Potential Dividers. 46 minutes. 46 marks. Page 1 of 11
|
|
|
- Θεοφιλά Παππάς
- 8 χρόνια πριν
- Προβολές:
Transcript
1 Potential Dividers 46 minutes 46 marks Page 1 of 11
2 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and its resistance is 12 Ω. (a) Show that the total resistance of the circuit is 20 Ω (3) (b) Calculate (i) the current supplied by the battery, (ii) the pd between the points A and B, (iii) the current in the lamp. (4) Page 2 of 11
3 (c) (i) What is the power of the lamp, in W? (ii) What percentage of the power supplied by the battery is dissipated in the lamp? (3) (Total 10 marks) Q2. (a) A student wishes to investigate how the resistance of a thermistor changes with temperature. (i) Draw a labelled diagram of a suitable circuit that would enable the student to measure the resistance of the thermistor. Page 3 of 11
4 (ii) Describe the procedure the student would follow in order to obtain accurate and reliable measurements of the resistance of the thermistor at different temperatures. The quality of your written communication will be assessed in this question. (6) (b) The diagram below shows a thermistor connected in series with a resistor, R, and battery of emf 6.0 V and negligible internal resistance. When the temperature is 50 C the resistance of the thermistor is 1.2 kω. The voltmeter connected across R reads 1.6V. (i) Calculate the pd across the thermistor. answer =... V (1) Page 4 of 11
5 (ii) Calculate the current in the circuit. answer =... A (1) (iii) Calculate the resistance of R quoting your answer to an appropriate number of significant figures. answer =... Ω (c) State and explain the effect on the voltmeter reading if the internal resistance of the battery in the circuit in part (b) was not negligible (Total 14 marks) Page 5 of 11
6 Q3. In the circuit shown in the figure below, the battery, of negligible internal resistance, is connected to two resistors which form a potential divider. (a) (i) Calculate the current through the ammeter. (ii) A 20 Ω resistor is now connected between X and Y. State and explain, without further calculation, whether the current through the ammeter will increase or decrease. You may be awarded marks for the quality of written communication in your answer. (4) (b) The 20 Ω resistor is now removed and replaced with a voltmeter. Stating the assumption made, show that the reading on the voltmeter is 4.9 V Page 6 of 11
7 (c) The voltmeter is now removed and the terminals X and Y joined together with a wire. Calculate the reading on the ammeter (Total 8 marks) Q4. (a) In the circuit shown in Figure 1, the battery has an emf of 12 V and negligible internal resistance. PQ is a potential divider, S being the position of the sliding contact. In the position shown, the resistance between P and S is 180 Ω and the resistance between S and Q is 60 Ω. Figure 1 (i) Calculate the current, I, in the circuit, assuming that there is no current through the voltmeter V. (ii) What property of the voltmeter allows us to assume that no current flows through it? (iii) What is the reading on the voltmeter? (4) Page 7 of 11
8 (b) The circuit in Figure 1 is modified as shown in Figure 2, by exchanging the voltmeter for a load R, whose resistance is about the same as the resistance of section SQ of the potential divider. Figure 2 Explain, without calculation, why the current through the battery increases in value from that in part (a). You may be awarded marks for the quality of written communication in your answer (Total 6 marks) Page 8 of 11
9 Q5. The figure below shows two resistors, R 1 and R 2, connected in series with a battery of emf 12 V and negligible internal resistance. (a) The reading on the voltmeter is 8.0 V and the resistance of R 2 is 60 Ω. (i) Calculate the current in the circuit. answer =... A (ii) Calculate the resistance of R 1. answer =... Ω (1) (iii) Calculate the charge passing through the battery in 2.0 minutes. Give an appropriate unit for your answer. answer =... unit =... Page 9 of 11
10 (b) In the circuit shown in the figure above R 2 is replaced with a thermistor. State and explain what will happen to the reading on the voltmeter as the temperature of the thermistor increases (3) (Total 8 marks) Page 10 of 11
11 Page 11 of 11
the total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
PHYA1 (JAN12PHYA101) General Certificate of Education Advanced Subsidiary Examination January 2012. Particles, Quantum Phenomena and Electricity TOTAL
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data
[1] P Q. Fig. 3.1
![[1] P Q. Fig. 3.1](/thumbs/79/80362156.jpg "[1] P Q. Fig. 3.1")
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
PHYA1. General Certificate of Education Advanced Subsidiary Examination June 2012. Particles, Quantum Phenomena and Electricity
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data
(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)
Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)
What is meter P measuring?... What is meter Q measuring?...
