Rlc circuit Definition and 308 Threads

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.

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  1. cianfa72

    About the definition of resonance frequency

    Hi, I'm confused about the meaning of resonance angular frequency for an RLC series circuit. Call ##\omega_0=\sqrt { 1/LC }## and ##Q= {\omega_0 L} /R##. Then consider the admittance as transfer function $$Y(s) = \frac {1} {L} \frac {s} {s^2 + s \omega_0/Q + \omega_0^2}$$ This transfer function...
  2. Z

    How to solve this driven RLC circuit?

    Here is the circuit as it appears in MIT OCW Vibrations and Waves Problem Solving course Here is my own picture I wrote equations for the three loops. Outer Loop Through ##C## $$-V_0\sin{\omega t}+IR+\frac{Q}{C}=0\tag{1}$$ Outer Look Through ##L## $$-V_0\sin{\omega...
  3. Z

    How to calculate quality factor for RLC circuit?

    Using Faraday's law we have $$\mathcal{E}=\oint\vec{E}\cdot d\vec{l}=\frac{Q}{C}+IR=-L\dot{I}\tag{1}$$ where ##I=\dot{Q}##. After rearranging the expression we get $$\ddot{Q}+\frac{R}{L}\dot{Q}+\frac{1}{LC}Q=0\tag{2}$$ $$\ddot{Q}+\gamma\dot{Q}+\omega_0^2Q=0\tag{3}$$ If the system is...
  4. Z

    How to obtain amplitude of current in parallel RLC circuit?

    If we apply KVL to the three separate loops involving the AC voltage we obtain expressions for ##I_R, I_L##, and ##I_C##. $$-V(t)+I_R(t)R=0$$ $$\implies I_R(t)=\frac{V_0}{R}\sin{(\omega t)}$$ $$-V(t)=-L\dot{I}_L(t)$$ $$\implies I_L(t)=\frac{V_0}{\omega L}\sin{(\omega t-\pi/2)}$$...
  5. M

    B Initial current in an RLC circuit

    suppose that we have an RLC circuit where initially, the capacitor is fully charged, the charge in the capacitor is given by ##q(t) = q_{max} e^{-Rt/2L} \cos(\omega t)##, if we want to find the current, we would differentiate the charge, so $$\Large i(t) = \frac{d q}{dt} = \frac{d}{dt} (q_{max}...
  6. T

    Power dissipated over 1 cycle of a AC source-free RLC series circuit?

    I tried to start by assuming that we need to integrate something over 1 period (2pi). Therefore, we need i(t)^2 R integrated over something. From there, I recognized that this is an underdamped model since R/2L < 1/sqrt(LC). I believe that i(t) can be represented by i(t) = e^(-at)[A_1 cos(w_d t)...
  7. Z

    What is the unknown circuit element in RLC circuit given plot of V, I?

    Here is the circuit and here is the plot of current and voltage we don't know which is which initially. Just by looking at this plot, I conclude that the element cannot be a resistor because if it were then the phase would need to be zero. Next, suppose the element is an inductor. Then...
  8. Tesla In Person

    Phase difference RLC circuit

    For a parallel RLC circuit, I have found the complex impedance to be 1/ (1/R -j(1/wL +wC)) . I need to find the phase difference between the voltage and current in the circuit. I know it's given by tan^-1(im(z)/re(z)) but how do I do it here as the expression is a fraction?
  9. Z

    Calculation of current in driven series RLC circuit

    The notes are in an attached pdf on pages 10-13. We start with the driven RLC circuit below The AC source voltage is ##V(t)=V_0\sin{(\omega t +\phi)}## and we would like to find the current ##I(t)=I_0\sin{(\omega t)}##. Using Faraday's law we have...
  10. M

    Series RLC circuit connected to a DC battery

    How do I solve the differential equation? Please give me a hint.
  11. J

    Engineering Get Expert Help with Your RLC Circuit Design | Easy Step-by-Step Guide

    I wrote them on the image
  12. L

    Comp Sci Use a simulator to produce a resonance curve for this RLC circuit

    my issue here is what would i put in for frequency ? unless i use the formula to find the resonance frequency i have only used multisim live and you cant put in Vs 10 +j20
  13. Franklie001

