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)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: o ook at the picture below. As a windmill's blade rotates, the height of its tip above ground is…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Newton's law of cooling says that a hot object cools rapidly when the difference between its…

Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

Q: Solve for x a.16 b. 48 c. 24 d.72

A: Given: A polygon with exterior angles 5x, 4x, 3x, 2x, x respectively.

Q: = 3 cos? ( - 0), r(0) = de 8

Q: Apply Newton's Method using the given initial guess. y = x³ - 2x - 2, X₁ = 0 X₁ = 0 x₂ = x3 = X4 =…

Q: (ii) Show that for Joel to save $ 10 000 after 5 years, he must earn interest at a rater determined…

Q: Find the charge on the capacitor in an LRC-Series circuit if L = 10 henry, R = 20 ohms, C = 0.01…

A: The charge on the capacitor in the LRC-series circuit, with L=10 henry, R=20 ohms, C=0.01 farad, and…

Q: An Alternating current "i" at any time t is given by i = sin 3t.Find the RMS Value of the current…

A: This question is related to integration.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT A physical spring system follows the equation + ki = 0, with…

A: Finding the general solution with k>0.

Q: 1. Given the equation sin(y) + cos(r) = 2, find

Q: Solve the DE'S ;- with NoA-hamogeneust

Q: Solve the equation cos(20) + cos(40) = 0 for all 0 E [0,27T).

A: I am attaching image so that you understand each and every step.

Q: 2. Solve the equation 3x² = ex, by applying 4 iterations of: a. Bisection Method (use the interval…

A: Here we have to solve the given equation 3x2 = ex by using bisection method, secant method,…

Q: Assume that a body cools according to the Newton's Law of cooling. Find the temperature (T) at time…

A: Answer

Q: (b). Apply Newton's Raphson method and find the roots of the equation e-2x = 5x + 2, correct to four…

Q: Determine whether these statement forms are logically equivalent. In each case, construct a truth…

A: Boolean algebra is a branch of mathematics that is concerned with binary variables and operations on…

Q: (": (3) 121M (13) 3. 7 = 63

Q: SHOW FULL SOLUTION. DIFFERENTIAL CALCULUS. To measure the area of a quadrangle, two students decided…

A: Given: speed of student A is 2 paces per second and speed of student B is 3 paces per 2 seconds. To…

Q: (b) Figure Q4(b) shows a circuit for a battery having a constant voltage of 60 volts. The circuit is…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

Let A be a non-singular matrix, det(A) ± 0. a) Show that µ(A) does not change if the operator A is multiplied by an arbitrary constant. b) Multiply one row of the Matrix A by some scalar a, and denote the new matrix by Aq. Show that µ(Aª) → ∞ as a → ∞.
An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: c) Determine the particular solution of the non-homogeneous differential equation qp, posing the simultaneous equations and their corresponding solution to establish the value of the indeterminate coefficients. d) Determine the general solution for the charge on the capacitor, that is, q(t) = qh + qp
After reading the selections about number systems and arithmetic in Egypt, Mesopotamia, India and the Islamic area, what similarities do you find in their development? What differences?
Set 2: A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180 degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature of the roast follows Newton's Law of Cooling, T(t) = Ta +(To-Ta)e-kt, where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient temperature" means the temperature of the space the object is in.) (a) Find the values of To and Ta for this problem. (b) Find the value of k for this problem. Then write down the function T(t) which gives the temper- ature of the pork roast in degrees Fahrenheit as a function of time t in minutes. (c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
In Figure 6.50, HP = 4, PJ = 5, and LP = 8. Find PM. M SOLUTION Applying Theorem 6.3.5, we have HP PJ = LP· PM Then 4.5 8. PM 8. PM = 20 PM = 2.5 Figure 6.50
Solve part b
3. Find the first four solutions to cos t) = -1.
An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: e) Determine the particular solution of q(t) by establishing the values of the constants C1 & C2, through the application of the initial values. f) Draw the graph of the final solution q(t) obtained (you can use an application and paste the graph).