DOCSLIB.ORG

We Are Working with Cambridge International Towards Endorsement of This Title

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
We Are Working with Cambridge International Towards Endorsement of This Title We are working with Cambridge International towards endorsement of this title. DRAFT Original material © Cambridge University Press 2019. This material is not final and is subject to further changes prior to publication. ISBN_Marketing_Sample.indd 1 23-Jul-19 6:52:07 AM We are working with Cambridge International towards endorsement of this title. Contents Contents How to use this series 00 3.4 Mass and inertia 000 3.5 Moving through fluids 000 How to use this book 00 3.6 Newton’s third law of motion 000 3.7 Understanding SI units 000 Introduction 00 4 Forces 000 1 Kinematics 000 4.1 Combining forces 000 1.1 Speed 000 4.2 Components of vectors 000 1.2 Distance and displacement, scalar 4.3 Centre of gravity 000 and vector 000 4.4 The turning effect of a force 000 1.3 Speed and velocity 000 4.5 The torque of a couple 000 1.4 Displacement–time graphs 000 1.5 Combining displacements 000 5 Work, energy and power 000 1.6 Combining velocities 000 5.1 Doing work, transferring energy 000 1.7 Subtracting vectors 000 5.2 Gravitational potential energy 000 1.8 Other examples of scalar and 5.3 Kinetic energy 000 vector quantities 000 5.4 Gravitational potential to kinetic energy transformations 000 2 Accelerated motion 000 5.5 Down, up, down: energy changes 000 2.1 The meaning of acceleration 000 5.6 Energy transfers 000 2.2 Calculating acceleration 000 5.7 Power 000 2.3 Units of acceleration 000 2.4 Deducing acceleration 000 6 Momentum 000 2.5 Deducing displacement 000 6.1 The idea of momentum 000 2.6 Measuring velocity and acceleration 000 6.2 Modelling collisions 000 2.7 Determining velocity and acceleration 6.3 Understanding collisions 000 in the laboratory 000 6.4 Explosions and crash-landings 000 2.8 The equations of motion 000 6.5 Collisions in two dimensions 000 2.9 Deriving the equations of motion 000 6.6 Momentum and Newton’s laws 000 2.10 Uniform and non-uniform acceleration 000 6.7 Understanding motion 000 2.11 Acceleration caused by gravity 000 2.12 Determining g 000 7 Matter and materials 000 2.13 Motion in two dimensions: projectiles 000 7.1 Density 000 2.14 UnderstandingDRAFT projectiles 000 7.2 Pressure 000 7.3 Archimedes’ principle 000 3 Dynamics 000 7.4 Compressive and tensile forces 000 3.1 Force, mass and acceleration 000 7.5 Stretching materials 000 3.2 Identifying forces 000 7.6 Elastic potential energy 000 3.3 Weight, friction and gravity 000 iii Original material © Cambridge University Press 2019. This material is not final and is subject to further changes prior to publication. ISBNpre_i-xii.indd 3 29-Jul-19 3:39:37 PM We are working with Cambridge International towards endorsement of this title. CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS: COURSEBOOK 8 Electric current 000 13.3 Interference 000 8.1 Circuit symbols and diagrams 000 13.4 The Young double-slit experiment 000 8.2 Electric current 000 13.5 Diffraction gratings 000 8.3 An equation for current 000 14 Stationary waves 000 8.4 The meaning of voltage 000 14.1 From moving to stationary 000 8.5 Electrical resistance 000 14.2 Nodes and antinodes 000 8.6 Electrical power 000 14.3 Formation of stationary waves 000 9 Kirchhoff’s laws 000 14.4 Determining the wavelength