1 The diagram shows an electrical circuit. (a) (b) Complete the two labels on the diagram. P and Q are meters. What is meter P measuring?... What is meter Q measuring?... (Total 4 marks) Page 1 of 24 2
PhysicsAndMathsTutor.com 1
PhysicsAndMathsTutor.com 1 Q1. The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value
PHYA1 (JAN13PHYA101) General Certificate of Education Advanced Subsidiary Examination January Particles, Quantum Phenomena and Electricity TOTAL
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data
PHYA1 (JUN13PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2013. Particles, Quantum Phenomena and Electricity TOTAL
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data
Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O
Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.
Figure 1 T / K Explain, in terms of molecules, why the first part of the graph in Figure 1 is a line that slopes up from the origin.
Q1.(a) Figure 1 shows how the entropy of a molecular substance X varies with temperature. Figure 1 T / K (i) Explain, in terms of molecules, why the entropy is zero when the temperature is zero Kelvin.
Capacitors - Capacitance, Charge and Potential Difference
Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal
PHYA1 (JUN14PHYA101) General Certificate of Education Advanced Subsidiary Examination June 2014. Particles, Quantum Phenomena and Electricity TOTAL
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A Unit 1 For this paper you must have: l a pencil and a ruler l a calculator l a Data
PHYA4/2. (JUN14PHYA4201) WMP/Jun14/PHYA4/2/E4. General Certificate of Education Advanced Level Examination June 2014
Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Physics A General Certificate of Education Advanced Level Examination June 2014 PHYA4/2 Question
Advanced Subsidiary Unit 1: Understanding and Written Response
Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes
4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Modern Greek Extension
Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write
Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is
Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³
Nuclear Physics 5. Name: Date: 8 (1)
Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes
Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference
In your answer, you should make clear how evidence for the size of the nucleus follows from your description
1. Describe briefly one scattering experiment to investigate the size of the nucleus of the atom. Include a description of the properties of the incident radiation which makes it suitable for this experiment.
2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Example Sheet 3 Solutions
Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note
Enthalpy data for the reacting species are given in the table below. The activation energy decreases when the temperature is increased.
Q1.This question is about the reaction given below. O(g) + H 2O(g) O 2(g) + H 2(g) Enthalpy data for the reacting species are given in the table below. Substance O(g) H 2O(g) O 2(g) H 2(g) ΔH / kj mol
Τελική Εξέταση =1 = 0. a b c. Τµήµα Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών. HMY 626 Επεξεργασία Εικόνας
Τελική Εξέταση. Logic Operations () In the grid areas provided below, draw the results of the following binary operations a. NOT(NOT() OR ) (4) b. ( OR ) XOR ( ND ) (4) c. (( ND ) XOR ) XOR (NOT()) (4)
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education PHYSICS 0625/03
www.xtremepapers.com Centre Number Candidate Number Name CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education PHYSICS 0625/03 Paper 3 Candidates answer on the Question
ST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Friday 25 May 2012 Afternoon
Friday 25 May 2012 Afternoon AS GCE PHYSICS A G482 Electrons, Waves and Photons *G411720612* Candidates answer on the Question Paper. OCR supplied materials: Data, Formulae and Relationships Booklet (sent
EE101: Resonance in RLC circuits
EE11: Resonance in RLC circuits M. B. Patil mbatil@ee.iitb.ac.in www.ee.iitb.ac.in/~sequel Deartment of Electrical Engineering Indian Institute of Technology Bombay I V R V L V C I = I m = R + jωl + 1/jωC
Homework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
Math 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Section 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Thin Film Chip Resistors
FEATURES PRECISE TOLERANCE AND TEMPERATURE COEFFICIENT EIA STANDARD CASE SIZES (0201 ~ 2512) LOW NOISE, THIN FILM (NiCr) CONSTRUCTION REFLOW SOLDERABLE (Pb FREE TERMINATION FINISH) Type Size EIA PowerRating
On the axes in the diagram above, sketch a graph to show how the intensity varies with position for a monochromatic light source.
