Rlc circuit problems and solutions pdf

Rlc circuit problems and solutions pdf

We have the circuit on the right, with a driving voltage US = 5 V, and we want to know U and I. General Solution for RLC Circuit ÎWe assumesteady state solution of form I m is current amplitude φis phase by which current “lags” the driving EMF Must determine I m and φ ÎPlug in solution: differentiate & integrate sin(ωt-φ) iI t= m sin(ω−φ) cos sin cos sin() ()m mm m I I Lt IR t t t C ω ωφ ωφ ωφ ε ω ω −+ −− −= m sin di q LRi t AC Circuits Example Problems 150 — L50 50 PE4k = 3. Chapter 4 Transients Step-by-Step Solution Circuits containing a resistance, a source, and an inductance (or a capacitance) 1. + – vs R1 R2 L i(t) v(t) + – C t = 0 Figure P 9. Q C respectively. E1. Questions: [a] Sketchthecircuitdiagram. 1-2 The Natural Response of RL and RC Circuits. Circuit (b) is a series circuit: each node is connected to exactly two components and the same current must ow through each. Problem 5: RLC circuit with passive nonlinear resistor. Solutions to the problems in Circuit Theory 1. Assume that all circuits are in sinusoidal steady state. • If σ > 0, pole is at <e(s) < 0, stable i. describing the circuit. ) Therefore, the given wave is headed in the ! x-direction. Using a parallel RC circuit which has a power supply of 100 –V, 60 Hz, and a current flow through the resister of is 10 amps and the current flow through the capacitor is 10 amps. It is driven by the DC current source Is whose time evolution is shown on Figure 7. c u r i n e o m d s C f " B 3 8 9 7 1 4. RC . V R = i R; V L = L di dt; V C = 1 C Z i dt : * A parallel RLC circuit driven by a constant voltage source is trivial to analyze. 0 1 ( ) ( ) ( ) 1 2 2 dt dv t RC v t LC d v t Describing equation : The circuit has two initial conditions that must be satisfied, so the solution for v(t) must have two constants. Establish the initial conditions for the system 2. 2 for a case where the capacitor is initially charged and no current is flowing. Then open switch at t=0. 1 H, and C = 0. 73. 2. The oscillations of the LC circuit are analogous to the mechanical oscillations of the spring mass system. We proceed as follows: 1. R = 1000 Ω; the total resistance in the circuit is then The series RLC circuit above has a single loop with the instantaneous current flowing through the loop being the same for each circuit element. VR and Vin are not in phase at this frequency. 1. To analyze an ac circuit containing resistors, capacitors, and inductors, it is helpful to think of each device’s reactance and find the equivalent reactance using the rules we used for equivalent resistance in the past. Over-damped response 3. 16. ECE2205, Second-OrderRLC Circuit Analysis 9–5 • For systems having only real poles, each pole contributes an output waveform of the same general kind, all of which are added together. 2 AC Circuits with a Source and One Circuit Element Before examining the driven RLC circuit, let’s first consider cases where only one circuit element (a resistor, an inductor or a capacitor) is connected to a sinusoidal voltage source. Draw the phasor of the current through the capacitor along the positive direction of the y axis and the phasor of the current through the inductor along the negative direction of the y axis. 0 µH, C = 10. 7. When a voltage source is connected to an RLC circuit, energy is provided to compensate the energy dissipation in the resistor, and the oscillation will no longer damp out. Cotter RLC CIRCUITS GENERAL RC/RL SOLUTION Step by Step Procedure (cont. Parallel RLC Circuit Example Problems with Solutions. The little wiggles on VR are real! This behavior is due to the transient solution (homogeneous solution) to the differential eq. docx Page 15 of 25 2016-01-07 8:48:00 PM Analytical solution of the RLC series circuit. linear, lumped parameter circuits, for the initial conditions have been incorporated into the equivalent circuit. 2-6 Problem available in WileyPLUS at instructor’s discretion. series. 14. the voltage across each branch is the same, B. CIRCUIT THEOREMS - ?? complex circuit problems and solutions Pre Algebra With Pizzazz Test Of Genius Solutions, Cay Horstmann Solutions Bing, Fundamentals Of Complex Analysis With Applications To Engineering And Science Solutions, Manually Remove Adobe Reader, Active Reading 3 Answer Key, Mensuration Problems With Solutions Pdf, Wiley Financial the homogeneous equation for the undriven, parallel RLC circuit, we can write the form of the homogeneous solution for our driven, parallel RLC circuit as iLH(t) = K 1es1t +K 2es2t (12. Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. It is also useful for circuits with multiple essential nodes and meshes, for the simultaneous ODEs have been reduced to simultaneous algebraic equations. * De ne !1 and !2 (see gure) as frequencies at which Im = I AC Circuits Basics, Impedance, Resonant Frequency, RL RC RLC LC Circuit Explained, Physics Problems - Duration: 1:00:12. c ODEs and Electric Circuits 5 I. Transient analysis(or just transients) of electrical circuits is as important as steady-state analysis. Circuit (a) is a parallel circuit: there are only two nodes and all four components are connected between them. TRANSIENT ANALYSIS OF ELECTRIC POWER CIRCUITS BY THE typical problem solutions which give better insight into the theory and the RLC circuits under a. 19. 3. So, we need to assign four mesh currents. Define a series RL circuit: The combination of a resistor and inductor connected in series to an AC source. An inductor has a 54. Be able to determine the natural responses of parallel and series RLC circuits Be able to determine the step responses of parallel and series RLC circuits PDF Practice Problems Chapter Alternating Current Circuits uvm edu ~mmsander ph Pract pdf PDF Book Series Circuit Problems And Solutions (PDF, ePub, Mobi)dokkudock arrive at a solution. In order to solve them we have to remember a few rules from what we learned about series and parallel circuits. The total opposition to current flow in an AC circuit. Ver 2427 E1. Since the inductive and capacitive reactance’s X L and X C are a function of the supply frequency, the sinusoidal response of a series RLC circuit will therefore vary with frequency, ƒ. If the charge C R L V on the capacitor is Qand the current flowing in the circuit is I, the voltage across R, Land C are RI, LdI dt and. Write the circuit equation and reduce it to a first-order differential equation. In an RC circuit, the impedance is determined by both the resistance and the capacitive reactance combined The circuit phase angle is the angle between the total current and the source voltage In a lag network, the output voltage lags the input voltage in phase In a lead network, the output voltage leads the input voltage RLC Circuits 2 If the resistance in the circuit is small, the free oscillations are of the form q C = q C0 e!t/"cos(# 1 t+$) (4) Where q C0 and ! are determined by initial conditions, and ! 1 =! 0 1"(! 0 #) [] "2 1/2 (5) This solution is plotted in Fig. a. • A catch: We need transforms to get the problem to the ω domain, and inverse transforms to get the solutions back to the time domain! 5 EE 1202 Lab Briefing #5 Time the homogeneous equation for the undriven, parallel RLC circuit, we can write the form of the homogeneous solution for our driven, parallel RLC circuit as iLH(t) = K 1es1t +K 2es2t (12. Download [PDF] Solutions To Problems In Basic Circuit Parallel RLC Circuit. The inductor phasoris +90 and the capacitor phasoris -90 relative to the resistor phasor. 3 Circuit Analysis in S Domain Circuit analysis in s domain nStep 1 : Transform the time domain circuit into s-domain circuit. Since the current through each element is known, the voltage can be found in a straightforward manner. rlc circuits problems and solutions A9907A6133EF68E0BE1691E6FDDF7BA7 ePanorama - software and tools for electronics design 1. Critically-damped response How to draw the phasor diagram of a parallel RLC circuit: Draw the phasor of voltage along the x axis as well as the phasor of current through the resistor. RLC Resonant Circuits Andrew McHutchon April 20, 2013 1 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. EE 201 RLC transient – 1. complex circuit problems and solutions Pre Algebra With Pizzazz Test Of Genius Solutions, Cay Horstmann Solutions Bing, Fundamentals Of Complex Analysis With Applications To Engineering And Science Solutions, Manually Remove Adobe Reader, Active Reading 3 Answer Key, Mensuration Problems With Solutions Pdf, Wiley Financial Alternating Currents: LRC circuit Using Phasors, we can construct the phasordiagram for an LRC Circuit. The state equations of this RLC circuit are x˙ = y −f(x) (24) y˙ = −x (25) where x is the current, y is the capacitor voltage, and f(x)is the nonlinear resistor’s effect. 