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
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 Spring '08
 Kim
 Magnetism

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