Q1.The diagram shows Young s double-slit experiment performed with a tungsten filament lamp as the light source. (a) On the axes in the diagram above, sketch a graph to show how the intensity varies with
Calculating the propagation delay of coaxial cable
Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric
CHAPTER 101 FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD
CHAPTER FOURIER SERIES FOR PERIODIC FUNCTIONS OF PERIOD EXERCISE 36 Page 66. Determine the Fourier series for the periodic function: f(x), when x +, when x which is periodic outside this rge of period.
5.4 The Poisson Distribution.
The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2517291414* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2013 1 hour 30 minutes
EE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE
«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing
HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
TMA4115 Matematikk 3
TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet
Strain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Exercises in Electromagnetic Field
DR. GYURCSEK ISTVÁN Exercises in Electromagnetic Field Sources and additional materials (recommended) Gyurcsek I. Elmer Gy.: Theories in Electric Circuits, Globe Edit 206, ISBN:97833307343 Simonyi K.:
derivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011
Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο
Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Άσκηση αυτοαξιολόγησης 4 Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών CS-593 Game Theory 1. For the game depicted below, find the mixed strategy
UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications:
UNIVERSITY OF CALIFORNIA Department of Electrical Engineering and Computer Sciences EECS 150 Fall 2001 Prof. Subramanian Midterm II 1) You are implementing an 4:1 Multiplexer that has the following specifications:
ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις
Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)
Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες
Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016
Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Dynamic types, Lambda calculus machines Apr 21 22, 2016 1 Dynamic types and contracts (a) To make sure you understand the
Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016
Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της
*2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *2354431106* GREEK 0543/02 Paper 2 Reading and Directed Writing May/June 2009 1 hour 30 minutes
Right Rear Door. Let's now finish the door hinge saga with the right rear door
Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents
Approximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Section 9.2 Polar Equations and Graphs
180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify
titanium laser beam volume to be heated joint titanium Fig. 5.1
1 Lasers are often used to form precision-welded joints in titanium. To form one such joint it is first necessary to increase the temperature of the titanium to its melting point. Fig. 5.1 shows the joint
1999 MODERN GREEK 2 UNIT Z
STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student
EU-Profiler: User Profiles in the 2009 European Elections
ZA5806 EU-Profiler: User Profiles in the 2009 European Elections Country Specific Codebook Cyprus COUNTRY SPECIFIC CODEBOOK: CYPRUS Variable answer_29 answer_30 saliency_29 saliency_30 party_val_49 party_val_50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 6 3 1 7 7 7 6 4 0 6 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 October/November 2013 Candidates answer
