What is Lc circuit: Definition and 104 Discussions

An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency.
LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal; this function is called a bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners and frequency mixers.
An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance. Any practical implementation of an LC circuit will always include loss resulting from small but non-zero resistance within the components and connecting wires. The purpose of an LC circuit is usually to oscillate with minimal damping, so the resistance is made as low as possible. While no practical circuit is without losses, it is nonetheless instructive to study this ideal form of the circuit to gain understanding and physical intuition. For a circuit model incorporating resistance, see RLC circuit.

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  1. Z

    Self-inductance of LC circuit given rate of capacitor discharge.

    We seem to have the following circuit and the differential equation ##\ddot{q}+\omega^2q=0## where ##\omega=\frac{1}{\sqrt{LC}}##. The solution is $$q(t)=A\cos{(\omega t+\phi)}$$ Since ##I(t)=-\dot{q}(t)## we have $$I(t)=-\dot{q}(t)=A\omega\sin{(\omega t+\phi)}$$ At ##t=0## we have...
  2. M

    B Why do capacitors not discharge everything immediately in LC circuits?

    I just started taking LC circuits, and I was wondering, when capacitors charge without a resistance, they charge immediately, so when they discharge in an LC circuit, why don't they "send" all of their charge immediately? Is it because that's how capacitors work in general, or is it because of...
  3. dragonshadowbob

    Determining Inductance L in an LC Circuit

    Here is the circuit I'm working with. So, I was able to get the correct equation by using the Equation Omega=I max/Q max = 1/sqrt(LC). I calculated Qmax by multiplying 150V * .5microfarad, and Imax by doing the 40V/150Ohms. Then, I just solved for L and got the correct answer. My question is...
  4. Kyuubi

    Current on Infinite Periodic LC Circuit

    I wrote down the equation of motion for In(t) and I'm trying to match it with infinite spring mass system equation solution. In the spring mass system, we consider A to be the equilibrium length of the springs, and we can thus write Xn(t) = X(nA,t) and put it back into the equation of motion...
  5. sol47739

    Am vs Fm variable capacitor receiver, what is the difference?

    What is the difference between a variable capacitor in a AM receiver and a variable capacitor in a FM receiver? I understand that Am is amplitude modulation and that the signal is carried over a changing amplitude and that the frequency is constant. And the opposite in FM signals. And a variable...
  6. ermia

    Solving LC circuit with energy conservation

    krotovs solution is based on energy conservation. My question is that why the solution didn't consider inductors energy? the question: The solution:
  7. L

    I Explaining Current Behavior in an LC Circuit

    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...
  8. A

    Inductor Efficiency via LC Oscillator

    I want to create an LC circuit with varying inductors and compare those inductors for efficiency. Would it be accurate to suggest measuring the area under the curve of the first cycle of the resonant frequency would determine which of the inductors are most efficient? If the area is greater...
  9. LCSphysicist

    Signs of the voltage drops in this LC Circuit

    I have been studying electronical circuit. In general, it is not difficult and is more about to solve EDO. The main problem is, really, the signs. See as follows: $$V_{L} = L dI/dt, V_{c} = +- Q/C$$ ? Should i put a minus sign there? Or shout i maintain the signs? When do i know what sign to...
  10. LarryS

    EM Waves Generated by an LC Circuit?

    I am not an electrical or electronic engineer. I am trying to understand how a simple, series LC circuit running at it's resonant frequency can generate EM waves. I believe, based on what I have read, that the frequency of the generated EM waves will be the resonant frequency of the circuit...
  11. Andrei0408

    Equation Demonstration -- Comparing a pendulum's motion to an LC circuit

    I've just learned about simple harmonic motion and I've been given the following examples: The physical pendulum (for small oscillations sin(theta)~theta), with the formula (1st pic), and the LC circuit, with the formula (2nd pic). If possible, I need the demonstration for these 2 formulas...
  12. J

    In an LC circuit the current does no drop to 0

    in an LC circuit the current does no drop to 0 but varies sinusoidally. The capacitor is recharged with a different polarization. Why is this so?
  13. L

    Basics of RF coil development for MRI

    Hi all, I'm trying to understand basics of radiofrequency (RF) coil development for magnetic resonance imaging (MRI). For example, the problem is to develop simple surface single-loop RF coil tuned to 100 MHz. In program Coil32, I set the following parameters: diameter of the loop D = 20 mm...
  14. Zack K

    How exactly do inductors work in an LC circuit?