3) 12. It can correctly predict the impulsive response, Driven RLC Circuits Challenge Problem Solutions Problem 1: Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs leads (if either): (a) Voltage across the capacitor or voltage across the resistor TRANSIENT ANALYSIS OF ELECTRIC POWER CIRCUITS BY THE typical problem solutions which give better insight into the theory and the RLC circuits under a. Please note that AC circuits are linear and that is why Superposition theorem is valid to solve them. Pan 20 12. 1 Circuit Analysis Problem Sheet 1 - Solutions 1. C. 3 H and a capacitor with capacitance 15 μF. The Organic Chemistry Tutor 192,587 views The following plots show VR and Vin for an RLC circuit with: R = 100 W, L = 0. Practice Problem 1: R-L DC Circuit I. Problem. T. The format followed in this document is as follows. These questions are related to RL Series Circuit, RC Series Circuit, and RLC Series Circuit. 70 For Prob. the Thevenin Impedance is purely real). Chapter 19, Solution 6. As with most things this is not true. In RLC parallel circuit, resistor, inductor, and capacitors are connected in parallel across Alternating current source. In contrast to the RLC series circuit, the voltage across each component is the same and is taken as reference in the phasor diagram. Selecting appropriate RLC circuit component values to meet design specifications. ) vi) For t→∞, assume the circuit has been stable for a long time, as in (iii), and replace C's with open circuits and L's with wires. rlc series circuit problems with solutions pdf Chapter 21: RLC Circuits. Determine where and . e. vii) To find RTh, remove the C or L from the circuit and find the Thevenin resistance Problem 5: RLC circuit with passive nonlinear resistor. and . Suppose the circuit parameters in a series RLC circuit are: L = 1. Problems 411 ESE 271 / Spring 2013 / Lecture 17 Series RLC circuit 2 This is second order equation and it is not easy even for step function Vs …. The voltage across the resistor in the circuit of Figure 3. RL Series Circuit RC Series Circuit RLC Series Circuit Impedance in an AC Circuit. 1. • However, by transforming them to the ω domain (a radian frequency domain, ω = 2 π f), the problems become algebra problems. 203) where K 1 and K 2 are as yet unknown constants that will be determined from the initial conditions after the total solution has been formed. Hint: Use the direct method. (The vector relationship is summarized in Equation 34-20b. When we solve for the voltage and/or current in an AC circuit we are really solving a differential equation. Where R is a resistance and X represents Reactance. Solution with AC Circuit Analysis Problem 1. circuit analysis lies in the automatic inclusion of the initial conditions in the transformation process, thus providing a complete (transient and steady state) solution. T F At the resonant frequency 100, circuit impedence is purely real. 89, and are adjustable voltage sources in the range V, and and represent their internal resistances. There are four meshes in the circuit. RL . (b) Solve DE for I through R1 (c) What type of damping does this have? What R1 is needed for the other Resonance in series RLC circuits 0 I! I V C V R V L V m60 max m Imax m = p 2 1! 0! 2 * The maximum power that can be absorbed by the resistor is Pmax = 1 2 (Imax m) 2 R = 1 2 V2 =R. Solution Mesh Analysis. 70. The basic technique used for solving dc combination-circuit problems is the use of equivalent circuits. Redraw the circuit (nothing about the Laplace transform changes the types of elements or their interconnections). complex circuit problems and solutions Pre Algebra With Pizzazz Test Of Genius Solutions, Cay Horstmann Solutions Bing, Fundamentals Of Complex Analysis With Applications To Engineering And Science Solutions, Manually Remove Adobe Reader, Active Reading 3 Answer Key, Mensuration Problems With Solutions Pdf, Wiley Financial (12. EE 188 Practice Problems for Exam 3, Spring 2009 Include units in your answers where appropriate. nStep 2 : Solve the s-domain circuit. Solving Differential Equations - intmath. Parallel RLC circuit. Example 5: Figure 9 represents an approximate equivalent circuit of a field effect transistor amplifier. . This is similar to 2-D vector addition. complex circuit problems and solutions Complex Circuit Problems And Solutions by Wrox Press Complex Circuit Problems And Solutions The way to solve a complex problem is to break it down into a series of simpler problems. 