MA 36600 MIDTERM #2 REVIEW
5
•
Let
Q
=
Q
(
t
) denote the charge in an electric circuit at time
t
; it is measured in coulombs. Similarly,
I
=
dQ
dt
denotes the current; it is measured in amperes. We think of
Q
as the “displacement”
u
(
t
), and
I
as
the “velocity”
u
°
(
t
). Say that we have four objects in our circuit:
i.
Inductor
(which acts like the mass): The voltage across an inductor is proportional to the
change in the current:
V
inductor
∝
dI
dt
=
⇒
V
inductor
=
L
dI
dt
for some positive constant
L
. We call
L
the
inductance
; it is measured in henrys.
ii.
Resistor
(which acts like a damping force):
Ohm’s Law
asserts that the voltage across a resistor
is proportional to the current:
V
resistor
∝
I
=
⇒
V
resistor
=
IR
for some positive constant
R
. We call
R
the
resistance
; it is measured in ohms.
iii.
Capacitor
(which acts like a spring): The voltage across a capacitor is proportional to the
charge:
V
capacitor
∝
Q
=
⇒
V
capacitor
=
1
C
Q
for some positive constant
C
. We call
C
the
capacitance
; it is measured in farads.
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.
 Spring '09
 EdrayGoins

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