potential energy is zero.
At max or min position, the spring exerts a force to move the mass.
At equilibrium position, the force is zero, but the momentum carries the
mass past that point to continue the os
cillations.
For the LC circuit, the capacitor stores potential energy as charge builds up
on the plates. The inductor resists changes in the current, so it keeps
current flowing when the charge (and therefore the voltage) on the
capacitor is zero.
Spring & mass
LC circuit
Energy
Potential, Kinetic
E field, B Field
Force
Spring
Voltage on Capacitor
Continue motion
momentum
Inductor
Approach 2
: Follow the change in electrical values.
Vc
I
ΔI/Δt
V
L
+ max
Current
direction
changing
0
+max

max
+, decreasing
+ in
creasing
+
de
creasing

decreasing
0
+max
0
0

, increasing
+
de
creasing

decreasing
+ decreasing

max
Current
direction
changing
0

max
+max

,decreasing

increasing

de
cr
easing
+de
creasing
0

max
0
0
This is plotted below:
Notice that
the voltage across the inductor is a quarter cycle ahead of the
current and the current is a quarter cycle ahead of the voltage on the
capacitor. When we used to use E for volt
age, the mnemonic for
remembering this was “ELI the ICE man”
{
E leads I for L; I leads E for C}
Animation of current flow:
http://www.falstad.com/circuit/index.html
Shows fields oscillating
http://www.walter

fendt.de/ph11e/osccirc.htm
Circuit info. and animation
http://www.allaboutcircuits.com/vol_2/chpt_6/5.html
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