0 Qreactance at 60. (d). B. Electricity and magnetism. ODE, ICs, general solution of parallel voltage 2. Driven RLC Circuits Challenge Problem Solutions Problem 1: Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs leads (if either): (a) Voltage across the capacitor or voltage across the resistor * A series RLC circuit driven by a constant current source is trivial to analyze. An R-L circuit consists of a 100 volt DC battery connected in series with a 2 henry inductoranda 6 ohmresistor. RLC transients. With some differences: • Energy stored in capacitors (electric fields) and inductors (magnetic fields) can trade back and forth during the transient, leading to possible “ringing” effects. 0 nF, R = 100Ω, and the source voltage is 220 V. Before beginning plot your course. This part covers the applications of MATLAB in circuit analysis. We can assume that f(x)is a continuous function, because a resistor is a physical device. Be able to determine the natural responses of parallel and series RLC circuits Be able to determine the step responses of parallel and series RLC circuits PDF Practice Problems Chapter Alternating Current Circuits uvm edu ~mmsander ph Pract pdf PDF Book Series Circuit Problems And Solutions (PDF, ePub, Mobi)dokkudock Solution. c u r i n e t o m d p s C f " B 3 8 h t p: / w. 6 Recall the Norton Equivalent of an RLC circuit is a current source in parallel with a resistor and a capacitor or an inductor. source that produces a 100 v 1-50 Ha For the case of a resistor in an AC circuit the V R across the resistor is in phase with the current I through the resistor. Any voltages or currents with values given are Laplace-transformed using the functional and operational tables. Find the value of C for which the Norton Equivalent is a current source in parallel with only a resistor (i. 1 Analysis of Circuits (2014) E1. For electromagnetic waves in vacuum, the directions of the electric and magnetic fields, and of wave propagation, form a right-handed coordinate system, as shown. By: Neil E. Figure 19. 3 The Step Response of . An RLC circuit is called a second-order circuit as any voltage or current in the circuit can be described by a second-order Circuit for Problem 12 13. there is always a part that is wired in series. Fig. You home is wired in A. RLC series circuit: regimes of operation (1) • Let’s consider V(t) to be a dirac-like impulsion (not physical…) at t=0. c State Space Approach to Solving RLC circuits Eytan Modiano. Problem-Solving Strategy: AC Circuits. Natural Response of Parallel RLC Circuits The problem – given initial energy stored in the inductor and/or capacitor, find v(t) for t ≥ 0. 0 1--17. Eytan Modiano Slide 2 Learning Objectives – Solve for the complete solution using initial conditions. Our task is to solve the differential equation. The topics covered in Part II are dc analysis, transient analysis, alternating current analysis, and Fourier analysis. 13 A 3. ctsnet. To simplify a complex circuit to a simple circuit containing only one load, equivalent circuits are substituted (on paper) for the complex circuit they represent. ODEs and Electric Circuits 1 I. RLC Series Circuit Problems with Solutions. Using KCL find the output voltage v 2 in terms of input voltage v 1 . In series: Current remains constant throughout the whole circuit. To find z11 and z21, consider the circuit below. Solution of First-Order Linear Differential Equation Thesolutiontoafirst-orderlineardifferentialequationwithconstantcoefficients, a1 dX dt +a0X =f(t), is X = Xn Chapter 19, Problem 6. From KVL, 2𝑉 𝐶 2 +⁡𝑅 𝐿 𝑉𝐶 +⁡1 𝐿𝐶 𝑉𝐶=⁡ 1 𝐿𝐶 𝑉𝑖 Differentiate throughout, then replace 𝑉𝐶̇⁡ ⁡ to get ̈+⁡𝑅 𝐿 ̇+⁡1 𝐿𝐶 circuit analysis lies in the automatic inclusion of the initial conditions in the transformation process, thus providing a complete (transient and steady state) solution. Practice Problem 1: R-L DC Circuit Rlc Circuits Problems And Solutions 7 / 9 2 0 1 5 w. In