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
A bicyclist covers the first leg of a journey that is d1meters in t1seconds at a speed of v1m/s and the second leg of d2meters i
Murljashka [212]

According to motion in straight line  t1≠t2


A biker travels d1 meters in t1 seconds at v1 m/s for the first leg and d2 meters in t2 seconds at v2 m/s for the second leg. It's possible that t1t2 if his average speed is equal to the average of v1 and v2.
An object is said to be in motion if its position in relation to its surroundings changes over time. It is a shift in an object's position over time. The only type of motion that exists is motion in a straight line.


A reference system is constantly used to describe a particle's motion. An arbitrary origin point is used to create a reference system, and a coordinate system is imagined to be connected to it. The reference system for a specific problem is the coordinate system that has been selected for it. For the majority of the problems, we typically select an earth-based coordinate system as the reference system.


To learn more about Motion in straight lines please visit -brainly.com/question/17675825
#SPJ1

4 0
2 years ago
A cylindrical metal specimen having an original diameter of 11.77 mm and gauge length of 46.1 mm is pulled in tension until frac
Marta_Voda [28]

Answer:

% reduction in area = 54.26 %

percentage elongation = 43.16 %

Explanation:

a) percentage reduction in area = \frac{(A_1 - A_2)}{A_1 } * 100

A_1  =\pi r^2 = \pi * 5.88^2=108.8 mm2

A_2=\pi * 3.98^2= 49.97 mm2

% reduction in area =\frac{(108.8 - 49.97)}{108.8} * 100 = 54.26 %

b)percentage elongation = \frac{(66 - 46.1)}{46.1} *100 = 43.16 %

5 0
3 years ago
12.5 Round to the nearest hundredth.
7nadin3 [17]
I think its 13...........
7 0
2 years ago
An airplane accelerates down a runway at 3 m/s2 for 32 s until is finally lifts off the ground. Determine the distance traveled
Alex Ar [27]

Answer:

12 or 24

Explanation:

i think it is i hope it is right

4 0
2 years ago
If the potential difference across the bulb in a camping lantern is 9.0 V, what is the
Gre4nikov [31]

Answer:

9V

Explanation:

The potential difference across the terminal as the same and thats because we are assuming that the source has no internal resistance.

Internal resistance are usually little resistances in the supply.

4 0
2 years ago
Other questions:
  • You used three methods of analysis to find the acceleration of the cart on the track: a two-point difference from v(t), an avera
    7·2 answers
  • A light train made up of two cars is traveling at 100 km/h when the brakes are applied to both cars. Knowing that car A has a ma
    10·1 answer
  • Four engineers propose designs for door locks that are triggered by a sample of
    13·1 answer
  • Consider a linear harmonic oscillator and let, yo and y, be its real, normalized ground and first
    11·1 answer
  • A slinky is traveling down the stairs, like in the video clip below. What is the total KINETIC ENERGY of the slinky at the botto
    15·1 answer
  • A truck covers 40.0 m in 7.80 s while uniformly slowing down to a final velocity of 1.70 m/s. Please provide with explanation an
    6·1 answer
  • Are you going to finish that CROISSANT?
    7·2 answers
  • Please help im down bad
    8·1 answer
  • Which of the following is not a longitudinal
    8·2 answers
  • SOMEONE PLEASE HELP MEEEEEEE
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!