and speed of sound 000 9.1 Kirchhoff’s first law 000 9.2 Kirchhoff’s second law 000 15 Atomic structure 000 9.3 Applying Kirchhoff’s laws 000 15.1 Looking inside the atom 000 9.4 Resistor combinations 000 15.2 Alpha-particle scattering and the nucleus 000 10 Resistance and resistivity 000 15.3 A simple model of the atom 000 10.1 The I–V characteristic for a 15.4 Nucleons and electrons 000 metallic conductor 000 15.5 Forces in the nucleus 000 10.2 Ohm’s law 000 15.6 Discovering radioactivity 000 10.3 Resistance and temperature 000 15.7 Radiation from radioactive substances 000 10.4 Resistivity 000 15.8 Energies in a and β decay 000 11 Practical circuits 000 15.9 Equations of radioactive decay 000 11.1 Internal resistance 000 15.10 Fundamental particles 000 11.2 Potential dividers 000 15.11 Families of particles 000 11.3 Sensors 000 15.12 Another look at β decay 000 11.4 Potentiometer circuits 000 15.13 Another nuclear force 000 12 Waves 000 P1 Practical skills for AS 000 12.1 Describing waves 000 P1.1 Practical work in physics 000 12.2 Longitudinal and transverse waves 000 P1.2 Using apparatus and following instructions 000 12.3 Wave energy 000 P1.3 Gathering evidence 000 12.4 Wave speed 000 P1.4 Precision, accuracy, errors and 12.5 The Doppler effect for sound waves 000 uncertainties 000 12.6 Electromagnetic waves 000 P1.5 Finding the value of an uncertainty 000 12.7 Electromagnetic waves 000 P1.6 Percentage uncertainty 000 12.8 Orders of magnitude 000 P1.7 Recording results 000 12.9 The nature of electromagnetic waves 000 P1.8 Analysing results 000 12.10 Polarisation 000 DRAFTP1.9 Testing a relationship 000 13 Superposition of waves 000 P1.10 Combining uncertainties 000 13.1 The principle of superposition P1.11 Identifying limitations in of waves 000 procedures and suggesting improvements 000 13.2 Diffraction of waves 000 iv Original material © Cambridge University Press 2019. This material is not final and is subject to further changes prior to publication. ISBNpre_i-xii.indd 4 29-Jul-19 3:39:37 PM We are working with Cambridge International towards endorsement of this title. Contents 16 Circular motion 000 20.5 Changing temperature 000 16.1 Describing circular motion 000 20.6 Ideal gas equation 000 16.2 Angles in radians 000 20.7 Modelling gases: the kinetic model 000 16.3 Steady speed, changing velocity 000 20.8 Temperature and molecular kinetic energy 000 16.4 Angular speed 000 16.5 Centripetal forces 000 21 Uniform electric fields 000 16.6 Calculating acceleration and force 000 21.1 Attraction and repulsion 000 16.7 The origins of centripetal forces 000 21.2 The concept of an electric field 000 17 Gravitational fields 000 21.3 Electric field strength 000 21.4 Force on a charge 000 17.1 Representing a gravitational field 000 17.2 Gravitational field strengthg 000 22 Coulomb’s law 000 17.3 Energy in a gravitational field 000 22.1 Electric fields 000 17.4 Gravitational potential 000 22.2 Coulomb’s law 000 17.5 Orbiting under gravity 000 22.3 Electric field strength for a radial field 000 17.6 The orbital period 000 22.4 Electric potential 000 17.7 Orbiting the Earth 000 22.5 Gravitational and electric fields 000 18 Oscillations 23 Capacitance 000 18.1 Free and forced oscillations 000 23.1 Capacitors in use 000 18.2 Observing oscillations 000 23.2 Energy stored in a capacitor 000 18.3 Describing oscillations 000 23.3 Capacitors in parallel 000 18.4 Simple