Response of First Order RL and RC Circuits
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Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram
Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is common for the resistor R and the capacitor C, which is here the source current I (because it passes through both R and C without being divided). Figure (1) Series RC circuit * Now we know that I and resistor voltage VR are in phase or have the same phase angle (there zero crossings are the same on the time axis) and VR is greater than I in magnitude. * Since I equal the capacitor current IC and we know that IC leads the capacitor voltage VC by 90 degrees, we will add VC on the phasor diagram as follows: * Now, the source voltage VS equals the vector summation of VR and VC: Figure (2) Series RC circuit Phasor Diagram Prepared by: Eng. Wiam Anabousi - Important notes on the phasor diagram of series RC circuit shown in figure (2): A- All the vectors are rotating in the same angular speed ω. B- This circuit acts as a capacitive circuit and I leads VS by a phase shift of Ө (which is the current angle if the source voltage is the reference signal). Ө ranges from 0o to 90o (0o < Ө <90o). If Ө=0o then this circuit becomes a resistive circuit and if Ө=90o then the circuit becomes a pure capacitive circuit. C- The phase shift between the source voltage and its current Ө is important and you have two ways to find its value: a- b- = - = - D- Using the phasor diagram, you can find all needed quantities in the circuit like all the voltages magnitude and phase and all the currents magnitude and phase. -
EE2003 Circuit Theory
Chapter 10: Sinusoidal Steady-State Analysis 10.1 Basic Approach 10.2 Nodal Analysis 10.3 Mesh Analysis 10.4 Superposition Theorem 10.5 Source Transformation 10.6 Thevenin & Norton Equivalent Circuits 10.7 Op Amp AC Circuits 10.8 Applications 10.9 Summary 1 10.1 Basic Approach • 3 Steps to Analyze AC Circuits: 1. Transform the circuit to the phasor or frequency domain. 2. Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, etc.). 3. Transform the resulting phasor to the time domain. Phasor Phasor Laplace xform Inv. Laplace xform Fourier xform Fourier xform Solve variables Time to Freq Freq to Time in Freq • Sinusoidal Steady-State Analysis: Frequency domain analysis of AC circuit via phasors is much easier than analysis of the circuit in the time domain. 2 10.2 Nodal Analysis The basic of Nodal Analysis is KCL. Example: Using nodal analysis, find v1 and v2 in the figure. 3 10.3 Mesh Analysis The basic of Mesh Analysis is KVL. Example: Find Io in the following figure using mesh analysis. 4 5 10.4 Superposition Theorem When a circuit has sources operating at different frequencies, • The separate phasor circuit for each frequency must be solved independently, and • The total response is the sum of time-domain responses of all the individual phasor circuits. Example: Calculate vo in the circuit using the superposition theorem. 6 4.3 Superposition Theorem (1) - Superposition states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltage across (or currents through) that element due to EACH independent source acting alone. -
Chung-Ang University School of Electrical and Electronics Engineering
Lecture 04 Chung-Ang University School of Electrical and Electronics Engineering Prof. Kwee-Bo SIM, Michael Circuit Theory Chapter 04 : Circuit Theorems Your success as an engineer will be directly proportional to your ability to communicate! - Charles K. Alexander ☞ Learning Objectives 2 Circuit Theory Chapter 04 : Circuit Theorems Your success as an engineer will be directly proportional to your ability to communicate! - Charles K. Alexander 4.1 Introduction A major advantage of analyzing circuits using Kirchhoff’s laws as we did in Chapter 3 is that we can analyze a circuit without tampering with its original configuration. A major disadvantage of this approach is that, for a large, complex circuit, tedious computation is involved. The growth in areas of application of electric circuits has led to an evolution from simple to complex circuits. To handle the complexity, engineers over the years have developed some theorems to simplify circuit analysis. Such theorems include Thevenin’s and Norton’s theorems. Since these theorems are applicable to linear circuits, we first discuss the concept of circuit linearity. In addition to circuit theorems, we discuss the concepts of superposition, source transformation, and maximum power transfer in this chapter. The concepts we develop are applied in the last section to source modeling and resistance measurement. 3 Circuit Theory Chapter 04 : Circuit Theorems Your success as an engineer will be directly proportional to your ability to communicate! - Charles K. Alexander 4.2 Linear Property (1/2) Linearity is the property of an element describing a linear relationship between cause and effect. Although the property applies to many circuit elements, we shall limit its applicability to resistors in this chapter. -
Phasor Analysis of Circuits
Phasor Analysis of Circuits Concepts Frequency-domain analysis of a circuit is useful in understanding how a single-frequency wave undergoes an amplitude change and phase shift upon passage through the circuit. The concept of impedance or reactance is central to frequency-domain analysis. For a resistor, the impedance is Z ω = R , a real quantity independent of frequency. For capacitors and R ( ) inductors, the impedances are Z ω = − i ωC and Z ω = iω L. In the complex plane C ( ) L ( ) these impedances are represented as the phasors shown below. Im ivL R Re -i/vC These phasors are useful because the voltage across each circuit element is related to the current through the equation V = I Z . For a series circuit where the same current flows through each element, the voltages across each element are proportional to the impedance across that element. Phasor Analysis of the RC Circuit R V V in Z in Vout R C V ZC out The behavior of this RC circuit can be analyzed by treating it as the voltage divider shown at right. The output voltage is then V Z −i ωC out = C = . V Z Z i C R in C + R − ω + The amplitude is then V −i 1 1 out = = = , V −i +ω RC 1+ iω ω 2 in c 1+ ω ω ( c ) 1 where we have defined the corner, or 3dB, frequency as 1 ω = . c RC The phasor picture is useful to determine the phase shift and also to verify low and high frequency behavior. The input voltage is across both the resistor and the capacitor, so it is equal to the vector sum of the resistor and capacitor voltages, while the output voltage is only the voltage across capacitor. -
Chapter 5: Circuit Theorems
Chapter 5: Circuit Theorems 1. Motivation 2. Source Transformation 3. Superposition (2.1 Linearity Property) 4. Thevenin’s Theorem 5. Norton’s Theorem 6. Maximum Power Transfer 7. Summary 1 5.1 Motivation If you are given the following circuit, are there any other alternative(s) to determine the voltage across 2Ω resistor? In Chapter 4, a circuit is analyzed without tampering with its original configuration. What are they? And how? Can we work it out by inspection? In Chapter 5, some theorems have been developed to simplify circuit analysis such as Thevenin’s and Norton’s theorems. The theorems are applicable to linear circuits. Discussion: Source Transformation, Linearity, & superposition. 2 5.2 Source Transformation (1) ‐ Like series‐parallel combination and wye‐delta transformation, source transformation is another tool for simplifying circuits. ‐ An equivalent circuit is one whose v-i characteristics are identical with the original circuit. ‐ A source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, and vice versa. • Transformation of independent sources The arrow of the current + + source is directed toward the positive terminal of the voltage source. ‐ ‐ • Transformation of dependent sources The source transformation + + is not possible when R = 0 for voltage source and R = ∞ for current source. 3 ‐ ‐ 5.2 Source Transformation (1) A voltage source vs connected in series with a resistor Rs and a current source is is connected in parallel with a resistor Rp are equivalent circuits provided that Rp Rs & vs Rsis 4 5.2 Source Transformation (3) Example: Find vo in the circuit using source transformation. -
Network Analysis
LECTURE NOTES ON NETWORK ANALYSIS B. Tech III Semester (IARE-R18) Ms. S Swathi Asistant professor ELECTRICAL AND ELECTRONICS ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) DUNDIGAL, HYDERABAD - 50043 1 SYLLABUS MODULE-I NETWORK THEOREMS (DC AND AC) Network Theorems: Tellegen‘s, superposition, reciprocity, Thevenin‘s, Norton‘s, maximum power transfer, Milliman‘s and compensation theorems for DC and AC excitations, numerical problems. MODULE-II SOLUTION OF FIRST AND SECOND ORDER NETWORKS Transient response: Initial conditions, transient response of RL, RC and RLC series and parallel circuits with DC and AC excitations, differential equation and Laplace transform approach. MODULE-III LOCUS DIAGRAMS AND NETWORKS FUNCTIONS Locus diagrams: Locus diagrams of RL, RC, RLC circuits. Network Functions: The concept of complex frequency, physical interpretation, transform impedance, series and parallel combination of elements, terminal ports, network functions for one port and two port networks, poles and zeros of network functions, significance of poles and zeros, properties of driving point functions and transfer functions, necessary conditions for driving point functions and transfer functions, time domain response from pole-zero plot. MODULE-IV TWO PORTNETWORK PARAMETERS Two port network parameters: Z, Y, ABCD, hybrid and inverse hybrid parameters, conditions for symmetry and reciprocity, inter relationships of different parameters, interconnection (series, parallel and cascade) of two port networks, image parameters. MODULE-V FILTERS Filters: Classification of filters, filter networks, classification of pass band and stop band, characteristic impedance in the pass and stop bands, constant-k low pass filter, high pass filter, m- derived T-section, band pass filter and band elimination filter. Text Books: 1. -
Current Source & Source Transformation Notes
EE301 – CURRENT SOURCES / SOURCE CONVERSION Learning Objectives a. Analyze a circuit consisting of a current source, voltage source and resistors b. Convert a current source and a resister into an equivalent circuit consisting of a voltage source and a resistor c. Evaluate a circuit that contains several current sources in parallel Ideal sources An ideal source is an active element that provides a specified voltage or current that is completely independent of other circuit elements. DC Voltage DC Current Source Source Constant Current Sources The voltage across the current source (Vs) is dependent on how other components are connected to it. Additionally, the current source voltage polarity does not have to follow the current source’s arrow! 1 Example: Determine VS in the circuit shown below. Solution: 2 Example: Determine VS in the circuit shown above, but with R2 replaced by a 6 k resistor. Solution: 1 8/31/2016 EE301 – CURRENT SOURCES / SOURCE CONVERSION 3 Example: Determine I1 and I2 in the circuit shown below. Solution: 4 Example: Determine I1 and VS in the circuit shown below. Solution: Practical voltage sources A real or practical source supplies its rated voltage when its terminals are not connected to a load (open- circuited) but its voltage drops off as the current it supplies increases. We can model a practical voltage source using an ideal source Vs in series with an internal resistance Rs. Practical current source A practical current source supplies its rated current when its terminals are short-circuited but its current drops off as the load resistance increases. We can model a practical current source using an ideal current source in parallel with an internal resistance Rs. -
33. RLC Parallel Circuit. Resonant Ac Circuits
University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II -- Lecture Notes PHY 204: Elementary Physics II (2021) 12-4-2020 33. RLC parallel circuit. Resonant ac circuits Gerhard Müller University of Rhode Island, [email protected] Robert Coyne University of Rhode Island, [email protected] Follow this and additional works at: https://digitalcommons.uri.edu/phy204-lecturenotes Recommended Citation Müller, Gerhard and Coyne, Robert, "33. RLC parallel circuit. Resonant ac circuits" (2020). PHY 204: Elementary Physics II -- Lecture Notes. Paper 33. https://digitalcommons.uri.edu/phy204-lecturenotes/33https://digitalcommons.uri.edu/ phy204-lecturenotes/33 This Course Material is brought to you for free and open access by the PHY 204: Elementary Physics II (2021) at DigitalCommons@URI. It has been accepted for inclusion in PHY 204: Elementary Physics II -- Lecture Notes by an authorized administrator of DigitalCommons@URI. For more information, please contact [email protected]. PHY204 Lecture 33 [rln33] AC Circuit Application (2) In this RLC circuit, we know the voltage amplitudes VR, VC, VL across each device, the current amplitude Imax = 5A, and the angular frequency ω = 2rad/s. • Find the device properties R, C, L and the voltage amplitude of the ac source. Emax ~ εmax A R C L V V V 50V 25V 25V tsl305 We pick up the thread from the previous lecture with the quantitative anal- ysis of another RLC series circuit. Here our reasoning must be in reverse direction compared to that on the last page of lecture 32. Given the -
5 RC Circuits
Physics 212 Lab Lab 5 RC Circuits What You Need To Know: The Physics In the previous two labs you’ve dealt strictly with resistors. In today’s lab you’ll be using a new circuit element called a capacitor. A capacitor consists of two small metal plates that are separated by a small distance. This is evident in a capacitor’s circuit diagram symbol, see Figure 1. When a capacitor is hooked up to a circuit, charges will accumulate on the plates. Positive charge will accumulate on one plate and negative will accumulate on the other. The amount of charge that can accumulate is partially dependent upon the capacitor’s capacitance, C. With a charge distribution like this (i.e. plates of charge), a uniform electric field will be created between the plates. [You may remember this situation from the Equipotential Surfaces lab. In the lab, you had set-ups for two point-charges and two lines of charge. The latter set-up represents a capacitor.] A main function of a capacitor is to store energy. It stores its energy in the electric field between the plates. Battery Capacitor (with R charges shown) C FIGURE 1 - Battery/Capacitor FIGURE 2 - RC Circuit If you hook up a battery to a capacitor, like in Figure 1, positive charge will accumulate on the side that matches to the positive side of the battery and vice versa. When the capacitor is fully charged, the voltage across the capacitor will be equal to the voltage across the battery. You know this to be true because Kirchhoff’s Loop Law must always be true. -
ELECTRICAL CIRCUIT ANALYSIS Lecture Notes
ELECTRICAL CIRCUIT ANALYSIS Lecture Notes (2020-21) Prepared By S.RAKESH Assistant Professor, Department of EEE Department of Electrical & Electronics Engineering Malla Reddy College of Engineering & Technology Maisammaguda, Dhullapally, Secunderabad-500100 B.Tech (EEE) R-18 MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY II Year B.Tech EEE-I Sem L T/P/D C 3 -/-/- 3 (R18A0206) ELECTRICAL CIRCUIT ANALYSIS COURSE OBJECTIVES: This course introduces the analysis of transients in electrical systems, to understand three phase circuits, to evaluate network parameters of given electrical network, to draw the locus diagrams and to know about the networkfunctions To prepare the students to have a basic knowledge in the analysis of ElectricNetworks UNIT-I D.C TRANSIENT ANALYSIS: Transient response of R-L, R-C, R-L-C circuits (Series and parallel combinations) for D.C. excitations, Initial conditions, Solution using differential equation and Laplace transform method. UNIT - II A.C TRANSIENT ANALYSIS: Transient response of R-L, R-C, R-L-C Series circuits for sinusoidal excitations, Initial conditions, Solution using differential equation and Laplace transform method. UNIT - III THREE PHASE CIRCUITS: Phase sequence, Star and delta connection, Relation between line and phase voltages and currents in balanced systems, Analysis of balanced and Unbalanced three phase circuits UNIT – IV LOCUS DIAGRAMS & RESONANCE: Series and Parallel combination of R-L, R-C and R-L-C circuits with variation of various parameters.Resonance for series and parallel circuits, concept of band width and Q factor. UNIT - V NETWORK PARAMETERS:Two port network parameters – Z,Y, ABCD and hybrid parameters.Condition for reciprocity and symmetry.Conversion of one parameter to other, Interconnection of Two port networks in series, parallel and cascaded configuration and image parameters. -
How to Design Analog Filter Circuits.Pdf
a b FIG. 1-TWO LOWPASS FILTERS. Even though the filters use different components, they perform in a similiar fashion. MANNlE HOROWITZ Because almost every analog circuit contains some filters, understandinghow to work with them is important. Here we'll discuss the basics of both active and passive types. THE MAIN PURPOSE OF AN ANALOG FILTER In addition to bandpass and band- age (because inductors can be expensive circuit is to either pass or reject signals rejection filters, circuits can be designed and hard to find); they are generally easier based on their frequency. There are many to only pass frequencies that are either to tune; they can provide gain (and thus types of frequency-selective filter cir- above or below a certain cutoff frequency. they do not necessarily have any insertion cuits; their action can usually be de- If the circuit passes only frequencies that loss); they have a high input impedance, termined from their names. For example, are below the cutoff, the circuit is called a and have a low output impedance. a band-rejection filter will pass all fre- lo~~passfilter, while a circuit that passes A filter can be in a circuit with active quencies except those in a specific band. those frequencies above the cutoff is a devices and still not be an active filter. Consider what happens if a parallel re- higlzpass filter. For example, if a resonant circuit is con- sonant circuit is connected in series with a All of the different filters fall into one . nected in series with two active devices signal source. -
The RC Circuit
The RC Circuit The RC Circuit Pre-lab questions 1. What is the meaning of the time constant, RC? 2. Show that RC has units of time. 3. Why isn’t the time constant defined to be the time it takes the capacitor to become fully charged or discharged? 4. Explain conceptually why the time constant is larger for increased resistance. 5. What does an oscilloscope measure? 6. Why can’t we use a multimeter to measure the voltage in the second half of this lab? 7. Draw and label a graph that shows the voltage across a capacitor that is charging and discharging (as in this experiment). 8. Set up a data table for part one. (V, t (0-300s in 20s intervals, 360, and 420s)) Introduction The goal in this lab is to observe the time-varying voltages in several simple circuits involving a capacitor and resistor. In the first part, you will use very simple tools to measure the voltage as a function of time: a multimeter and a stopwatch. Your lab write-up will deal primarily with data taken in this part. In the second part of the lab, you will use an oscilloscope, a much more sophisticated and powerful laboratory instrument, to observe time behavior of an RC circuit on a much faster timescale. Your observations in this part will be mostly qualitative, although you will be asked to make several rough measurements using the oscilloscope. Part 1. Capacitor Discharging Through a Resistor You will measure the voltage across a capacitor as a function of time as the capacitor discharges through a resistor.