    Engineering RLC circuit -- Phasor Transfer Function calculation

    Good morning, I need some help solving those two question. I've attached my attempted solution below. Could i solve the transfer function any further? Thank you for your help
  14. greg_rack

    Current flowing through resistor in RLC circuit (C in parallel with L)

    Hello guys, LRC circuits with an AC source are having the best over me... had some confusion in class with respect to which method is best using(phasors diagram, reactances or complex impedances) which I am trying to desperately sort out before my exam; here I will show you my best attempt on...
  15. A

    Adjusting the Power Factor of an RLC circuit

    a) An inductor should be added because that would cancel out the lag of the voltage with the current so that P = IV is at a maximum since V is ahead of I in an inductor b) ##cos(\phi) = \frac{R}{Z}##, ##R = Zcos(\phi) = 60\times 0.5 = 30 ohms## ##X_l - X_c = \sqrt{Z^2 - R^2} = \sqrt{60^2 -...
  16. P

    I Charge in RLC circuit when starting charges are 2Q and Q

    Hi all, I understand the standard solution where charge in an RLC circuit decreases from +Q to 0, for a capacitor with starting charges +Q and -Q. May I know what the terminal charge on a capacitor in an RLC circuit is, when it’s original charges are 2Q and 0? I am thinking it will be +Q and...
  17. I

    Cutoff frequency for this RLC circuit

    How would i find the cut of frequency of this RLC circuit .I have used LTspice to find it but what is the equation for finding it
  18. X

    Engineering How to Determine Voltage and Current in an RLC Circuit?

    Hi i want to know just how to approach this question. i know the omega=100 then should i find XL and XC? and then find the voltage in points c and d? also how do i find the current that enters point c? thanks a lot.
  19. Lotos

    Engineering Open Modelica, work with an RLC-circuit

    Good day. I am studying Open Modelica and building RLC. I was given the following task: From the initial network make one (sample graphics on Scilab but needs in Open Modelica) As you can see in the graph that is presented in scilab, the graphs start from different points. Here is a list of...
  20. wcjy

    RLC Circuit Analysis -- Two sources and two switches

    Hello, this is my working. My professor did not give any answer key, and thus can I check if I approach the question correctly, and also check if my answer is correct at the same time. When t < 0, capacitor acts as open circuit, $$V(0-) = V(0+) = 9V$$ When t = infinity, $$V( ∞) = 5V$$ (because...
  21. H

    Impedeance of parallel RLC circuit

    the impedance of the parallel RLC circuit is shown as attached. The equation above is the impedeance of RLC circuit in series, how can I convert that in parallel? Thanks.
  22. N

    Using Complex Impedances in these RLC Circuit Calculations

  23. C

    Can I simplify this RLC circuit problem using a different method?

    Hello, I have been thinking about this problem for a few hours, and I do not understand how I should proceed to solve it correctly. Section a is very simple, just substitute in the expression that gives us the values of L and C that the statement gives us. However, when I get to section b, I...
  24. A

    Engineering Troubles with a circuit analysis situation (RLC circuit)

    thanks
  25. C

    I How do I calculate the expected Gain?

    I am doing an experiment in electronics with AC RLC circuits, But there are a few things about what I need to do that I don't understand. First: While I know in the circuit diagram we include the internal resistance of the Inductor in series, but I don't know why we include it in series rather...
  26. baywa2

    Determine the capacitor value so that this circuit is in resonance

    L=100mh=0.1H ω=10^3 rad/s -> f = 159Hz XL= ωL= 2πfL= 2π*159*0.1= 99.90 Ω Z parallel = [(XL∠90º)*R2] / [(XL∠90º)-R2]= 37.13∠-21.8º XC= 1/ωC= 1/(2 π f C) I don't see how I am supposed to get to C
  27. DeclanKerr

    RLC Circuit Analysis with system of ODEs

    Summary: Looking for guidance on how to model an RLC circuit with a system of ODES, where the variables are the resistor and inductor voltages. This is a maths problem I have to complete for homework. The problem is trying to prove that the attached circuit diagram can be modeled using the...
  28. paulmdrdo

