D I= dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dl Q L + 0, dt C where C is the capacitance and L is the inductance, so d2Q L + 0. dt2 C The unit of charge is the coulomb, the unit of capacitance the farad, the unit of inductance the henry, the unit of current is the ampere, and time is measured in seconds. If L = 49 henry and C = 16 farad, find a formula for Q(t) if (a) Q(0) 0 and I(0) = 5: Q(t)-75sin(1/15t) = (a) Q(0) = 4 and I(0) = 0: Q(t) = 4cos(1/15t)
D I= dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dl Q L + 0, dt C where C is the capacitance and L is the inductance, so d2Q L + 0. dt2 C The unit of charge is the coulomb, the unit of capacitance the farad, the unit of inductance the henry, the unit of current is the ampere, and time is measured in seconds. If L = 49 henry and C = 16 farad, find a formula for Q(t) if (a) Q(0) 0 and I(0) = 5: Q(t)-75sin(1/15t) = (a) Q(0) = 4 and I(0) = 0: Q(t) = 4cos(1/15t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:The following problem concerns the electric circuit in the figure below.
с
Inductor
A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in the inductor, in
turn, charges up the capacitor until the capacitor is fully charged again. If Q(t) is the charge on the capacitor at time t, and I is the current, then
ما
I=
do
dt
If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation
dI Q
L
+
0,
dt
C
where C is the capacitance and L is the inductance, so
L
d2Q Q
dt² C
+
0.
The unit of charge is the coulomb, the unit of capacitance the farad, the unit of inductance the henry, the unit of current is the ampere, and time is measured in
seconds.
If L = 49 henry and C
=
16 farad, find a formula for Q(t) if
(a) Q(0) 0 and I(0)
(a) Q(0) = 4 and I(0) = 0: Q(t) = 4cos(1/15t)
5: Q(t) = 75sin(1/15)
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