AC Circuits Summary

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