Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
This problem concerns the electric circuit shown in the figure below. Сараcitor Resistor 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 dQ I = dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation IP L Q = 0. dt where C is the capacitance and L is the inductance, so d?Q L Q = 0. C dt? 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, d²Q dQ +R dt 1 Q = 0. C L dt? If L = 1 henry, R = 1 ohm, and C = 4 farads, find a formula for the charge when |(a) Q(0) = 0 and Q' (0) = 5: Q(t) = 5te^(-t/2.5) help (formulas) |(b) Q(0) = 5 and Q' (0) = 0: Q(t) = help (formulas)

This problem concerns the electric circuit shown in the figure below. Сараcitor Resistor 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 dQ I = dt If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation IP L Q = 0. dt where C is the capacitance and L is the inductance, so d?Q L Q = 0. C dt? 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, d²Q dQ +R dt 1 Q = 0. C L dt? If L = 1 henry, R = 1 ohm, and C = 4 farads, find a formula for the charge when |(a) Q(0) = 0 and Q' (0) = 5: Q(t) = 5te^(-t/2.5) help (formulas) |(b) Q(0) = 5 and Q' (0) = 0: Q(t) = help (formulas)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
See similar textbooks
icon
Related questions
Question
100%
This problem concerns the electric circuit shown in the figure below. Capacitor Resistor 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 OP dt I If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation IP dt L- + 0, where C is the capacitance and L is the inductance, so Q = 0. C dt? 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 +R dt2 Q = 0. dt If L = 1 henry, R = 1 ohm, and C = 4 farads, find a formula for the charge when (a) Q(0) = 0 and Q' (0) = 5: Q(t) = 5te^(-t/2.5) help (formulas) |(b) Q(0) = 5 and Q' (0) = 0: Q(t) help (formulas)
Transcribed Image Text:This problem concerns the electric circuit shown in the figure below. Capacitor Resistor 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 OP dt I If the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation IP dt L- + 0, where C is the capacitance and L is the inductance, so Q = 0. C dt? 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 +R dt2 Q = 0. dt If L = 1 henry, R = 1 ohm, and C = 4 farads, find a formula for the charge when (a) Q(0) = 0 and Q' (0) = 5: Q(t) = 5te^(-t/2.5) help (formulas) |(b) Q(0) = 5 and Q' (0) = 0: Q(t) help (formulas)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS