Experiment 6: Ohm's Law, RC and RL 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. -
Time Constant of an Rc Circuit
ECGR 2155 Instrumentation and Networks Laboratory UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering EXPERIMENT 10 – TIME CONSTANT OF AN RC CIRCUIT OBJECTIVES The purpose of this experiment is to measure the time constant of an RC circuit experimentally and to verify the results against the values obtained by theoretical calculations. MATERIALS/EQUIPMENT NEEDED Digital Multimeter DC Power Supply Alligator (Clips) Jumper Resistor: 20kΩ Capacitor: 2,200 µF (rating = 50V or more) INTRODUCTION The time constant of RC circuits are used extensively in electronics for timing (setting oscillator frequencies, adjusting delays, blinking lights, etc.). It is necessary to understand how RC circuits behave in order to analyze and design timing circuits. In the circuit of Figure 10-1 with the switch open, the capacitor is initially uncharged, and so has a voltage, Vc, equal to 0 volts. When the single-pole single-throw (SPST) switch is closed, current begins to flow, and the capacitor begins to accumulate stored charge. Since Q=CV, as stored charge (Q) increases the capacitor voltage (Vc) increases. However, the growth of capacitor voltage is not linear; in fact it is an exponential growth. The formula which gives the instantaneous voltage across the capacitor as a function of time is (−t ) VV=1 − eτ cS Figure 10-1 Series RC Circuit EXPERIMENT 10 – TIME CONSTANT OF AN RC CIRCUIT 1 ECGR 2155 Instrumentation and Networks Laboratory This formula describes exponential growth, in which the capacitor is initially 0 volts, and grows to a value of near Vs after a finite amount of time. -
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. -
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. -
Lab 5 AC Concepts and Measurements II: Capacitors and RC Time-Constant
Sonoma State University Department of Engineering Science Fall 2017 EE110 Laboratory Introduction to Engineering & Laboratory Experience Lab 5 AC Concepts and Measurements II: Capacitors and RC Time-Constant Capacitors Capacitors are devices that can store electric charge similar to a battery (but with major differences). In its simplest form we can think of a capacitor to consist of two metallic plates separated by air or some other insulating material. The capacitance of a capacitor is referred to by C (in units of Farad, F) and indicates the ratio of electric charge Q accumulated on its plates to the voltage V across it (C = Q/V). The unit of electric charge is Coulomb. Therefore: 1 F = 1 Coulomb/1 Volt). Farad is a huge unit and the capacitance of capacitors is usually described in small fractions of a Farad. The capacitance itself is strictly a function of the geometry of the device and the type of insulating material that fills the gap between its plates. For a parallel plate capacitor, with the plate area of A and plate separation of d, C = (ε A)/d, where ε is the permittivity of the material in the gap. The formula is more complicated for cylindrical and other geometries. However, it is clear that the capacitance is large when the area of the plates are large and they are closely spaced. In order to create a large capacitance, we can increase the surface area of the plates by rolling them into cylindrical layers as shown in the diagram above. Note that if the space between plates is filled with air, then C = (ε0 A)/d, where ε0 is the permittivity of free space. -
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. -
(ECE, NDSU) Lab 11 – Experiment Multi-Stage RC Low Pass Filters
ECE-311 (ECE, NDSU) Lab 11 – Experiment Multi-stage RC low pass filters 1. Objective In this lab you will use the single-stage RC circuit filter to build a 3-stage RC low pass filter. The objective of this lab is to show that: As more stages are added, the filter becomes able to better reject high frequency noise When plotted on a Bode plot, the gain approaches two asymptotes: the low frequency gain approaches a constant gain of 0dB while the high-frequency gain drops as 20N dB/decade where N is the number of stages. 2. Background The single stage RC filter is a low pass filter: low frequencies are passed (have a gain of one), while high frequencies are rejected (the gain goes to zero). This is a useful filter to remove noise from a signal. Many types of signals are predominantly low-frequency in nature - meaning they change slowly. This includes measurements of temperature, pressure, volume, position, speed, etc. Noise, however, tends to be at all frequencies, and is seen as the “fuzzy” line on you oscilloscope when you amplify the signal. The trick when designing a low-pass filter is to select the RC time constant so that the gain is one over the frequency range of your signal (so it is passed unchanged) but zero outside this range (to reject the noise). 3. Theoretical response One problem with adding stages to an RC filter is that each new stage loads the previous stage. This loading consumes or “bleeds” some current from the previous stage capacitor, changing the behavior of the previous stage circuit. -
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. -
Time Constant Calculations This Worksheet and All Related Files Are
Time constant calculations This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/, or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and conditions of this license allow for free copying, distribution, and/or modification of all licensed works by the general public. Resources and methods for learning about these subjects (list a few here, in preparation for your research): 1 Questions Question 1 Qualitatively determine the voltages across all components as well as the current through all components in this simple RC circuit at three different times: (1) just before the switch closes, (2) at the instant the switch contacts touch, and (3) after the switch has been closed for a long time. Assume that the capacitor begins in a completely discharged state: Before the At the instant of Long after the switch switch closes: switch closure: has closed: C C C R R R Express your answers qualitatively: ”maximum,” ”minimum,” or perhaps ”zero” if you know that to be the case. Before the switch closes: VC = VR = Vswitch = I = At the instant of switch closure: VC = VR = Vswitch = I = Long after the switch has closed: VC = VR = Vswitch = I = Hint: a graph may be a helpful tool for determining the answers! file 01811 2 Question 2 Qualitatively determine the voltages across all components as well as the current through all components in this simple LR circuit at three different times: (1) just before the switch closes, (2) at the instant the switch contacts touch, and (3) after the switch has been closed for a long time. -
Cutoff Frequency, Lightning, RC Time Constant, Schumann Resonance, Spherical Capacitance
International Journal of Theoretical and Mathematical Physics 2019, 9(5): 121-130 DOI: 10.5923/j.ijtmp.20190905.01 Solar System Electrostatic Motor Theory Greg Poole Industrial Tests, Inc., Rocklin, CA, United States Abstract In this paper, the solar system has been visualized as an electrostatic motor for the research of scientific concepts. The Earth and space have all been represented as spherical capacitors to derive time constants from simple RC theory. Using known wave impedance values (R) from antenna theory and celestial capacitance (C) several time constants are derived which collectively represent time itself. Equations from Electro Relativity are verified using known values and constants to confirm wave impedance values are applicable to the earth antenna. Dark energy can be represented as a tremendous capacitor voltage and dark matter as characteristic transmission line impedance. Cosmic energy transfer may be limited to the known wave impedance of 377 Ω. Harvesting of energy wirelessly at the Earth’s surface or from the Sun in space may be feasible by matching the power supply source impedance to a load impedance. Separating the various the three fields allows us to see how high-altitude lightning is produced and the earth maintains its atmospheric voltage. Spacetime, is space and time, defined by the radial size and discharge time of a spherical or toroid capacitor. Keywords Cutoff Frequency, Lightning, RC Time Constant, Schumann Resonance, Spherical Capacitance the nearest thimble, and so put the wheel in motion; that 1. Introduction thimble, in passing by, receives a spark, and thereby being electrified is repelled and so driven forwards; while a second In 1749, Benjamin Franklin first invented the electrical being attracted, approaches the wire, receives a spark, and jack or electrostatic wheel.