Can a capacitor discharge itself through an ideal inductor?

In summary, the energy transferred from a capacitor to an ideal inductor will be equal to the energy stored in the inductor. This means that the capacitor will not discharge itself through the inductor unless the inductor is also discharged. However, the current in the inductor will be non-zero which indicates that the charge on the capacitor will behave differently.
  • #1
mkbh_10
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0
Can a capacitor discharge itself through an ideal inductor ? If yes state the reason , if No how will the charge on the capacitor will behave ?
 
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  • #2
That sounds like homework - what do you think the answer is?
 
  • #3
So the capacitor equation is:

[tex]C \frac{du(t)}{dt} = i(t)[/tex]

where u - voltage, i - current, C capacitance

And for inductor:

[tex]L \frac{di(t)}{dt} = u(t)[/tex]

L - inductance

The energy transferred from capacitor to the circuit is given by:

[tex]W_C = - \int_{t_1}^{t_2} u(t)i(t)dt = C \int_{t_2}^{t_1} u(t)du = \left.\frac{1}{2} C u^2(t)\right|^{t_1}_{t_2} = \frac{1}{2} Cu^2(t_1) - \frac{1}{2} Cu^2(t_2)[/tex]

The energy transferred to inductor is given by (similarly):

[tex]W_L = \frac{1}{2} Li^2(t_2) - \frac{1}{2} Li^2(t_1)[/tex]

Obviously the energy transferred from capacitor is accumulated in inductor so:

[tex] W_C = W_L [/tex]

If we assume that inductor is discharged in the instant [tex]t_1[/tex] then [tex]i(t_1) = 0[/tex], and capacitor is charged to the volgate [tex]v(t_1) = V[/tex]. Assume that the capacitor is discharged in in [tex]t_2[/tex] instant. From the energy ballance we get the current:

[tex]i(t_2) = \sqrt{\frac{C}{L}} V[/tex]

Which is obviously different than 0. From this observation you get the answer to your question.
 

1. What is the purpose of a capacitor and an inductor?

A capacitor and an inductor are electronic components used to store and release energy. A capacitor stores energy in an electric field, while an inductor stores energy in a magnetic field. They are commonly used in electronic circuits to control current and voltage levels.

2. How do capacitors and inductors differ from each other?

Capacitors and inductors have different properties and functions. A capacitor is used to store and release electrical energy, while an inductor is used to store and release magnetic energy. They also have different reactions to changes in current and voltage. Capacitors resist changes in voltage, while inductors resist changes in current.

3. What are the units of measurement for capacitors and inductors?

The unit of measurement for a capacitor is farad (F), named after the scientist Michael Faraday. The unit of measurement for an inductor is henry (H), named after the scientist Joseph Henry. These units indicate the amount of energy each component can store.

4. How are capacitors and inductors used in electronic circuits?

Capacitors and inductors are used in electronic circuits to filter and regulate current and voltage levels. They can also be used to store energy and provide temporary power supply during power outages. In addition, they are commonly used in timing circuits and oscillators.

5. What are the advantages of using capacitors and inductors in electronic circuits?

Capacitors and inductors offer several advantages in electronic circuits. They are small in size, lightweight, and can store large amounts of energy. They also have low resistance, which allows for efficient energy transfer. In addition, they can be easily integrated into electronic circuits, making them versatile and widely used in various applications.

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