    I understand Faraday's law and about induced electric fields created by a changing magnetic fields, etc. But what causes the current to oscillate in an LC circuit, with no battery? If you picture that there is current going into an inductor, and that current is decreasing over time, then you...
  15. sneakycooky

    Find the charge q(t) for an LC circuit

    Homework Statement An LC circuit consists of an 82 mH inductor and a 17 microfarad capacitor that initially carries a 180 microC charge. The switch is open for t < 0 and is then closed at t = 0. a. Find the frequency of the resulting oscillations. b. At t = 1 ms, find the charge on the...
  16. Nikhil Rajagopalan

    Charging and Discharging of a capacitor in an LC circuit

    In an LC circuit, the capacitor that is initially charged to a finite value starts to discharge cross the inductor, initially the current increases and the inductor opposes it, but as the current is supplied against the back emf, due to the discharging of the capacitor, won't it reduce the value...
  17. S

    Engineering Solve LC Circuit Problem: Examples & Resources

    Homework Statement An image of the problem is attached. I have to find 2 currents in an LC circuit. Homework Equations V = L(di/dt) The Attempt at a Solution [/B] I have no clue how to do this type of problem. Are there any examples problems similar to this online? Or can someone give me...
  18. E

    Dispersion equation for an LC Circuit

    Need the dispersion equation for chain consisting of cell units ( LC unit scheme in attachments). I know I need to make complex Kirchhoff equations and after get the dispersion equation but absolutely don't know how to do it. All examples that I find in web very poor including books, articles...
  19. E

    Pulsating DC supply to LC circuit

    I have a very basic question for the professionals here, but I am having a small issue with my parallel LC circuit. I have an inductor that is 6.425mH, a capacitor that is 217uF (it is two 470uF aluminum electrolytic caps connected in series to make one non-polar 217uF cap). I am supplying the...
  20. R

    What is the maximum value of the current through the inductor?

    1. Homework Statement : Two identical uncharged capacitors A and B each of capacitance C and an inductor L are arranged as shown in the adjacent figure. At t=0, the switch S1 is closed while switch S2 remains open.At time t=to=√(LC)Π/2, switch S2 is closed and S1 is opened. After switch S2 is...
  21. E

    How to know when an LC circuit hits resonance

    I have been having issues with a series LC circuit. I have a supply voltage of 6.96 volts, across the inductor is 7.04 volts and the capacitor voltage is 7.17 volts. The capacitor has a capacitance of 45uFarad and a supply frequency of 250 hertz. I don't know what the inductance is of the...
  22. Paul Colby

    Voltage Monitor for an LC circuit

    Hi, I have an air wound 0.736 mH coil in series with a 3.5pF capacitor being driven with a function generator. Ideally the series resonant frequency should be around 3.13 MHz. The internal impedance of the function generator is 50 ohms or so. At resonance the voltage across the cap should be...
  23. yuvalidan

    What is the Hamiltonian for an LC circuit?