a purely capacitive circuit, the current leads the voltage by 90o, while in a pure inductive the current lags the voltage by 90o. Note that the circuitry to which the L and C are connected is converted to a Thevenin equivalent, which turns all the R's in the circuit into a single R. (b). Our goal is to determine the current iL(t) and the voltage v(t) for t>0. How does one solve the DC RLC circuit differential equation? Basically I am trying to find the current in a RLC (Resistance Inductor Capacitor) circuit as a When you are first faced with a series/ parallel combination circuit they seem almost down right impossible to solve to begin with. How to solve Electronics RLC Circuits and Resonance problems? You can easily solve all kind of Electronics questions based on RLC Circuits and Resonance by practicing the objective type exercises given below, also get shortcut methods to solve Electronics RLC Circuits and Resonance problems. 67 is Circuit Theory Problems Solutions - wiki. In both cases, it was simpler for the actual experiment to replace the battery and switch with a signal generator producing a square wave. The RLC Circuit. From KVL, 2𝑉 𝐶 2 +⁡𝑅 𝐿 𝑉𝐶 +⁡1 𝐿𝐶 𝑉𝐶=⁡ 1 𝐿𝐶 𝑉𝑖 Differentiate throughout, then replace 𝑉𝐶̇⁡ ⁡ to get ̈+⁡𝑅 𝐿 ̇+⁡1 𝐿𝐶 RLC Exam like Example Consider this circuit where the switch has been closed long enough for the circuit to stabilized. The RLC Circuit The RLC circuit is the electrical circuit consisting of a resistor of resistance R, a coil of inductance L, a capacitor of capacitance C and a voltage source arranged in series. Use [ (1 ) (1 )] [ (1 ) (1 )] 0 ( ) 0 1 ( ) 1 ( ) 1 Chapter 7 Response of First-order RL and RC Circuits 7. The circuit is connected to an AC voltage source with amplitude 25 V and frequency 50 Hz. Chapter 4 Transients RC AND RL CIRCUITS WITH GENERAL SOURCES The general solution consists of two parts. Be careful not to lose sight of your goal among all the bits and pieces, however. Compute the z parameters of the circuit in Fig. The Series RLC Resonance Circuit Introduction Thus far we have studied a circuit involving a (1) series resistor R and capacitor C circuit as well as a (2) series resistor R and inductor L circuit. 0 Hz what will be the maximum current if this inductor is connected to a 50. 1 and 2 illustrate series and parallel RLC circuits. The impedance, Z, of a component or a circuit is de ned as, Z = R + jX (1) Resonance in series RLC circuits 0 I! I V C V R V L V m60 max m Imax m = p 2 1! 0! 2 * The maximum power that can be absorbed by the resistor is Pmax = 1 2 (Imax m) 2 R = 1 2 V2 =R. pdf Solutions to the problems in Circuit Theory Sun, 09 Jun 2019 03:39:00 GMT Solutions to the problems in Circuit Theory 1. parallel. (a) Write the DE for circuit & initial conditions (current or voltage across each element). When transients occur, the currents and voltages in some parts of the circuit may many times exceed those that exist in normal behaviour and may destroy the circuit equipment in its proper operation. Determine the resonant frequency of the circuit and the amplitude of the current at resonance. Series RLC Circuit Task number: 1540 An AC circuit is composed of a serial connection of: a resistor with resistance 50 ω, a coil with inductance 0. com P517/617 Lec3, P2 R-C Circuits and AC waveforms • There are many different techniques for solving AC circuits, all of them are based on Kirchhoff's laws. Chapter 3 Nodal and Mesh Equations - Circuit Theorems 3-52 Circuit Analysis I with MATLAB Applications Orchard Publications 3. 10 H are connected in series in sn alternating circuit with frequency 50 Hz and amplitude of voltage 300 V. Practice Problem 1: R-L DC Circuit [d] Graph I(t). RLC Circuits – SciLab Examples rlcExamples. Note: VR << Vin at this frequency. The RLC circuit shown on Figure 6 is called the parallel RLC circuit. [PDF]Free Circuit Theory Problems Solutions download Book Circuit Theory Problems Solutions. Rlc Circuits Problems And Solutions 7 / 9 2 0 1 5 w. Then for t>0, V(t)=0 and the previous equation simplifies to • With solutions • Where the λare solutions of the characteristics polynomial is • The discriminant is • And the solutions are U(t) =Aeλ+t +Beλ−t 2 2 0 2 0 2 RLC Circuits – SciLab Examples rlcExamples. The RLC circuit is the electrical circuit consisting of a resistor of resistance R, a coil of inductance L, a capacitor of capacitance C and a voltage source arranged in series. The oscillations of charge, current and potential difference are called driven or forced oscillations. Problem 7 Solution. 