Inductors i think it'll make an harmonic type of move

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SUMMARY

This discussion focuses on the behavior of inductors in an LC circuit, specifically during the discharge of a fully charged capacitor. The governing equation derived from Kirchhoff's voltage law is q'' + (1/LC)q = 0, leading to the solution q(t) = Q*cos(ωt), where ω = (1/LC)^(1/2). This demonstrates the oscillatory behavior of charge in the circuit, highlighting that while inductors can produce harmonic motion, their primary function is to store energy in a magnetic field and control current flow in electronic circuits.

PREREQUISITES
  • Understanding of LC circuits and their components
  • Familiarity with Kirchhoff's voltage law
  • Knowledge of differential equations in electrical engineering
  • Basic concepts of energy storage in inductors
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  • Study the mathematical derivation of LC circuit behavior
  • Learn about the applications of inductors in filtering and signal processing
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Electrical engineers, students studying circuit theory, and anyone interested in the principles of inductors and their applications in electronic circuits.

ismael18
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as far as i know about inductors i think it'll make an harmonic type of move...
but it seems to make no sense
can anyone help?
 
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Since you weren't very explicit as to what kind of circuit you are talking about, let's keep it simple: An LC circuit with a fully charged capacitor at t=0.

Now let the capacitor discharge through the inductor. What happens?

The voltage drop across the capacitor is EC=-q/C, and that across the inductor is EL=-L(di/dt)=-L(d2i/dt2). I will let q" (q-double-prime) denote the second time derivative of q from now on.

Kirchhoff's voltage law says that the sum of the voltages around a closed loop in a circuit must be zero. This is just the conservation of energy in disguse. So, we have:

EI+EC=0

or

q"+(1/LC)q=0

The solution to this equation, with q(0)=Q and i(0)=q'(0)=0, is

q(t)=Q*cos(ωt),

where ω=(1/LC)1/2.

As you can see, the oscillatory behavior of q(t) is due to the combined influences of the element laws and the conservation of energy.
 


Inductors are passive electronic components that store energy in the form of a magnetic field. They are commonly used in electronic circuits to control the flow of current and to filter out unwanted signals.

While it is true that inductors can produce a harmonic motion, this is not their primary function. The harmonic motion is a result of the inductor's ability to store energy and release it in a controlled manner.

If you are having trouble understanding inductors and their role in electronic circuits, it is best to seek help from a knowledgeable source such as a teacher or a professional in the field. They can provide you with a better understanding of inductors and how they work in specific applications.
 

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