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
Mars2501 [29]
3 years ago
11

The voltage across the terminals of a 250nF capacitor is푣푣=�50푉푉, 푡푡≤0(푚푚1푒푒−4000푡푡+푚푚2푡푡푒푒−4000푡푡)푉푉, 푡푡 ≥0The initial current

in the capacitor is 400 mA. Assume the passive sign convention.a. What is the initial energy stored in the capacitor?b. Evaluate the coefficients A1 and A2. c. What is the expression for the capacitor current?
Physics
1 answer:
olga2289 [7]3 years ago
5 0

The first part of the question is not complete and it is;

The voltage across the terminals of a 250 nF capacitor is 50 V, A1e^(-4000t) + (A2)te^(-4000t) V, t0, What is the initial energy stored in the capacitor? Express your answer to three significant figures and include the appropriate units. t

Answer:

A) initial energy = 0.3125 mJ

B) A1 = 50 and A2 = 1,800,000

C) Capacitor Current is given by the expression;

I = e^(-4000t)[0.95 - 1800t]

Explanation:

A) In capacitors, Energy stored is given as;

U = (1/2)Cv²

Where C is capacitance and v is voltage.

So initial kinetic energy;

U(0) = (1/2)C(vo)²

From the question, C = 250 nF and v = 50V

So, U(0) = (1/2)(250 x 10^(-9))(50²) = 0.3125 x 10^(-3)J = 0.3125 mJ

B) from the question, we know that;

A1e^(-4000t) + (A2)te^(-4000t)

So, v(0) = A1e^(0) + A2(0)e^(0)

v(0) = 50

Thus;

50 = A1

Now for A2; let's differentiate the equation A1e^(-4000t) + (A2)te^(-4000t) ;

And so;

dv/dt = -4000A1e^(-4000t) + A2[e^(-4000t) - 4000e^(-4000t)

Simplifying this, we obtain;

dv/dt = e^(-4000t)[-4000A1 + A2 - 4000A2]

Current (I) = C(dv/dt)

I = (250 x 10^(-9))e^(-4000t)[-4000A1 + A2 - 4000tA2]

Thus, Initial current (Io) is;

Io = (250 x 10^(-9))[e^(0)[-4000A1 + A2]]

We know that Io = 400mA from the question or 0.4 A

Thus;

0.4 = (250 x 10^(-9))[-4000A1 + A2]

0.4 = 0.001A1 - (250 x 10^(-9)A2)

Substituting the value of A1 = 50V;

0.4 = 0.001(50) - (250 x 10^(-9)A2)

0.4 = 0.05 - (250 x 10^(-9)A2)

Thus, making A2 the subject, we obtain;

(0.4 + 0.05)/(250 x 10^(-9))= A2

A2 = 1,800,000

C) We have derived that ;

I = (250 x 10^(-9))e^(-4000t)[-4000A1 + A2 - 4000tA2]

So putting values of A1 = 50 and A2 = 1,800,000 we obtain;

I = (250 x 10^(-9))e^(-4000t)[(-4000 x 50) + 1,800,000 - 4000(1,800,000)t]

I = e^(-4000t)[0.05 + 0.45 - 1800t]

I = e^(-4000t)[0.95 - 1800t]

You might be interested in
The maximum pressure variations the human ear can withstand are about how much above and below atmospheric pressure?
Crank

The maximum pressure variations the human ear can withstand  above and below atmospheric pressure is around 30 pa. the normal atmospheric pressure is around 101325 pa. hence the variation in the maximum pressure for human ear is very small as compared to the atmospheric pressure. if the ear is exposed to a pressure greater than this , it can cause permanent damage to the ear.

4 0
3 years ago
As objects grow farther apart, what happens to the force of gravity between them?
Papessa [141]
It decreses Decreases
8 0
3 years ago
Evan drew a diagram to illustrate radiation
labwork [276]
The answer would be D, electromagnetic waves
8 0
3 years ago
Read 2 more answers
An angry physics student releases a wrecking ball as shown. The wrecking ball is just about to hit the building at the final tim
daser333 [38]

Answer:

the force between the building and the ball is non-conservative (friction-type force)

Explanation

Explanation:For this exercise the student must create an impulse to move the ball towards the building, in this part he performs positive work since the applied force and the displacement are in the same direction.

When the ball moves it has a kinetic energy and if its height increases or decreases its potential energy also changes, but the sum of being must be equal to the initial work.

When the ball arrives and collides with the building, non-conservative forces, of various kinds; rubbing, breaking, etc. It transforms this energy into a part of heat and another in mechanical energy that the building must absorb, let us destroy its wall

Consequently, the force between the building and the ball is non-conservative (friction-type force

6 0
3 years ago
A body weighs 63 N on the surface of the earth. What is the gravitational force on
myrzilka [38]

Answer:

Gravitational force mg' =(49)mg=49×63=28N.

Explanation:

What is the gravitational force on it due to the Earth , at a height equal to half the radius of the Earth ? (Given that the radius of Earth = 6400 km). Gravitational force mg ( This is not the real explanation)

3 0
2 years ago
Other questions:
  • Q: Which direction are the force vectors pointing for a bullet fired from a gun. Assume that the bullet is traveling to the righ
    9·2 answers
  • Are soaps salts true or false
    7·1 answer
  • What would happen if you held the South Pole of one magnet near the North Pole of another magnet of the same size?
    5·2 answers
  • Emmy is standing on a moving sidewalk that moves at +2 m/s. Suddenly, she realizes she might miss her flight, so begins to speed
    11·1 answer
  • A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 25.5 kg.
    5·1 answer
  • What the northernmost country in north america ​
    14·1 answer
  • This is the number of complete movements of a wave per second.
    14·1 answer
  • Need help ASAP please and thank you
    13·1 answer
  • Which of the following statements is true?
    10·1 answer
  • When you walk across the ground and push on it with your feet...
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!