# What is Lcr circuit: Definition and 22 Discussions

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components of this circuit, where the sequence of the components may vary from RLC.
The circuit forms a harmonic oscillator for current, and resonates in a similar way as an LC circuit. Introducing the resistor increases the decay of these oscillations, which is also known as damping. The resistor also reduces the peak resonant frequency. In ordinary conditions, some resistance is unavoidable even if a resistor is not specifically included as a component; an ideal, pure LC circuit exists only in the domain of superconductivity, a physical effect demonstrated to this point only at temperatures far below and/or pressures far above what are found naturally anywhere on the Earth's surface.
RLC circuits have many applications as oscillator circuits. Radio receivers and television sets use them for tuning to select a narrow frequency range from ambient radio waves. In this role, the circuit is often referred to as a tuned circuit. An RLC circuit can be used as a band-pass filter, band-stop filter, low-pass filter or high-pass filter. The tuning application, for instance, is an example of band-pass filtering. The RLC filter is described as a second-order circuit, meaning that any voltage or current in the circuit can be described by a second-order differential equation in circuit analysis.
The three circuit elements, R, L and C, can be combined in a number of different topologies. All three elements in series or all three elements in parallel are the simplest in concept and the most straightforward to analyse. There are, however, other arrangements, some with practical importance in real circuits. One issue often encountered is the need to take into account inductor resistance. Inductors are typically constructed from coils of wire, the resistance of which is not usually desirable, but it often has a significant effect on the circuit.

View More On Wikipedia.org
1. ### B How can scalars like voltage, impedance, etc. be added like vectors?

So we learnt about the different types of circuits and their behaviour when connected to an alternating current source. (DC was treated as an AC with 0 frequency and/or infinte time period). For purely inductive and purely capacitive circuits we were shown the derivation and why things are the...
2. ### Voltage theory for an LCR circuit

Summary:: I say the answer is A because these are reactive components that take and give back energy from the circuit so no voltage drop across the 2- L & C. Please let me know yours thoughts- thanks Hello I am a newby to electronics taking a class. Please review my thinking on this problem. I...
3. ### What will the phasor diagram of this LCR circuit looks like?

I know the current of capacitor and inductor must be parallel but pointing in opposite direction due to the fact they are connected in parallel thus having same voltage (please see attached screenshots). The current of resistor will simply be the sum of these two vectors, but what about its...
4. ### But is it the same for AC circuits?

Homework Statement For a series LCR circuit,the voltage across the resistance,capacitance and inductance is 10V each.If the capacitance is short circuited,the voltage across the inductance will be (a)10V (b)10/√2V (c) 10/3v (d)20V Homework Equations Potential difference across...
5. ### Engineering LCR circuit, calculating R when frequency width is given

Homework Statement Homework EquationsThe Attempt at a Solution LCR circuit, calculating R when frequency width is given Applying Kirchoff Voltage Loop Law, ## V_A – V_B + V_B - V_C + V_C – V_A = 0 ## ...(2) ## V_A – V_B ## is potential drop across inductor. Since current is flowing...
6. ### LCR Circuit with Driving Force

Homework Statement a. express the equation of motion b derive impedance at the resonant frequency (ω=ωo) c derive impedance at very high frequencies (ω>>ωo and ω>>R/L) Homework Equations Vo=ψ+(R/L)ψ+(1/LC)ψ Z=(1/iω)K(ω) K=1/((s-mω2)+ibω) The Attempt at a Solution Part a was simple, that was...
7. P

### LCR series circuits and average power

Homework Statement One type of tuning circuit used in radio receivers is a series LCR circuit. You like listening to a station1 that transmits 99.3 MHz in . The government wants to make 100.1 MHz available to station2. Assume that the transmitters of the two stations are equally powerful and...
8. ### Power consumption in LCR circuit

If we have a variable frequency AC supply in LCR circuit and when the frequency equals natural frequency the impedence is equal to resistance and the power consumption is purely that of resistive load circuit. Is this true even for other frequencies i.e. do reactance participates in power...
9. ### Damped ocillator LCR circuit

Homework Statement Homework EquationsThe Attempt at a Solution For part (a) i did the following; the time for it to decay to 40% is half the period of the square wave = 0.00002 seconds So, 0.4qm = qm ## e^(\frac{-0.00002R}{2L})cos(25000*2*\pi*0.00002) ## But the cosine term yields -1 which...
10. ### Differential equation for an LCR circuit

