Oscillations in an LC circuit (Question from Irodov)

In summary, this student is trying to solve for the Qmax for a LC oscillation, and they made an assumption about the current. After discussing it with their friends, they were able to figure out the answer.
  • #1
Anubhav
5
1
Homework Statement
1. The problem statement, all variables and given/known data
In an oscillating circuit consisting of of a parallel-plate capacitor and an inductance coil with negligible active resistance the oscillations with energy are sustained. The capacitor plates were slowly drawn apart to increase the scillation frequency -fold. What work was done in the process?
Relevant Equations
Variables have meaning as usual
€=permitivity of vaccum
Energy in LC oscillations =W
Energy of charged capacitor=(Q^2)/2C
Force between plates of parallel plate capacitor=(Q^2)/2€A
https://www.physicsforums.com/attachments/282131
16195584671893895411783627819363.jpg
 
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  • #4
1619559658292.png


For those who want to read it without breaking their neck ...

I can also decipher another relevant equation (## \ \omega = \displaystyle {1\over\sqrt{LC}}\ ##)
So inceasing ##\omega## n times means changing ##\ d \rightarrow n^2d\ ##.
Unclear to me what is conserved -- is ##\ q\ ## the same as ##\ Q_{\text{max}}\ ## ? and is that invariant ?
Then where does the mechanical work energy go ?

##\ ##
 
  • #5
I'm sorry for inconvenience ..I shall delete this thread and reframe the entire Q properly again
 
  • #6
Pinging @DaveE

Congratulations with the badge ! I'm sure there is no broom, and I'm certain they don't have cookies either (my clumsy way to distinguish you from @davenn)​
@Anubhav shouldn't apologize too much. Plenty effort demonstrated. I'm just filing away at his (her?) assumptions to test them. Can you handle this one in a more didactically responsible way :smile: ?

I ask myself: Would there be much difference between this case of changing ##d## and the DC case ?

##\ ##
 
  • #7
BvU said:
Pinging @DaveE

Congratulations with the badge ! I'm sure there is no broom, and I'm certain they don't have cookies either (my clumsy way to distinguish you from @davenn)​
@Anubhav shouldn't apologize too much. Plenty effort demonstrated. I'm just filing away at his (her?) assumptions to test them. Can you handle this one in a more didactically responsible way :smile: ?

I ask myself: Would there be much difference between this case of changing ##d## and the DC case ?

##\ ##
Hello sir..Thanks for your I read your reply and gave it a thought again...
Also I have posted a typed image of Question as certain elements were missing in Q which I wrote
I am happy to inform you that after discussion with my friends I was able to solve it and got the right answer.
Actually I had assumed the Total energy of LC oscillations to be constant. Obviously that was wrong.
In my another attempt I wrote Change in energy of LC oscillations [i.e change in Qmax^2/(2C)] as function of integration of F(x).dx (where x is distance between plates)
Differentiation of this leads to a differential equation solving which gives Qmax as function of x..
Then change in energy of LC oscillations gives Total work done.
Ans comes out to be W(n-1)
Screenshot_20210428-183828~2.png
 
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Likes BvU
  • #8
Assumption: current does not change. (No dissipation, is like amperian currents in a permanent magnet).
So:
## V_C \rightarrow nV_C ##
## V^2_C \rightarrow n^2V^2_C ##
## C \rightarrow C/n^2 ##
So ## 1/2 ~CV_C^2 ## is unchanged; inductance energy is unchanged; circuit energy is unchanged; work = 0.

Probably wrong somewhere.Probably assumption of no current change.
 
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Related to Oscillations in an LC circuit (Question from Irodov)

1. What is an LC circuit?

An LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected together. These two components are usually arranged in a closed loop, with the inductor and capacitor connected in parallel or in series. LC circuits are commonly used in electronic devices for generating and controlling oscillations.

2. What is the significance of oscillations in an LC circuit?

Oscillations in an LC circuit are important because they allow the circuit to store and release energy in a periodic manner. This can be useful for various applications, such as in radio and television broadcasting, where the oscillations are used to transmit signals.

3. How do oscillations occur in an LC circuit?

Oscillations in an LC circuit occur when the capacitor and inductor exchange energy back and forth. Initially, when the circuit is turned on, the capacitor is charged and the inductor has no current. As the capacitor discharges, it creates a magnetic field in the inductor, causing the current to increase. This current then charges the capacitor in the opposite direction, and the cycle repeats, resulting in oscillations.

4. What factors affect the frequency of oscillations in an LC circuit?

The frequency of oscillations in an LC circuit is affected by the values of the inductance (L) and capacitance (C) components. The frequency can be calculated using the formula f = 1/(2π√(LC)), where f is the frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads. Additionally, the initial charge on the capacitor and any external resistances can also affect the frequency.

5. How can the oscillations in an LC circuit be damped?

Oscillations in an LC circuit can be damped by introducing a resistance (R) into the circuit. This resistance dissipates energy from the circuit, causing the oscillations to decrease in amplitude over time. The rate of damping can be controlled by adjusting the value of the resistance component.

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