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.
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...