harmonic motion 000 23.4 Capacitors in series 000 18.5 Representing s.h.m. graphically 000 23.5 Comparing capacitors and resistors 000 18.6 Frequency and angular frequency 000 23.6 Capacitor networks 000 18.7 Equations of s.h.m. 000 23.7 Charge and discharge of capacitors 000 18.8 Energy changes in s.h.m. 000 18.9 Damped oscillations 000 24 Magnetic fields and 18.10 Resonance 000 electromagnetism 000 24.1 Producing and representing magnetic fields 19 Thermal physics 000 000 19.1 Changes of state 000 24.2 Magnetic force 000 19.2 Energy changes 000 24.3 Magnetic flux density 000 19.3 Internal energy 000 24.4 Measuring magnetic flux density 000 19.4 The meaning of temperature 000 24.5 Currents crossing fields 000 19.5 Thermometers 000 24.6 Forces between currents 000 19.6 Calculating energy changes 000 24.7 Relating SI units 000 DRAFT24.8 Comparing forces in magnetic, electric 20 Ideal gases 000 and gravitational fields 000 20.1 Particles of a gas 000 20.2 Explaining pressure 000 25 Motion of charged particles 000 20.3 Measuring gases 000 25.1 Observing the force 000 20.4 Boyle's law 000 25.2 Orbiting charged particles 000 v Original material © Cambridge University Press 2019. This material is not final and is subject to further changes prior to publication. ISBNpre_i-xii.indd 5 29-Jul-19 3:39:37 PM We are working with Cambridge International towards endorsement of this title. CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS: COURSEBOOK 25.3 Electric and magnetic fields 000 30 Medical imaging 000 25.4 The Hall effect 000 30.1 The nature and production of X-rays 000 25.5 Discovering the electron 000 30.2 X-ray attenuation 000 26 Electromagnetic induction 000 30.3 Improving X-ray images 000 30.4 Computerised axial tomography 000 26.1 Observing induction 000 30.5 Using ultrasound in medicine 000 26.2 Explaining electromagnetic induction 000 30.6 Echo sounding 000 26.3 Faraday’s law of electromagnetic induction 000 30.7 Ultrasound scanning 000 26.4 Lenz’s law 000 30.8 Positron Emission Tomography 000 26.5 Everyday examples of electromagnetic 31 Astronomy and cosmology 000 induction 000 31.1 Standard candles 000 27 Alternating currents 000 31.2 Luminosity and radiant flux intensity 000 27.1 Sinusoidal current 000 31.3 Stellar radii 000 27.2 Alternating voltages 000 31.4 The expanding Universe 000 27.3 Power and alternating current 000 P2 Planning, analysis 27.4 Rectification 000 and evaluation 000 28 Quantum physics 000 P2.1 Planning and analysis 000 28.1 Modelling with particles and waves 000 P2.2 Planning 000 28.2 Particulate nature of light 000 P2.3 Analysis of the data 000 28.3 The photoelectric effect 000 P2.4 Treatment of uncertainties 000 28.4 Threshold frequency and wavelength 000 P2.5 Conclusions and evaluation 28.5 Photons have momentum too 000 of results 000 28.6 Line spectra 000 Glossary 000 28.7 Explaining the origin of line spectra 000 28.8 Photon energies 000 Index 000 28.9 The nature of light: waves or particles? 000 28.10 Electron waves 000 28.11 Revisiting photons 000 29 Nuclear physics 000 29.1 Balanced equations 000 29.2 Mass and energy 000 29.3 Energy released in radioactive decay 000 29.4 Binding energy and stability 000 29.5 Randomness and radioactive decay 000 29.6 The mathematicsDRAFT of radioactive decay 000 29.7 Decay graphs and equations 000 29.8 Decay constant λ and half-life t1 000 2 vi Original material © Cambridge University Press 2019.
