Discussion Question 12B
P212, Week 12
Phasors
Next, we encounter the rich subject of
driven RLC circuits
.
The
most basic example is shown in the diagram: a resistor, a
capacitor, and inductor, and an AC generator all connected in
series.
The
generator
is just a fancy type of battery that produces
not a constant “DC” voltage as we have encountered so far, but an
oscillating “
AC
” voltage.
The voltage from the generator
oscillates sinusoidally at some angular frequency
ω
, and has a
maximum magnitude
E
max
(also called the “amplitude” or “
peak
voltage
”).
If the AC generator weren’t present, our circuit would be a plain old undriven LC circuit with
some resistance
R
thrown in.
It would support a nice oscillating current of frequency
ω
0
= 1/
√
LC
… except the resistor would damp out the oscillations over time.
To keep the circuit
going, we attach the generator to
drive
the oscillations.
But
… the AC generator is driving the
circuit at its
own
frequency
ω
, which need
not
be the same as the circuit’s
resonant frequency
ω
0
.
The result is something of a mess.
/
The generator forces the current to oscillate at
frequency
ω
, but if
ω
doesn’t match
ω
0
, the driving voltage will be
out of phase
with the current.
To help us visualize what is going on, we use
phasors
.
A phasor is just a way of graphically
representing the timedependence
of something which oscillates
.
Specifically, a phasor is a
vector in the
xy
plane.
We then imagine that this vector
rotates
around the origin in a
counterclockwise direction, with angular velocity
ω
radians/second.
The phasor describes the
behavior of
something
oscillating with frequency
ω
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Kim
 Magnetism, Alternating Current, RC circuit, LC circuit

Click to edit the document details