dt2 Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R, dQ L + R Q = 0. di2 dt If L = 1 henry, R = ; ohm, andC = 16 farads, find a formula for the charge when (a) Q(0) = 0 and Q'(0) = 6: Q(t) = (b) Q(0) = 6 and Q'(0) = 0: Q(t) =
dt2 Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R, dQ L + R Q = 0. di2 dt If L = 1 henry, R = ; ohm, andC = 16 farads, find a formula for the charge when (a) Q(0) = 0 and Q'(0) = 6: Q(t) = (b) Q(0) = 6 and Q'(0) = 0: Q(t) =
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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Transcribed Image Text:This problem concerns the electric circuit shown in the figure below.
Сараcitor
Resistor
Inductor
Transcribed Image Text: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
dQ
I =
dt
If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation
dI
L
+
= 0,
dt
where C is the capacitance and L is the inductance, so
dQ
+
dt?
= 0.
Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R,
dQ
dQ
1
+ R
+
O =
dt²
dt
If L = 1 henry, R = ; ohm, and C = 16 farads, find a formula for the charge when
(a) Q(0) = 0 and Q'(0) = 6:
Q(t) =
= 6 and Q'(0) = 0:
(b) Q(0)
Q(t) =
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