    Engineering Solve 2nd Order RLC Circuit Problem | Get Answers Now

    I was stuck with the last line of my solution please help me find the correct answer to this problem. TIA!
  29. ItsTheSebbe

    Finding the bandwidth of a parallel RLC circuit (+MATLAB)

    Homework Statement The attempt at a solution Constructing the total impedance of the circuit as follows, $$\frac{1}{Z_T}=\frac{1}{Z_R}+\frac{1}{Z_C}+\frac{1}{Z_L}$$ where $Z_R=R$, $Z_C=-j\frac{1}{\omega C}$ and $Z_L=j\omega L$. $$\frac{1}{Z_T}=\frac{1}{R}+j\omega C+\frac{1}{j\omega L}$$...
  30. J

    Engineering AC Source driving an RLC circuit....

    Homework Statement 10 v, 100 hz goes into a circuit of a 1o resistor, a 1o inductive reactance and a 1o capacitive reactance that are in series. What is the current. What is the V across the cap. Homework Equations and the attempt at a solution[/B] So I know I = V/Z and Z = sqrt( R^2 +...
  31. MaxR2018

    Engineering RLC circuit solved with Laplace transformation

    Hi, i need some help here. Can you help me?:sorry: Here is the problem. Exercise statement: The switch have been closed for a long time y is opened at t=0. Using Laplace's transtormation calculate V0(t) for t ≥ 0 This is what i made to solve it: 1) I know while the switch is closed, the...
  32. Felipe Lincoln

    Verifying Kirchoff's law in an AC RLC circuit

    Homework Statement I have the following RLC circuit with an sinusoidal voltage generator and I want to verify the Kirchoff's first law with an oscilloscope. To measure the peak voltage in each of the components I just permute the positions between the component and the resistor. The question...
  33. M

    Hi, can somebody explain this RLC circuit to me?

    Hello to everbody can you help me how come C6 to be 10p and c5 13.5 and and l1 to be 190n and L6 240n i start with 100Meghz, with one circuits 50/XL or 50/XC now become three different thanks i understand the first circuit, i understand the second circuit, but now they make three circuits how...
  34. T

    For a damped RLC circuit, why must R be small?

    Homework Statement I'm reading the textbook section covering damped series RLC circuits (provided below). I'm wondering why the author stipulates "When R is small..." Homework Equations Given above. The Attempt at a Solution Given above. Any gentle and courteous comments are welcome!
  35. J

    Engineering What is the Time Constant for an RLC Circuit?

    Homework Statement Homework Equations I know for RL circuit T = L/R For RC circuit it is RC But how to go ahead for RLC circuit.The Attempt at a Solution I calculated for RL as 1/4 = 0.25 And RC as 1 Then I added both time constant and got 1.25 Book answer is 0.5. How to solve this? In...
  36. R

    Engineering Impulse Response of an RLC Circuit

    I bolded the portions I need help with. 1. Homework Statement A series circuit consists of a resistor with a resistance of 16 ohms, an inductor with inductance of 2 H, and a capacitor with a capacitance of 0.02 F. At time t = 0 there is no charge on the capacitor and no current in the circuit...
  37. Drakkith

    Engineering Finding Current in a Parallel RLC Circuit

    Homework Statement Find io for t≥0. Express your answer in terms of t, where t is in milliseconds. There is no energy stored in the circuit in (Figure 1) when the switch is closed at t = 0. Homework Equations ##x(t)=x_f+[B_1cos(ω_dt)+B_2sin(ω_dt)]e^{-αt}## The Attempt at a Solution Let...
  38. Jayalk97

    Engineering Underdamped Parallel RLC Circuit

    Hey guys, so I'm having trouble with this circuit analysis question. I need to find voltage across the capacitor as a function of time. I nearly finished analyzing but I'm having trouble solving for the initial value constants in the voltage equation. So first I used KCL to create the equation...
  39. W

    RLC Circuits - Q Factor and Amplitude

    Homework Statement Imagine you have two RLC circuits you are trying to scan for resonances. They have identical resonant frequencies, but circuit 1 has a very high Q-factor (Q1 >> 1), and circuit 2 has a very low Q-factor (Q2 < 1). Let's assume you are already on resonance and looking at V(out)...
  40. C

