1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Harrizon [31]
3 years ago
10

From mechanics, you may recall that when the acceleration of an object is proportional to its coordinate, d2xdt2=−kmx=−ω2x , suc

h motion is called simple harmonic motion, and the coordinate depends on time as x(t)=Acos(ωt+ϕ), where ϕ, the argument of the harmonic function at t=0, is called the phase constant. Find a similar expression for the charge q(t) on the capacitor in this circuit. Do not forget to determine the correct value of ϕ based on the initial conditions described in the problem. Express your answer in terms of q0 , L, and C. Use the cosine function in your answer.
Physics
1 answer:
marysya [2.9K]3 years ago
6 0

Answer:

    q = q₀ sin (wt)

Explanation:

In your statement it is not clear the type of circuit you are referring to, there are two possibilities.

1) The circuit of this problem is a system formed by an Ac voltage source and a capacitor, in this case all the voltage of the source is equal to the voltage at the terminals of the capacitor

                    ΔV = ΔV_{C}

we assume that the source has a voltage of the form

                    ΔV = ΔV₀o sin wt

The capacitance of a capacitor is

                   C = q / ΔV

                  q = C ΔV sin wt

the current in the circuit is

                    i = dq / dt

                    i = c ΔV₀ w cos wt

if we use

                  cos wt = sin (wt + π / 2)

we make this change by being a resonant oscillation

we substitute

                  i = w C ΔV₀ sin (wt + π/2)

With this answer we see that the current in capacitor has a phase factor of π/2 with respect to the current

2) Another possible circuit is an LC circuit.

In this case the voltage alternates between the inductor and the capacitor

                     V_{L} + V_{C} = 0

                      L di / dt + q / C = 0

the current is

                      i = dq / dt

                       

they ask us for a solution so that

                    L d²q / dt² + 1 / C q = 0

                     d²q / dt² + 1 / LC q = 0

this is a quadratic differential equation with solution of the form

                    q = A sin (wt + Ф)

to find the constant we derive the proposed solution and enter it into the equation

                di / dt = Aw cos (wt + Ф)

                d²i / dt²= - A w² sin (wt + Ф)

                 - A w² + 1 /LC  A = 0

                  w = √ (1 / LC)

To find the phase factor, for this we use the initial conditions for t = 0

in the case of condensate for t = or the charge is zero

                 0 = A sin Ф

                  Ф = 0

             

                  q = q₀ sin (wt)

You might be interested in
Define the types of friction and give FOUR examples of each
Verdich [7]

Answer:

Static Friction - acts on objects when they are resting on a surface

Sliding Friction -  friction that acts on objects when they are sliding over a surface

Rolling Friction - friction that acts on objects when they are rolling over a surface

Fluid Friction - friction that acts on objects that are moving through a fluid

Explanation:

Examples of static include papers on a tabletop, towel hanging on a rack, bookmark in a book , car parked on a hill.

Example of sliding include sledding, pushing an object across a surface, rubbing one's hands together, a car sliding on ice.

Examples of rolling include truck tires, ball bearings, bike wheels, and car tires.

Examples of fluid include water pushing against a swimmer's body as they move through it , the movement of your coffee as you stir it with a spoon,  sucking water through a straw, submarine moving through water.

4 0
3 years ago
Does a generator start a Direct Current?
lesya [120]
A direct-current (DC) generator is a rotating machine that supplies an electrical output with unidirectional voltage and current. ... The field is produced by direct current in field coils or by permanent magnets on the stator. The output, or armature, windings are placed in slots in the cylindrical iron rotor.
3 0
3 years ago
Which of the following describes a referee's job?
Serhud [2]

Answer:

C. Supervising the game to make sure teams are playing fairly

5 0
3 years ago
What was the largest group in the colonies in the year leading up to the American revoulation
Degger [83]
Answer: The English origin was the largest

7 0
2 years ago
Read 2 more answers
About 10-15% of all galaxies are which shape?
myrzilka [38]
The answer is; Irregular.
4 0
3 years ago
Other questions:
  • -) Given that 1 inch = 0.0254 m, 1 mile = 1760 yards and 1 yard = 36 inches. Convert 5
    6·1 answer
  • How to describe the motion of an object that has an acceleration of 0 m/s
    11·1 answer
  • The mass of a single gold atom is 3.27×10-22 grams. how many gold atoms would there be in 236 milligrams of gold?
    5·2 answers
  • To create electromagnetic induction, which of the following has to move?
    13·2 answers
  • 1. What are three questions you should ask before joining a club?
    13·1 answer
  • A resistor with an unknown resistance is connected in parallel to a 13 Ω resistor. When both resistors are connected in parallel
    15·2 answers
  • The FIRST step in cloud formation is.... A) warmed air cools and condenses. B) solar energy causes warm air to rise. C) solar en
    15·1 answer
  • Select the correct answer. Which of the following is a category of dance? O A. Group dance OB. Solo dance O C. Partner dance OD.
    11·1 answer
  • The girl in the diagram is accelerating down the hill, What is the girl’s acceleration.
    6·2 answers
  • 77. The first law of motion applies to
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!