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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)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 69E
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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)
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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