    Homework Statement Hi i got a problem in lc circuit, I need to find the hamiltonian to this circuit , I think that I did well but I am not sure, the problem and my attempt in the following file. Homework EquationsThe Attempt at a Solution
  24. Vanessa Avila

    (LC Circuit) Finding cap charge after connecting to inductor

    Homework Statement A capacitor with a capacitance of C = 5.95×10−5 F is charged by connecting it to a 12.0 −V battery. The capacitor is then disconnected from the battery and connected across an inductor with an inductance of L = 1.50 H . What is the charge on the capacitor after a time...
  25. clamatoman

    Solving for Imax and Energy in an LC Circuit: Homework Help

    Homework Statement 4700uF Capacitor is initially charged to 9.0V, then the voltage source is removed and the capacitor is connected across a 1.50H inductor. Solve for: Energy of the Circuit, Imax, and Time after Circuit connected whed Energy of the capacitor =Energy of the inductor Homework...
  26. A

    LC circuit current of inductor

    Homework Statement In the figure given, find i(t) for the inductor My problem is though when we found i(t) with a source we find the transient response and the steady state response... I know how to do the transient response of an RLC circuit not an LC one... do i just consider R to be 0...
  27. O

    Engineering What is the time constant in an LC circuit.

    Homework Statement I wrote an exam today and a question worth quite a bit of points asked Determine the value of a capacitor in a series circuit that will give a time constant of 4.0 ms and is isn series with an inductance of 3mH Homework EquationsThe Attempt at a Solution I do not believe...
  28. R

    LC circuit -- Calculate the work done

    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 ##W## are sustained. The capacitor plates were slowly drawn apart to increase...
  29. A

    LC Circuit Problem Homework: Calculate Values of L & R

    Homework Statement When the current in the portion of the circuit shown in the figure below is 4.00 A and increases at a rate of 0.500 A/s, the measured voltage is ∆ = 15.0 V. When the current is 4.00 A and decreases at the rate of 0.500 A/s, the measured voltage is ∆ = 10.0 V. Calculate the...
  30. Luek

    Energy stored in a LC circuit

    Homework Statement Energy in the circuit remains constant. When the current is flowing, the energy stored is all stored in the inductor. When the current stops flowing, it is because all the energy is stored in the capacitor. Find the fraction of energy stored in the inductor when half of the...
  31. S

    Can a Center Tapped LC Circuit Reduce Potential Difference Across the Inductor?

    My objective is to make a lc circuit that will have a potential difference across the inductor that is lower than that of the capacitor. A spark gap must also be used. Will this work and will the resonant frequency be the same as if it was wired conventionally?
  32. DoobleD

    Solving a parallel LC circuit with DC current

    Take the following circuit (capacitor initially not charged) : I am trying to solve for the current everywhere as a function of time. I set up the following equations (are they right ?) : Then, any way I try it, I end up with some messy integrals. Even using wolfram alpha to get those...
  33. R

    Engineering LC circuit (Differential Equation)

    Homework Statement An inductor with value L and a capacitor with value C are connected in series to a power source. At time t, the voltage of the power source (i.e. the voltage across both the inductor and capacitor) is given by ## v(t)=Asin(\frac{2t}{\sqrt{LC}}) ##. If the voltage across the...
  34. Dorian Black

    Limitations of LC Circuit Charging with Constant EMF

    Hi, A capacitor has both its terminals connected together using a wire in a rather lengthy circular fashion, hence acting as a significant inductance. If the area encircled by this 'circuit' is subjected to a linearly rising magnetic field (B=k x t) where k is a constant, the emf induced -due...
  35. PratyashAstro

    Derivation of self inductance formula in an LC circuit

    My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor : L = 1/(4π^2 . f^2 . C) Here, f = different resonant frequencies, C = capacitance of the capacitor in the LC...
  36. F

    LC circuit in external static magnetic field

    Homework Statement What effect would placing an LC circuit in a steady magnetic field have have on its resonant frequency? The inductor contains a paramagnet. This is asked about at very low temperature. Homework EquationsThe Attempt at a Solution Apart from initial changes due to Lenz's Law...
  37. I

    Series lc circuit and clamp-on ammeter

    In a series LC resonant circuit the capacitor acts to cancel out the inductance of the the circuit. With no inductance in the circuit the magnetic field will collapse. So my question is, with this collapse of the magnetic field will it be be harder to measure the current in the circuit with a...
  38. Rugile

    Average power in series LC circuit

    Homework Statement A voltage source is connected to a series LC circuit. The frequency of the source is resonant. The voltage amplitude of capacitor is 1V. Find the average power in the circuit. Homework EquationsThe Attempt at a Solution I realize that if there is no active resistance the...
  39. K

    What happens when a battery is connected to an ideal LC circuit?

