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
forsale [732]
3 years ago
12

LC CIRCUIT: A 20.00-F capacitor is fully charged by a 100.00-V battery, then disconnected from the battery and connected in seri

es with a 0.280-mH inductor at t=0. Thus, the initial current 1-0. See circuit below after the charged capacitor is connected to the inductor. (a) What is the angular oscillation frequency o of the circuns (b) What is the maximum charge on the positive capacitor plate? (c) What is the energy stored in the capacitor at t - 0? (d) Using conservation of energy, find the current I when the charge reaches one-third the maximum charge. (e) Using conservation of energy, find the maximum current Imax 000000
Physics
1 answer:
klio [65]3 years ago
3 0

Answer:

(a) w=13.363\ rad/sec

(b) Q_m=2000\ coul

(c) E_{max}=100,000\ J

(d) I=25,197.63\ A

(e) I_{max}=26,726.12\ A

Explanation:

<u>LC Circuit</u>

The dynamics of an LC circuit is explained as the energy stored in the capacitor C in the form of an electrical field is transferred to the inductor L as a magnetic field. The energy stored in a capacitor is

\displaystyle E_c=\frac{CV^2}{2}

Where V is the potential between its plates where a charge Q is stored. The relation between them is

\displaystyle C=\frac{Q}{V}

The energy stored in an inductor of self-inductance L is

\displaystyle E_c=\frac{LI^2}{2}

Where I is the current flowing through the inductor. If we apply the principle of conservation of energy, the loss of electric energy in the capacitor will transform into magnetic energy in the inductor and vice-versa.

The angular frequency of oscillation of a LC circuit is

\displaystyle w=\sqrt{\frac{1}{LC}}

The question provides the following data

V_m=100\ V,\ C=20\ F,\ L=0.28\ mH=0.00028\ H

(a) The angular frequency is

\displaystyle w=\sqrt{\frac{1}{(0.00028)(20)}}

w=13.363\ rad/sec

(b) When the voltage is at maximum, the charge will also be maximum, its value can be computed solving for Q

\displaystyle C=\frac{Q_m}{V_m}

Q_m=V_mC=100(20)=2000

Q_m=2000\ coul

(c) At t=0, the voltage is at maximum, so the energy stored is

\displaystyle E_{max}=\frac{CV_m^2}{2}

\displaystyle E_{max}=\frac{20\ 100^2}{2}=100,000

E_{max}=100,000\ J

(d) If the charge reaches 1/3 of the initial value, it means 2/3 of the charge were transformed in magnetic energy. Let's call E_t to the transferred electric energy to magnetic energy, and E_1 to the remaining electric energy in the capacitor. Knowing Q_1=1/3Q_m

\displaystyle Q_1=\frac{2000}{3}=666.67\ coul

\displaystyle V_1=\frac{666.67}{20}=33.33\ V

\displaystyle E_1=\frac{(20)\ 33.33^2}{2}=11,111.11\ J

The energy transfered is

E_t=100,000-11,111.11=88,888.89\ J

We can compute the current solving for I in:

\displaystyle E_t=\frac{LI^2}{2}

\displaystyle I=\sqrt{\frac{2E_t}{L}}

Calculating I

\displaystyle I=\sqrt{\frac{2(88,888.89)}{0.00028}}

I=25,197.63\ A

(e) To find I_{max}, we'll assume all the electric energy is transformed to magnetic, so

\displaystyle I_{max}=\sqrt{\frac{2E_{max}}{L}}

\displaystyle I_{max}=\sqrt{\frac{2(100,000)}{0.00028}}

I_{max}=26,726.12\ A

You might be interested in
Which of these actions will increase friction? Select three options. Scratching a surface to make it rougher polishing a surface
k0ka [10]

Answer:

scratching a surface to make it rougher

increasing the size of a flying object

adding extra weight to an object

Explanation:

5 0
3 years ago
Read 2 more answers
If BHALA AHMAD KHAN applied the 20N force is applied on an object moving with the velocity 30 m/s. calculate the power in KW.
Leokris [45]

Answer:0.6kw

Explanation:

Power=force×velocity

Power=20×30=600w

In kw it's going to be 600/1000=0.6kw

4 0
3 years ago
A string is tied between two posts separated by 2.4 m. When the string is driven by an oscillator at frequency 567 Hz, 5 points
Alex787 [66]

Explanation:

The given data is as follows.

       Length (l) = 2.4 m

       Frequency (f) = 567 Hz

Formula to calculate the speed of a transverse wave is as follows.

                  f = \frac{5}{2l} \times v

Putting the gicven values into the above formula as follows.

                  f = \frac{5}{2l} \times v

                 567 Hz = \frac{5}{2 \times 2.4 m} \times v

                      v = 544.32 m/s

Thus, we can conclude that the speed (in m/s) of a transverse wave on this string is 544.32 m/s.

5 0
3 years ago
A charge of 5.67 x 10^-18 C is placed 3.5 x 10^-6 m away from another charge of -
Fudgin [204]
+ 1.58 e -15

Please hit thanks button! :)
5 0
2 years ago
A feather is dropped onto the surface of the moon. How far will the feather have fallen if it reaches the surface in 9.00 second
Natali5045456 [20]

The feather's vertical position y is determined by

y=\dfrac12g_{\text{moon}}t^2

We take the feather's starting position to be the origin, and the downward direction to be positive. Then

y=\dfrac12\left(1.63\,\dfrac{\mathrm m}{\mathrm s^2}\right)\left(9.00\,\mathrm s\right)^2=66.0\,\mathrm m

so the answer is D.

3 0
3 years ago
Other questions:
  • The more particles a substance has at a given temperature, the more thermal energy it has.
    7·1 answer
  • Your backpack has a mass of 8 kg. You lift it from the ground to a height of
    8·1 answer
  • What is the potential energy of the bowling ball as it sits on top of a building ?​
    6·1 answer
  • Air at 80 kPa and 127°C enters an adiabatic diffuser steadily at a rate of 6000 kg/h and leaves at 100 kPa. The velocity of the
    8·1 answer
  • There is a girl pushing on a large stone sphere. The sphere has a mass of 8200 kgand a radius of 90 cm and floats with nearly ze
    15·1 answer
  • What features make a question scientific, and why are some questions beyond the boundaries of scientific investigation?. .Cite a
    13·1 answer
  • Which statement is true with respect to an atom?
    5·2 answers
  • Solve this question with explanation <br> Best answer will be brainliest <br> 40 points given
    7·2 answers
  • As the bell rings, which energy transformation occurs? A. Mechanical energy is converted into sound energy. B. Chemical energy i
    15·2 answers
  • Two speakers in a stereo emit identical pure tones. As you move around in front of the speakers, you hear the sound alternating
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!