Load more

Recommended publications
  • Chapter 73 Mean and Root Mean Square Values
    CHAPTER 73 MEAN AND ROOT MEAN SQUARE VALUES EXERCISE 286 Page 778 1. Determine the mean value of (a) y = 3 x from x = 0 to x = 4 π (b) y = sin 2θ from θ = 0 to θ = (c) y = 4et from t = 1 to t = 4 4 3/2 4 44 4 4 1 1 11/2 13x 13 (a) Mean value, y= ∫∫ yxd3d3d= xx= ∫ x x= = x − 00 0 0 4 0 4 4 4 3/20 2 1 11 = 433=( 2) = (8) = 4 2( ) 22 π /4 1 ππ/4 4 /4 4 cos 2θπ 2 (b) Mean value, yy=dθ = sin 2 θθ d =−=−−cos 2 cos 0 π ∫∫00ππ24 π − 0 0 4 2 2 = – (01− ) = or 0.637 π π 144 1 144 (c) Mean value, y= yxd= 4ett d t = 4e = e41 − e = 69.17 41− ∫∫11 3 31 3 2. Calculate the mean value of y = 2x2 + 5 in the range x = 1 to x = 4 by (a) the mid-ordinate rule and (b) integration. (a) A sketch of y = 25x2 + is shown below. 1146 © 2014, John Bird Using 6 intervals each of width 0.5 gives mid-ordinates at x = 1.25, 1.75, 2.25, 2.75, 3.25 and 3.75, as shown in the diagram x 1.25 1.75 2.25 2.75 3.25 3.75 y = 25x2 + 8.125 11.125 15.125 20.125 26.125 33.125 Area under curve between x = 1 and x = 4 using the mid-ordinate rule with 6 intervals ≈ (width of interval)(sum of mid-ordinates) ≈ (0.5)( 8.125 + 11.125 + 15.125 + 20.125 + 26.125 + 33.125) ≈ (0.5)(113.75) = 56.875 area under curve 56.875 56.875 and mean value = = = = 18.96 length of base 4− 1 3 3 4 44 1 1 2 1 2x 1 128 2 (b) By integration, y= yxd = 2 x + 5 d x = +5 x = +20 −+ 5 − ∫∫11 41 3 3 31 3 3 3 1 = (57) = 19 3 This is the precise answer and could be obtained by an approximate method as long as sufficient intervals were taken 3.
    [Show full text]
  • True RMS, Trueinrush®, and True Megohmmeter®
    “WATTS CURRENT” TECHNICAL BULLETIN Issue 09 Summer 2016 True RMS, TrueInRush®, and True Megohmmeter ® f you’re a user of AEMC® instruments, you may have come across the terms True IRMS, TrueInRush®, and/or True Megohmmeter ®. In this article, we’ll briefly define what these terms mean and why they are important to you. True RMS The most well-known of these is True RMS, an industry term for a method for calculating Root Mean Square. Root Mean Square, or RMS, is a mathematical concept used to derive the average of a constantly varying value. In electronics, RMS provides a way to measure effective AC power that allows you to compare it to the equivalent heating value of a DC system. Some low-end instruments employ a technique known as “average sensing,” sometimes referred to as “average RMS.” This entails multiplying the peak AC voltage or current by 0.707, which represents the decimal form of one over the square root of two. For electrical systems where the AC cycle is sinusoidal and reasonably undistorted, this can produce accurate and reliable results. Unfortunately, for other AC waveforms, such as square waves, this calculation can introduce significant inaccuracies. The equation can also be problematic when the AC wave is non-linear, as would be found in systems where the original or fundamental wave is distorted by one or more harmonic waves. In these cases, we need to apply a method known as “true” RMS. This involves a more generalized mathematical calculation that takes into consideration all irregularities and asymmetries that may be present in the AC waveform: In this equation, n equals the number of measurements made during one complete cycle of the waveform.
    [Show full text]
  • Basic Statistics = ∑
    Basic Statistics, Page 1 Basic Statistics Author: John M. Cimbala, Penn State University Latest revision: 26 August 2011 Introduction The purpose of this learning module is to introduce you to some of the fundamental definitions and techniques related to analyzing measurements with statistics. In all the definitions and examples discussed here, we consider a collection (sample) of measurements of a steady parameter. E.g., repeated measurements of a temperature, distance, voltage, etc. Basic Definitions for Data Analysis using Statistics First some definitions are necessary: o Population – the entire collection of measurements, not all of which will be analyzed statistically. o Sample – a subset of the population that is analyzed statistically. A sample consists of n measurements. o Statistic – a numerical attribute of the sample (e.g., mean, median, standard deviation). Suppose a population – a series of measurements (or readings) of some variable x is available. Variable x can be anything that is measurable, such as a length, time, voltage, current, resistance, etc. Consider a sample of these measurements – some portion of the population that is to be analyzed statistically. The measurements are x1, x2, x3, ..., xn, where n is the number of measurements in the sample under consideration. The following represent some of the statistics that can be calculated: 1 n Mean – the sample mean is simply the arithmetic average, as is commonly calculated, i.e., x xi , n i1 where i is one of the n measurements of the sample. o We sometimes use the notation xavg instead of x to indicate the average of all x values in the sample, especially when using Excel since overbars are difficult to add.
    [Show full text]
  • Physics 115A: Statistical Physics
    Physics 115A: Statistical Physics Prof. Clare Yu email: [email protected] phone: 949-824-6216 Office: 210E RH Fall 2013 LECTURE 1 Introduction So far your physics courses have concentrated on what happens to one object or a few objects given an external potential and perhaps the interactions between objects. For example, Newton’s second law F = ma refers to the mass of the object and its acceleration. In quantum mechanics, one starts with Schroedinger’s equation Hψ = Eψ and solves it to find the wavefunction ψ which describes a particle. But if you look around you, the world has more than a few particles and objects. The air you breathe and the coffee you drink has lots and lots of atoms and molecules. Now you might think that if we can describe each atom or molecule with what we know from classical mechanics, quantum mechanics, and electromagnetism, we can just scale up and describe 1023 particles. That’s like saying that if you can cook dinner for 3 people, then just scale up the recipe and feed the world. The reason we can’t just take our solution for the single particle problem and multiply by the number of particles in a liquid or a gas is that the particles interact with one another, i.e., they apply a force on each other. They see the potential produced by other particles. This makes things really complicated. Suppose we have a system of N interacting particles. Using Newton’s equations, we would write: d~p d2~x i = m i = F~ = V (~x , ~x , ..., ~x ) (1) dt dt2 ij −∇ i 1 2 N Xj6=i where F~ij is the force on the ith particle produced by the jth particle.
    [Show full text]
  • Glossary of Transportation Construction Quality Assurance Terms
    TRANSPORTATION RESEARCH Number E-C235 August 2018 Glossary of Transportation Construction Quality Assurance Terms Seventh Edition TRANSPORTATION RESEARCH BOARD 2018 EXECUTIVE COMMITTEE OFFICERS Chair: Katherine F. Turnbull, Executive Associate Director and Research Scientist, Texas A&M Transportation Institute, College Station Vice Chair: Victoria A. Arroyo, Executive Director, Georgetown Climate Center; Assistant Dean, Centers and Institutes; and Professor and Director, Environmental Law Program, Georgetown University Law Center, Washington, D.C. Division Chair for NRC Oversight: Susan Hanson, Distinguished University Professor Emerita, School of Geography, Clark University, Worcester, Massachusetts Executive Director: Neil J. Pedersen, Transportation Research Board TRANSPORTATION RESEARCH BOARD 2017–2018 TECHNICAL ACTIVITIES COUNCIL Chair: Hyun-A C. Park, President, Spy Pond Partners, LLC, Arlington, Massachusetts Technical Activities Director: Ann M. Brach, Transportation Research Board David Ballard, Senior Economist, Gellman Research Associates, Inc., Jenkintown, Pennsylvania, Aviation Group Chair Coco Briseno, Deputy Director, Planning and Modal Programs, California Department of Transportation, Sacramento, State DOT Representative Anne Goodchild, Associate Professor, University of Washington, Seattle, Freight Systems Group Chair George Grimes, CEO Advisor, Patriot Rail Company, Denver, Colorado, Rail Group Chair David Harkey, Director, Highway Safety Research Center, University of North Carolina, Chapel Hill, Safety and Systems
    [Show full text]
  • Power Transmission [120 Marks]
    Power transmission [120 marks] t I 1. The graph shows the variation with time of the current in the primary coil of an ideal transformer. [1 mark] The number of turns in the primary coil is 100 and the number of turns in the secondary coil is 200. Which graph shows the variation with time of the current in the secondary coil? 2. The diagram shows a diode bridge rectification circuit and a load resistor. [1 mark] The input is a sinusoidal signal. Which of the following circuits will produce the most smoothed output signal? The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root 3. [1 mark] mean square voltage (Vrms) 60 V. What are the frequency of the ac power supply and the average power dissipated in the resistor? A capacitor consists of two parallel square plates separated by a vacuum. The plates are 2.5 cm × 2.5 cm squares. The capacitance of the capacitor is 4.3 pF. Calculate the distance between the plates. 4a. [1 mark] 4b. The capacitor is connected to a 16 V cell as shown. [2 marks] Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged. ε ε 4c. The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity = 3.0 0. [2 marks] Explain whether the magnitude of the charge on plate A increases, decreases or stays constant. In a different circuit, a transformer is connected to an alternating current (ac) supply.
    [Show full text]
  • Sinusoidal Response and Phasor Transformation
    EECE 301 Network Analysis II Dr. Charles Kim Class Note 10: Steady-State Sinusoidal Response and Phasor Transformation A. Steady-State Sinusoidal Response---S-domain perspective 1. Sinusoidal Source (i) Periodic ( cosine or sine) function with period T, where T = 2π / w . (ii)Expressed by: Max (or peak) value, Angular Speed (w), and Phase angle(φ) = + φ v(t) Vm cos(wt ) (iii) "Average", "Mean-Square", and "Root-Mean-Square (RMS)" values: t +T 1 o Time Average (or "DC equivalent" or "DC" value): v(t) = ∫v(t)dt T to t +T 1 o Mean-Square Value (or "Normalized Power): v2 (t) = ∫v2 (t)dt T to + 1 to T RMS (or "Effective Value"): v(t) = ∫v2 (t)dt RMS T t0 2. Steady-State Response of a sinusoidal source---S-Domain Perspective (i) There could be another discussion on this in differential equation perspective (ii) Since we just passed through s-domain and transfer function, we see in s-domain's perspective. (iii)From the discussion of steady-state sinusoidal response, we had the following formula: y(t) = A | H ( jw) | cos[wt + φ + θ (w)] , where, input is given with x(t) = Acos[wt + φ] |H(jw)| is the magnitude of the steady-state transfer function of a circuit. and, θ(w) is the phase angle of the steady-state transfer function H(jw) (iv) If we compare the input and the output (response), the input frequency is kept intact, while the magnitude and phase angle are changed. (v) Also, the magnitude and the phase angle change is determined by the steady-state transfer function of a circuit, and the transfer function is also determined by the circuit elements, (R, L, and C) (vi) Therefore, if we ignore the frequency (which does not change), we can express the sinusoidal inputs and outputs only with magnitudes and phase angles.---> This is the basic idea behind the Phasor Transformation.
