where is the inductance in henrys, R is the resistance in ohms, is the capacitance in farads,, is the electromotive force in volts, is the charge in coulombs on the capacitor as time t, and is the current in amperes. Find the current at time if the charge on the capacitor is initially zero, the initial current is zero;
[Hint: Differentiate both sides of the differential equation in (20) to obtain a homogenous linear second-order equation for Then use (20) to determine
Section 4.3 (4, 8, 34)
??
.
??
"
-
????
'
+
??????
=
??
??
.
????
"
-
????
'
+
??????
=
??
3
34. RLC Series Circuit
. In the study of an electric circuit consisting of a resistor, capacitor,
inductor, and an electromotive force (see
Figure 4.9)
, we are led to an initial value problem of
the form
??
????
????
+
????
+
??
??
=
??
?
??
?
,
??
?
??
?
=
??
??
,
??
?
??
?
=
??
??
w
here
??
is the inductance in henrys, R is the resistance in ohms,
??
is the
capacitance in
farads,
??
(
??
)
, is the electromotive force in volts,
??
(
??
)
is the charge in coulombs on the capacitor
as
time t, and
??
=
????
????
is the current in amperes. Find the
current
at time
??
if the charge on the
capacitor is initially zer
o, the initial
current is zero;
??
=
10
??
,
??
=
20
?
,
C
=
?
6260
?
-
1
??
,
??????
??
?
??
?
=
100
??
.
[Hint:
Differentiate
both sides of the
differential equation in (20) to obtain a
homogenous
linear
second
-
order equation for
??
?
??
?
.
Then
use (20) to determine
????
??
??
????
??
=
0
Section 4.4 (2, 6, 19)
??
.
??
"
-
????
'
+
????
=
??
??
??????
?
????
??
.
??
"
(
??
)
+
??
??
'
(
??
)
-
??
(
??
)
=
??????
??
????
.
????
"
+
??????
'
-
????
=
-
??
????
-
????
Section 4.3 (4, 8, 34)
??. ??"-????' + ??????=??
??. ????"-????' + ??????=??3
34. RLC Series Circuit. In the study of an electric circuit consisting of a resistor, capacitor,
inductor, and an electromotive force (see Figure 4.9), we are led to an initial value problem of
the form
??
????
????
+????+
??
??
=????,????=??
??
,????=??
??
where ?? is the inductance in henrys, R is the resistance in ohms, ?? is the capacitance in
farads, ??(??), is the electromotive force in volts, ??(??) is the charge in coulombs on the capacitor
as time t, and ??=
????
????
is the current in amperes. Find the current at time ?? if the charge on the
capacitor is initially zero, the initial current is zero;
??=10 ??,??=20 ?,C=6260
-1
??,?????? ????=100 ??. [Hint: Differentiate both sides of the
differential equation in (20) to obtain a homogenous linear second-order equation for ????. Then
use (20) to determine
????
????
???? ??=0
Section 4.4 (2, 6, 19)
??. ??"-????'+????=??
??
??????? ????
??. ??"(??) +????'(??) - ??(??)=?????? ??
????.????"+??????'-????=-??????
-????
Gaddicus
math_hw.docx
0
