2
MA 36600 LECTURE NOTES: MONDAY, APRIL 6
Circuits.
Consider a circuit that contains three devices:
i. an inductor (which behaves like a mass),
ii. a resistor (which behaves like friction), and
iii. a capacitor (which behaves like a spring).
Such a circuit is called an
LRC Circuit
.
Let
Q
=
Q
(
t
) denote the charge at time
t
,
I
=
I
(
t
) denote the current at time
t
, and
V
=
V
(
t
) denote
the voltage at time
t
. We have the following relations:
i. For an inductor,
V
inductor
∝
dI
inductor
dt
=
⇒
V
inductor
=
L
·
dI
inductor
dt
.
The constant
L
is called the
inductance
.
ii. For a resistor,
V
resistor
∝
I
resistor
=
⇒
V
resistor
=
R
·
I
resistor
.
The constant
R
is called the
resistance
. (This is called
Ohm’s Law
.)
iii. For a capacitor,
V
capacitor
∝
Q
capacitor
=
⇒
V
capacitor
=
1
C
·
Q
capacitor
=
⇒
dV
capacitor
dt
=
1
C
·
I
capacitor
.
The constant
C
is called the
capacitance
.
The constants
L
,
R
, and
C
motivate the name “
LRC
Circuit.”
In order to form di±erential equations, we need an equivalent of Newton’s Laws of Motion for circuits.
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 Spring '09
 EdrayGoins
 Inductor, Electrical resistance, Electrical impedance

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