    [Show full text]
  • Chapter24-1.Pdf
    Chapter 24 Alternating-Current Circuit Outline 24-1 Alternating Voltage and Circuit 24-1 Alternating Voltage and Circuit In an alternating circuit, the magnitude and direction of the voltage and current change periodically, and they are a function of time: The current and voltage is the so-called alternating current (AC) and voltage, respectively. Figure 24-1 An AC Generator Connected to a Lamp V = Vmax sinωt (24 −1) Where, ω = 2πf, (f = 60 Hz). According to Ohm’s law, V V I = = max sinωt = I sinωt R R max Root Mean Square (rms) Value Both alternating voltage and current have a zero value. So direct average gives no information (or useless). IdtIn order to eval ltuate an alt lttiernating parame titer in quan tity, we use root mean square (rms): We square the alternating current I, I 2 = I 2 sin 2 ωt max Now, we can average I2, 1 (I 2 ) = I 2 av 2 max RMS is square root of the above eq., 1 I = I rms 2 max Rms: Square, average, square root Any quantity x that varies with time as x=xmaxsinωt, or x=xmaxcosωt, obey the relationships: RMS Value of a Quantity with Sinusoid Time Dependence 1 (x2 ) = x2 av 2 max 1 x = x (24 − 4) rms 2 max So, the rms value of the voltage in a AC circuit is 1 V = V (24 − 5) rms 2 max Also suitable for current ! Exercise 24-1 Typical household circuit operates with an rms voltage of 120V. What is the maximum, or peak value of the voltage in the circuit? Solution 1 Since V = V , we have rms 2 max The maximum and peak is: VVmax ==2rms 2(120 V ) = 170 V “Average” Power Since P = I2 R, Replace I with Irms, we have the average value of P 2 Pav = Irms R Apply Ohm’s law, V 2 P = rms (24 − 6) av R Rms can operate directly for Ohm law ! A Resistor Circuit An AC generator with a maximum voltage of 24.0 V and a frequency of 60.0 Hz is connected to a resistor with a resistance R= 265 Ω.
    [Show full text]
  • Functional Waveforms for Electronics
    4/6/2017 Functional Waveforms for Electronics Lesson 16 EET 150 Learning Objectives In this lesson you will: see typical waveforms used in electronic circuits learn how to identify these waveforms by their shape identify the amplitudes of these waves learn where these waves are used see what instruments can produce and measure waveforms 1 4/6/2017 Common Waveforms-Sine Wave Sine Waveform 3 3 Characteristics 2 Amplitude Measures RMS 1 Peak Peak-to-peak value Peak v(t) 0 to Peak value Amplitude Amplitude Peak 1 Measured with zero reference 2 3 Root Mean Square 3 0 2 4 6 8 10 (RMS) Value 0 t 10 Time 0.707 of Peak Value RMS factor of 0.707 only valid for Sine waves Sine waves used to test amplifiers Common Waveforms-Sine Wave Example What is peak-to-peak value of the waveform shown? What is peak 1.414 value of the V RMS 2 Vp waveform shown? 4 Vpp What is RMS value of the waveform shown? VRMS =0.707(2) VRMS = 1.414 V 2 4/6/2017 Common Waveforms-Sine Wave Sine wave with DC offset DC offset Sine Waveform raises entire 6 6 wave above zero 4 2.5 Waveform v(t) 2 Symmetric about 2.5 Amplitude +2.5 0 DC offsets can 2 be either 3 positive or 0 2 4 6 8 10 negative 0 t 10 Time Common Waveforms-Square Wave Square Wave Voltage Measures 3 3 Peak-to-peak value RMS 2 Peak value 1 Peak Peak Measured with zero s(t) to reference 0 Peak Amplitude 1 Root Mean Square (RMS) Value 2 3 Equals peak value 3 0 2 4 6 8 10 0 t 10 Square wave can Time Be off set with DC 3 4/6/2017 Common Waveforms-Pulse Train Pulse Train has only positive values Signal used in computer circuits.
