Linear Second Order Differential Equation
Gaddicus
question_34.docx34. RLC Series Circuit. In the study of an electric circuit consisting of a resistor, capacitor, inductor, and an electromotive force, 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;
[Hint: Differentiate both sides of the differential equation in (20) to obtain a homogenous linear second-order equation for Then use (20) to determine
34. RLC Series Circuit
. In the study of an electric circuit consisting of
a resistor, capacitor, inductor, and an elec
tromotive force
, 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 th
e 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
34. RLC Series Circuit. In the study of an electric circuit consisting of
a resistor, capacitor, inductor, and an electromotive force, 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