Homework Statement Find the differential equation that Q(t) satisfies. 2. Relevent equations Kirchoffs loop law and voltage across a capacitor, resistor and inductor. The Attempt at a Solution [/B] So I'm thinking, by Kirchoffs voltage rule, that the sum of the voltages in this circuit...
11. ### Problem in understanding analytical solution of LCR circuit

Hi all, I in my text they first did a phasor-diagram solution to a series LCR circuit and brought Z= under root of (R^2 +(Xc^2-XL^2)). After this they use a differential equation for series LCR circuit and actually did not solve such hard two degree differential equation, rather they...
12. ### Analyzing the LCR Circuit: Oscillatory Currents

Homework Statement I have the LCR circuit attached below. At time t=0 the capacitor is uncharged and the switch is closed. By solving an appropriate differential equation, show that the current through the resistor is oscillatory provided L<4CR2. By considering the boundary conditions at...
13. ### Solving a series LCR circuit via two methods

Given a series LCR circuit with a driving voltage V=V0cos(ωt), would it be possible to obtain a solution for I(t) by the two methods listed below? 1. Summing the voltages, i.e LdI/dt+IR+Q/C=V0cos(ωt) and solving the DE. 2. Using I=V/Z where Z is the total complex impedance and solving for I in...
14. ### Physics Lab, Transient response of LCR circuit, lorentzian curve

I wasn't exactly paying much attention during our lab, partially because it was right in the middle of midterms and I wanted to solely focus on those. Now it is coming back to bite me as I am not entirely sure how to complete my lab report, or the theory behind the lab really. If you would like...
15. ### Calculating quality factor in a series LCR circuit?

Homework Statement My tutor's notes say that quality factor is supposed to be = 2π (Max. energy stored)/(energy dissipated in one cycle) . So for a standard series LCR circuit, he says: max energy = 0.5 L I2 energy lost per cycle = 0.5 R I2 2π/ω . ..and at resonance he calculates it to be...
16. ### Initial current in a voltage driven LCR circuit

A switch is closed in a voltage driven series LCR circuit. Will the initial current (j(0)) be 0, regardless of the type of voltage source? Will j'(0) = V(0)/L, where V(t) is the source voltage? Feedback much appreciated.
17. ### LCR circuit and frequency equation

Homework Statement Im doing a lab experiment on LCR circuits and have gotten a graph of 1/capacatance against frequency^2. With my results I got the slope to be 0.89±0.01 and the intercept is 358708±43189 Homework Equations the equation that was given was frequency^2=(1/4*pi*L)[(1/C) -...
18. ### Solving LCR Circuit: Find C, I_rms, I_rms at Resonance

Homework Statement Consider a series LCR circuit with R= 69.0 Ω and L= 0.100 H, driven by a sinusoidal emf with Erms= 6.70 V at frequency f= 250 Hz. The sinusoidal current leads the emf by 54.0 degrees. a) Calculate the capacitance C. b) What is the rms current in the circuit? c) If...
19. ### Finding Current and Potential Difference in a LCR Circuit

Homework Statement There is a circuit, with the L and R in parallel and then there is a capacitor as well. There is a switch and a battery source. The E = 12 V and R is 1.37ohms. The switch is closed and the capacitor is uncharged and all currents are 0 Homework Equations That's what...
20. ### Damped Resonance Frequency OF series LCR circuit

the solution for current I, for series LCR circuit is I = (E/Z)sin(wt+\phi) Where Z = \sqrt{R^2 + (X_{L}-X_{C})^{2}} So for Resonance (i.e. maximum Current Amplitude) of LCR Circuit the necessary condition seems to be X_{L}=X_{C} Which gives \omega=1/\sqrt{LC} But some text-books and wikipaedia...
21. ### LCR Circuit with Capacitor as diminishing power source

Hey guys First off id like to say this is an awesome forum from what I've seen, and has since been bookmarked at the top of my list as i am an avid physics enthusiast (but **** at spelling :) ) Ok, to the nitty gritty. I have the following circuit (attached) Now, there are two questions...
22. B

### Resonance frequency in an LCR circuit

Hello everyone! I've been trying to derive the expression w = sqrt( (1/(LC)) - (R_l^2 / L^2) ) where w is the resonace frequency, L is the inductance of the inductor, R_l is the resistance in the inductor, R is the resistance of the resistor and C is the capacitance of the capacitator...