4
MA 36600 LECTURE NOTES: MONDAY, MARCH 9
Figure 4.
Graph of Solution
u
(
t
) =
u
c
(
t
) +
U
(
t
) under Resonance
0
2.5
5
7.5
10
12.5
15
17.5
20
20
16
12
8
4
4
8
12
16
20
ii.
Ohm’s Law
asserts that the voltage across a resistor is proportional to the current:
V
resistor
∝
I
=
⇒
V
resistor
=
I R
for some positive constant
R
. We call
R
the
resistance
; it is measured in ohms.
iii. 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.
iv. The voltage in the battery is a function of time:
V
battery
=
E
(
t
)
.
We call such an electrical circuit an
RLC Circuit
. We have chosen our units so that
1 volt = 1 henry
×
1
ampere
sec
= 1 ampere
×
1 ohm = 1 farad
−
1
×
1 coulomb
.
We think of voltage
V
as being similar to force
F
.
Just as Newton’s Second Law of Motion states that
F
=
m a
is the sum of the forces on an object,
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 Spring '09
 EdrayGoins
 Volt, Electric charge, positive constant R.

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