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This problem concerns the electric circuit shown in the figure below. Capacitor Resistor www 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 I dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation L dI Q + = dt C 0, where C is the capacitance and L is the inductance, so d² Q L Q + dt2 C = 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, L- d² Q dt2 + R dQ dt 1 Q = 0. If L1 henry, R = 1 ohm, and C (a) Q(0) = 0 and Q'(0) = = 3: Q(t) = help (formulas) (b) Q(0) Q(t) = = 3 and Q'(0) = = 0: help (formulas) = Book: Section 2.4 of Notes on Diffy Qs 4 farads, find a formula for the charge when

This problem concerns the electric circuit shown in the figure below. Capacitor Resistor www 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 I dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation L dI Q + = dt C 0, where C is the capacitance and L is the inductance, so d² Q L Q + dt2 C = 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, L- d² Q dt2 + R dQ dt 1 Q = 0. If L1 henry, R = 1 ohm, and C (a) Q(0) = 0 and Q'(0) = = 3: Q(t) = help (formulas) (b) Q(0) Q(t) = = 3 and Q'(0) = = 0: help (formulas) = Book: Section 2.4 of Notes on Diffy Qs 4 farads, find a formula for the charge when

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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This problem concerns the electric circuit shown in the figure below. Capacitor Resistor www 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 I dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation L dI Q + = dt C 0, where C is the capacitance and L is the inductance, so d² Q L Q + dt2 C = 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, L- d² Q dt2 + R dQ dt 1 Q = 0. If L1 henry, R = 1 ohm, and C (a) Q(0) = 0 and Q'(0) = = 3: Q(t) = help (formulas) (b) Q(0) Q(t) = = 3 and Q'(0) = = 0: help (formulas) = Book: Section 2.4 of Notes on Diffy Qs 4 farads, find a formula for the charge when
Transcribed Image Text:This problem concerns the electric circuit shown in the figure below. Capacitor Resistor www 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 I dQ dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation L dI Q + = dt C 0, where C is the capacitance and L is the inductance, so d² Q L Q + dt2 C = 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, L- d² Q dt2 + R dQ dt 1 Q = 0. If L1 henry, R = 1 ohm, and C (a) Q(0) = 0 and Q'(0) = = 3: Q(t) = help (formulas) (b) Q(0) Q(t) = = 3 and Q'(0) = = 0: help (formulas) = Book: Section 2.4 of Notes on Diffy Qs 4 farads, find a formula for the charge when
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