# Explaining Current Behavior in an LC Circuit

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• lukka98
In summary: I don't know what the expression is, but it is like a drop of energy that goes from the inductor to the capacitor.In summary, it seems like the inductor opposes "to the flow" at maximum initially, and then it allow the current to flow greater and greater but with slow increasing until its maximum, then the current cannot drop down instantly to zero so an emf rising and with decreasing current charge the capacitor but opposite in sign, and then the cycle continue.
lukka98
Without mathematical formulas, but only with a "Physical intuitive meaning", why if at t=0, I have a charged capacitor, and I connect it through a wire ,forming a closed path, to a inductor the current increasing with time and his derivative decreasing?

To me seems like the inductor oppose "to the flow" at maximum initially, and then it allow the current to flow greater and greater but with slow increasing until its maximum, then the current cannot drop down instantly to zero so an emf rising and with decreasing current charge the capacitor but opposite in sign, and then the cycle continue.
I can say is just a conservation of energy between magnetic(L) and potential(C), but I cannot understand why the current has the behavior it has.

I said with no formulas because I have understand how to find all about LC with math, but I don't understand how happen physically.

thanks.

Delta2
lukka98 said:
I said with no formulas because I have understand how to find all about LC with math, but I don't understand how happen physically.
Can you show us the two differential equations relating voltage and current for inductors and capacitors? If you really do understand those two equations and how they govern the trading back-and-forth of the energy storage in a lossless parallel LC "tank" circuit, then you should have a good intuition for the physical situation.

It's similar to the Simple Harmonic Motion (SHM) of a mass hanging on a spring. When you stretch the mass/spring out a bit and let it go, what happens?

DaveE and vanhees71
berkeman said:
Can you show us the two differential equations relating voltage and current for inductors and capacitors? If you really do understand those two equations and how they govern the trading back-and-forth of the energy storage in a lossless parallel LC "tank" circuit, then you should have a good intuition for the physical situation.

It's similar to the Simple Harmonic Motion (SHM) of a mass hanging on a spring. When you stretch the mass/spring out a bit and let it go, what happens?
I solve it using Laplace transformation, and "analyzing" the T(s), so at the end I have:
##V_c (t) = \frac{Q}{C} *cos(\omega_0 t)## so the graph is a cos with angular frequency ##\omega_0## of (1/LC)^(1/2).
V_c(t) = V_L(t), and ##\frac{dI}{dt} = \frac{Q}{LC}## with Q the initial charge of capacitor.
Current is the first derivative of V_c(t), so I can see how the derivative behave, and current increasing and voltage too.

But initially current is at 0, derivative is max, and voltage is max.
And I cannot understand why the variation of current is max at initial time, the math say me that but I don't understand...
I can say because the voltage is max, so = L*I', so derivative should be max but.

lukka98 said:
I solve it using Laplace transformation

Hmm, I prefer to just use the simple form of the two differential equations to build intuition about how the LC tank works:
$$v(t) = L\frac{di(t)}{dt}$$
$$i(t) = C\frac{dv(t)}{dt}$$
The energy in the tank circulates back and forth between the current stored in the inductor and the voltage across the capacitor. When one is max, the other is zero. The phase difference between ##v(t)## and ##i(t)## is 90 degrees, due to the interrelationship of the two differential equations.

https://www.electrical4u.com/lc-circuit-analysis/

lukka98 said:
And I cannot understand why the variation of current is max at initial time, the math say me that but I don't understand
Look again at one of those equations:
$$V_C = V_L = L \frac{dI}{dt}$$
The rate of inductor current change is proportional to the capacitor voltage. At ##t=0## the capacitor voltage is at it's maximum value, so is the rate of change of the inductor current. Then the inductor current flowing through the capacitor causes its voltage to decease (the other equation).

That is just how inductors work, you can't instantly create the magnetic field that results from current flowing, you have to "charge" it up. In the same way that you can't instantly change the voltage of a capacitor.

lukka98
berkeman said:
Hmm, I prefer to just use the simple form of the two differential equations to build intuition about how the LC tank works:
$$v(t) = L\frac{di(t)}{dt}$$
$$i(t) = C\frac{dv(t)}{dt}$$
The energy in the tank circulates back and forth between the current stored in the inductor and the voltage across the capacitor. When one is max, the other is zero. The phase difference between ##v(t)## and ##i(t)## is 90 degrees, due to the interrelationship of the two differential equations.

View attachment 292016
https://www.electrical4u.com/lc-circuit-analysis/
Ok, what disturbed me is that the voltage across capacitor is equal at every time to the e.m.f. generated by inductor... or i believe so.
I see like there are two generator equal in magnitude but opposite in direction, or the voltage across the inductor is like a "drop" of potential?

You have to be careful with the signs. Just use Faraday's Law in integral form with the integration path along the circuit.

At the end you should get
$$\ddot{I}=-\frac{1}{LC} I \; \Rightarrow \; I(t)=I_0 \cos(\omega t -\varphi_0),$$
where ##I_0## and ##\varphi_0## are to be determined by the initial conditions and ##\omega=1/\sqrt{LC}##.

## 1. What is an LC circuit?

An LC circuit is a type of electronic circuit that consists of an inductor (L) and a capacitor (C) connected in series or parallel. It is used to store and release energy in the form of electrical oscillations.

## 2. How does an LC circuit work?

When an LC circuit is connected to a power source, the capacitor stores energy in the form of an electric field and the inductor stores energy in the form of a magnetic field. The energy is constantly exchanged between the two components, causing the circuit to oscillate at its resonant frequency.

## 3. What is resonance in an LC circuit?

Resonance in an LC circuit occurs when the frequency of the alternating current matches the natural frequency of the circuit. This causes the circuit to vibrate at maximum amplitude, resulting in a large amount of energy being stored and released.

## 4. How does an LC circuit explain current behavior?

The current behavior in an LC circuit is determined by the properties of the inductor and capacitor, as well as the frequency of the power source. When the circuit is in resonance, the current will be at its maximum and the voltage across the components will be in phase.

## 5. What are some real-world applications of LC circuits?

LC circuits are commonly used in electronic devices such as radios, televisions, and computers. They are also used in wireless communication systems, electric power transmission, and medical equipment. Additionally, LC circuits are used in research and development for testing and measuring the properties of materials and electronic components.

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