    [Show full text]
  • Alternating Voltage
    ALTERNATING VOLTAGE AC (Alternating Current) waveforms refer to continually changing time‐varying voltages and currents. The magnitude and direction of these voltages and currents vary in a set manner from a minimum to a maximum value, in a specific time interval. This is in contrast to DC (Direct Current), where currents or voltages do not change in magnitude or direction. AC waveforms can be sinusoidal (sine wave), square or triangular. The only waveform available in nature is the sinusoidal. The square and the triangular waveforms are made from sinusoidal waveforms with the help of electronic circuitry. The voltage-time graph shows various properties of an electrical signal. The diagram shows a sine wave but these properties apply to any signal with a constant shape. Periodic Waveform is a waveform that continuously repeats itself. Period (T) is the time interval in seconds that the waveform takes to repeat itself from start. Frequency (f) is the number of times the waveform repeats itself within a one second time period. Frequency is the reciprocal of the time period, (ƒ = 1/T) with the unit Hz. Instantaneous Value (v) is the voltage of the waveform at any instant of time. Amplitude or Maximum or Peak Value (Vp) is the maximum voltage of the waveform using the zero level as reference. Peak‐to‐Peak Value (Vp‐p) is the voltage between the positive peak (maximum) and the negative peak (minimum) and is twice the peak voltage (amplitude). Root-Mean-Square (RMS) or Effective Value (Vrms) is the amount of DC voltage that is required for producing the same amount of power as the AC waveform.
    [Show full text]
  • Harmonics What Are They.Pdf
    Harmonics - what are they. how to measure them and how to solve the problem (in connection with Standards IEEE 1 159- 1995 & IEEE 5 19- 1992 ). AVISHAI RASH BScEE&PE Consulting Engineer Yericho 1 P.O.Box 39292 Tel-Aviv 61392 Phone & Fax : 03-6043807 Celular : 050-349030 E-mail : a [email protected] It is common these days to hear or to read with frequencies of 50-100-150-200-250 about “Harmonics” . In fact if we use this ....2500Hz ... that are added to the expression alone without any additional fundamental on a steady state base , as term or without any connection to a opposed to instantaneous disturbings physical value it has no electrical (dropout, dip, sag, notch, swell, etc..) meaning. Harmonics exist in power systems and are 0 What are Harmonics ? ( Basic terms ) known for years , so why should we care To express a deviation from a pure sine about them today ? wave usually the term Harmonics The main reasons are : components is used .Together with the -Harmonics are harming many consumers use of the term “Harmonics” we mention in the power supply networks . the name of the famous mathematician -Accorbg to new standards tcday the level Fourier who developed a mathematical of harmonics in the supply network is way to investigate a complex wave and to limited. express it in a form that is simple and -Due to harmonics existence available useful. power is reduced . These are the main reasons why these T” days we hear more about harmonics and other kind of disturbances in the power supply network .Together with the growth in awareness to harmonics two phenomena arose : -Many people began to deal with harmonics.
    [Show full text]
  • The Mean Value and the Root-Mean-Square Value 14.2   
    The Mean Value and the Root-Mean-Square Value 14.2 Introduction Currents and voltages often vary with time and engineers may wish to know the mean value of such a current or voltage over some particular time interval. The mean value of a time-varying function is defined in terms of an integral. An associated quantity is the root-mean-square (r.m.s). For example, the r.m.s. value of a current is used in the calculation of the power dissipated by a resistor. • be able to calculate definite integrals Prerequisites • be familiar with a table of trigonometric Before starting this Section you should ... identities • calculate the mean value of a function Learning Outcomes • calculate the root-mean-square value of a On completion you should be able to ... function 10 HELM (2008): Workbook 14: Applications of Integration 1 ® 1. Average value of a function Suppose a time-varying function f(t) is defined on the interval a ≤ t ≤ b. The area, A, under the Z b graph of f(t) is given by the integral A = f(t) dt. This is illustrated in Figure 5. a f(t) f(t) m a b t a b t (a) the area under the curve from t = a to t = b (b) the area under the curve and the area of the rectangle are equal Figure 5 On Figure 3 we have also drawn a rectangle with base spanning the interval a ≤ t ≤ b and which has the same area as that under the curve. Suppose the height of the rectangle is m.
    [Show full text]