    Hi All , I was thinking about the time domain unit step response of ideal series LC crcuit. If both cap and inductor are ideal and unchrged initially and I am looking at voltage across capacitor. Connecting a battery to LC circuit at t=t1 , would the circuit oscillate ? I am not able to...
  40. Y

    Understanding Kirchhoff's Law in LC Circuits: Exploring the Confusion

    I am confused with explanation about Kirchhoff's law in LC circuit. Please refer to the file I attached for the LC circuit. First, the switch was connected to the emf and the capacitor was charged to its full capacitance. Then the switch is connected to the capacitor, the capacitor will start to...
  41. nmbr28albert

    The Lagrangian Solution of an LC Circuit

    One way to solve the simple LC circuit with 1 inductor and 1 capacitor is to use the Lagrangian formulation of mechanics and consider charge q as the generalized coordinate. When writing down your Lagrangian, the energy of the inductor \frac{1}{2}L(\frac{dq}{dt})^2 is treated as the kinetic...
  42. A

    Solve Freq of Coupled LC Circuit with Inductor

    Homework Statement I have to find the normal frequencies of a coupled LC circuit. However, this LC circuit is coupled by an inductor, not a capacitor. __|C|________|C|__ |...|...| ^I(1)...|...^I(2) |...|...| {L}...{L'}...{L} |...|...| |...|...| -------------------- I'm sorry, I didn't have a...
  43. dwn

    How Do You Calculate Charge and Current Change Rate in LC Circuits?

    I'm having a difficult time finding any information in regards to LC circuits. The total energy in an circuit is 5.0*10^-6 J. If C= 15 microfarads, what is the charge on the capacitor? the ans is 12 microC An circuit has an inductance of 15 mH and a capacitance of 10 µF. At one...
  44. amjad-sh

    Electomagnetic oscillation in lc circuit

    Hi, We know that when we connect a charged capacitor to a coil, the capacitor will discharge in the coil that means that the current will flow in the circuit in decreasing manner with respect to time .So an emf will be created in a way that oppose the decrease. Bin will has the same...
  45. Crazymechanic

    Lc Circuit Question: Understanding Oscillations and Polarity Changes

    So I have a question about the circuit. Now we know that when the C is discharging there is a current through the inductor , now there can be these oscillations because the inductor time delays the current (because of back emf) that wants to run to the other side of the capacitor as it would...
  46. R

    Engineering Proving the Form of a Homogenous LC Circuit?

    Homework Statement I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic...
  47. skate_nerd

    LC circuit, space between dielectric plates

    Homework Statement If the max E-field in the capacitor is E=1.2(103) N/C and the space between the plates is filled with a dielectric of constant 100,000, what is the separation between the plates? Homework Equations I know C=kεoA/d where k is the dielectric constant, A is the area of...
  48. P

    AP Physics E&M MC: Electric Field, Induction, LC Circuit

    Homework Statement Answer is B. Answer is E. Answer is E. Homework Equations E=F/q E=V/d Right hand rule for inductors The Attempt at a Solution Quite confused for these problems. For number 18, I'm quite baffled as to where the 0.04 meters even comes from. What I had...
  49. R

    Finding resistance in an LC Circuit (FM Radio)

    Homework Statement The figure shows a simple FM antenna circuit in which L = 8.22 µH and C is variable (the capacitor can be tuned to receive a specific station). The radio signal from your favorite FM station produces a sinusoidal time-varying emf with an amplitude of 12.2 µV and a frequency...