    Calculating Currents & Voltages of an RLC Circuit

    Homework Statement An RLC circuit contains the following components in series: a 15Ω resistor, a 200μF capacitor, and a 12mH inductor. What are the currents and voltages through each component? It's known that the current through the resistor is 1.75A⋅cos(250πt) Homework Equations χL=ω*L...
  41. e0ne199

    Engineering Problem with series RLC circuit and dependent source

    Homework Statement here is my problem : Homework Equations like usual, the problem is related with RLC circuits and transients The Attempt at a Solution [/B] from here, the solution is obviously wrong because from the solution, its alpha should be -300 and not -0.4...and from the...
  42. M

    Solve RLC Circuit Problem Homework

    Homework Statement http://imgur.com/a/3xSYb Homework Equations RLC equations: q= Qmax e ^ -Rt/2L cos wd t wd = [ 1/LC - (R/2L)^2] ^ 1/2 The Attempt at a Solution So, I am trying using Kirchoff law, but not sure what the question asks. I thought it may be a trick and after a long...
  43. gimak

    Finding the average energy in an RLC circuit

    Homework Statement Homework Equations Q(t) = Aei(wt+Φ); dQ/dt = i*w*Q(t); E = (L/2)(dQ/dt)2 + Q2/2C i = √-1 E above is average energy The Attempt at a Solution When I plug in Q(t) & dQ/dt into equation above (E) I get: A2L/2(w02-w2)cos[2(wt+Φ)] w02 = 1/LC After I plugged both of them in...
  44. Arman777

    RLC Circuit DC Homework Solution

    Homework Statement Homework Equations The Attempt at a Solution I used the loop rule where ##ΣΔV=0## and junction rule. From here I get 4 equations ##i_3=i_1+i_2## ##ε-i_3R_3-i_1R_1-L(di\dt)=0## ##ε-i_3R_3-i_2R_2-Q\C=0##...
  45. e0ne199

    Engineering Question about free source RLC circuit

    Homework Statement below is my question : Homework Equations all of the equatios used to solve this problems are equations for free source RLC circuit. The Attempt at a Solution so far i have solved problem (a), whose answer is -1400V/s, the problem is when i want to solve (b) and (c) do...
  46. R

    Plotting a RLC Circuit: Analyzing a Differential Equation

    I'm not sure about the physical behavior of a RLC circuit and I have to give a presentation that involves one. So I've decided to plot the current. I found a book that gives a differential equation to describe the circuit. ##L\frac{d^2i}{dt^2} + R\frac{di}{dt} + \frac{1}{C}i = \frac{dv}{dt}##...
  47. O

    How to solve the differential equation for driven series RLC circuit?

    Homework Statement It is the driven series RLC circuit. It is given in the following images. It is from the section 12.3 in this note. Homework Equations The differential equation, as given by 12.3.3, is ##L \frac{d^2 Q}{d t^2} + R \frac{d Q}{d t} + \frac{Q}{C} = V_0 \sin{(\omega t)}##...
  48. solour

    Alternating RLC circuit with an additional capacitor

    Homework Statement http://imgur.com/a/TOUjV part b, specifically finding the maximum charge for C1. The question that boggles me is whether Imax changes on the left side of the circuit, after the switch closes. Homework Equations V=IR Xc = 1/(wC) XL = wL The Attempt at a Solution I was able...
  49. S

    RLC Circuit lab equipment problem

    Hello all, I am a lab technician for a university and I am having some problem with some lab equipment. We are doing an RLC circuit lab with a frequency generator, oscilloscope, decade resistance box, capacitance box, and inductor. The equipment is connected in series, except for the...
  50. T

    Engineering Can the RLC Circuit Homework be Solved Using Different Methods?

    Homework Statement R = 125 ohms, L = 200 mH, C = 5 uF, initial current in L is -0.3A, and initial voltage across C is 25V. Homework Equations v(t) = (Bcos(wt)+Csin(wt))e^(-at) The Attempt at a Solution I've solved for v(t) t>0 and got 25e^(-800t)(cos(600t)+ (4/3)sin(600t)). The second...
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