6 and 19. We add the phasors of the resistor, the inductor, and the capacitor. electrical circuits, carried out in several European countries, points at similar ideas for different communities: diminishing intensity along a circuit, distribution of voltage in the branch, influence of the form of presentation of the circuit, etc. org SOLUTIONS TO PROBLEMS IN BASIC CIRCUIT THEORY Download Solutions To Problems In Basic Circuit Theory ebook PDF or Read Online books in PDF, EPUB, and Mobi Format. Solving Differential Equations (DEs) A differential equation (or "DE") contains derivatives or differentials. 4 A General Solution for Step and Natural The following plots show VR and Vin for an RLC circuit with: R = 100 W, L = 0. Circuits. 1 mF at a frequency of 100 Hz. An RLC circuit (also known as a resonant circuit or a tuned circuit) is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. Parallel RLC Circuit 1. In the circuit of Figure 3. Under-damped response 4. EXAMPLE: H(s) = 1 s +σ ←→s h(t) = e−σtu(t). To demonstrate the method used to solve combination circuit problems, the LaPlace Transform in Circuit Analysis Recipe for Laplace transform circuit analysis: 1. D. s 1 and s 2, the When you are first faced with a series/ parallel combination circuit they seem almost down right impossible to solve to begin with. the current through each branch is always the same. s 1 and s 2, the The hands-on approach is one of the best ways of learning MATLAB. It is better to have all the mesh currents loop in the same direction (usually clockwise) to prevent errors when writing out the equations. RLC Example Cont’d • Initial conditions, C is fully charged, acts a V source C has VC = 40V • L acts as a short before switch opens (no change in I) • Therefore, current controlled by R 2A 20 40 R V IL =IR = = = VL =0, V IR 40V R = = (b) Assuming an exponential solution then get the equations I(t)=Aest C s L sR 1 0 = 2 + + “Divided” RLC circuit Task number: 662 A capacitor with an unknown capacity, a resistor with resistance 50 Omega; and a coil with inductance 0. R-L Circuit: current I(t) EMF=100 R=6 L=2 0 2 4 6 8 10 12 14 16 1 2 t 3 4 5 ODEs and Electric Circuits 5 I. The instantaneous power is a function of time. In phase means that both waveforms peak at the same time. 14 Exercises Multiple Choice 1. In AC circuit analysis, if the circuit has sources operating at different frequencies, Superposition theorem can be used to solve the circuit. For which type of circuit is overloading a problem? current i(t). Practice Problem 1: R-L DC Circuit Workonthequestionsforthegivencircuit;indicatedlinksgive(partial)solutions. Many of those concepts are applicable to LC oscillations. , impulse response decays, circuit analysis lies in the automatic inclusion of the initial conditions in the transformation process, thus providing a complete (transient and steady state) solution. C = 1 C Z i dt : * A parallel RLC circuit driven by a constant voltage source is trivial to analyze. However, the average power per cycle is of more interest. Solution: The circuit of figure 9 is redrawn as shown in figure 10. 15. * De ne !1 and !2 (see gure) as frequencies at which Im = I 11. Part II consists of Chapters 4 to 8. Find € vC(t→∞) or € iL(t→∞). In a parallel circuit, A. I1 5Ω 10Ω 4I1 I2=0 Vo – + + V1 20 Ω V2 – + _ Solve the circuit by mesh analysis and find the current and the voltage across . Series RLC circuit. you must always have identical resistors in each branch. When there is a step change (or switching) in a circuit with capacitors and inductors together, a transient also occurs. RLC circuit problems must be solved using calculus. Circle T (true) or F (false) for each of these statements. We will show how that the angular frequency of the oscillations depends only on the inductance and capacitance of the circuit. The combination of a resistor and inductor connected in series to an AC source. rlc circuit problems and solutions pdf

qz, ec, pw, 4c, ys, ub, pu, ku, nw, xj, dx, e5, a0, pb, w6, 4g, gz, vr, 5y, b9, 1t, 0q, oe, di, fc, xm, qf, 2a, 1a, qi, wd,