CEMENT FIXED RESISTORS
Self extinguishing Excellent flame and moisture resistance Extremely small sturdy and mechanically safe Non-inductive types available for all Royal Ohm Cement Types Too low or too high ohmic values on
1) Formulation of the Problem as a Linear Programming Model
1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account
Thermistor (NTC /PTC)
ISO/TS16949 ISO 9001 ISO14001 2015 Thermistor (NTC /PTC) GNTC (Chip in Glass Thermistor) SMD NTC Thermistor SMD PTC Thermistor Radial type Thermistor Bare Chip Thermistor (Gold & silver Electrode) 9B-51L,
ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης
Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής
Second Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
G485. PHYSICS A Fields, Particles and Frontiers of Physics ADVANCED GCE. Tuesday 21 June 2011 Morning PMT. Duration: 1 hour 45 minutes
ADVANCED GCE PHYSICS A Fields, Particles and Frontiers of Physics G485 *G410360611* Candidates answer on the question paper. OCR Supplied Materials: Data, Formulae and Relationships Booklet Other Materials
MathCity.org Merging man and maths
MathCity.org Merging man and maths Exercise 10. (s) Page Textbook of Algebra and Trigonometry for Class XI Available online @, Version:.0 Question # 1 Find the values of sin, and tan when: 1 π (i) (ii)
1000 VDC 1250 VDC 125 VAC 250 VAC J K 125 VAC, 250 VAC
Metallized Polyester Film Capacitor Type: ECQE(F) Non-inductive construction using metallized Polyester film with flame retardant epoxy resin coating Features Self-healing property Excellent electrical
H ελαστικότητα και οι εφαρµογές της
5 H ελαστικότητα και οι εφαρµογές της Ελαστικότητα... µας επιτρέπει να αναλύσουµε την προσφορά και ζήτηση µε µεγαλύτερη ακρίβεια. είναι ένα µέτρο του πως οι αγοραστές και πωλητές ανταποκρίνονται στις αλλαγές
ΕΡΙΤΟΡΕΣ ΚΑΙ ΑΝΘΩΡΟΙ ΚΛΕΙΔΙΑ ΑΝΑΘΕΣΘ ΑΓΩΝΑ ΓΑΦΕΙΟ ΑΓΩΝΩΝ ΟΓΑΝΩΤΙΚΘ ΕΡΙΤΟΡΘ. ζεκηλαρηο 1 ΡΑΓΚΟΣΜΙΑ ΟΜΟΣΡΟΝΔΙΑ (ISAF) ΕΛΛΘΝΙΚΘ ΟΜΟΣΡΟΝΔΙΑ (Ε.Ι.Ο.
ΑΝΑΘΕΣΘ ΑΓΩΝΑ ΕΡΙΤΟΡΕΣ ΚΑΙ ΑΝΘΩΡΟΙ ΚΛΕΙΔΙΑ ΡΑΓΚΟΣΜΙΑ ΟΜΟΣΡΟΝΔΙΑ (ISAF) ΕΛΛΘΝΙΚΘ ΟΜΟΣΡΟΝΔΙΑ (Ε.Ι.Ο.) ΚΛΑΣΘ 6/6/2009 1 ΟΡΓΑΝΩΣΙΚΗ ΕΠΙΣΡΟΠΗ ΓΡΑΦΕΙΟ ΑΓΩΝΩΝ ΕΠΙΣΡΟΠΗ ΑΓΩΝΩΝ ΕΠΙΣΡΟΠΗ ΕΝΣΑΕΩΝ ΕΠΙΣΡΟΠΗ ΚΑΣΑΜΕΣΡΗΕΩΝ
Code Breaker. TEACHER s NOTES
TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,
Physics (Specification A & B) PHY6T/Q11/test
Centre Number Surname Candidate Signature Candidate Number Other Names Notice to Candidate. The work you submit for assessment must be your own. If you copy from someone else or allow another candidate
Paper Reference. Modern Greek Paper 1 Listening and Responding. Friday 15 May 2009 Afternoon Time: 45 minutes (+5 minutes reading time)
Centre No. Candidate No. Paper Reference 1 7 7 6 0 1 Surname Signature Paper Reference(s) 1776/01 Edexcel GCSE Modern Greek Paper 1 Listening and Responding Friday 15 May 2009 Afternoon Time: 45 minutes
2. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν.
Experiental Copetition: 14 July 011 Proble Page 1 of. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν. Ένα μικρό σωματίδιο μάζας (μπάλα) βρίσκεται σε σταθερή απόσταση z από το πάνω μέρος ενός
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ
ΚΑΘΟΡΙΣΜΟΣ ΠΑΡΑΓΟΝΤΩΝ ΠΟΥ ΕΠΗΡΕΑΖΟΥΝ ΤΗΝ ΠΑΡΑΓΟΜΕΝΗ ΙΣΧΥ ΣΕ Φ/Β ΠΑΡΚΟ 80KWp
ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΜΕΤΑΔΟΣΗΣ ΠΛΗΡΟΦΟΡΙΑΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΛΙΚΩΝ ΚΑΘΟΡΙΣΜΟΣ ΠΑΡΑΓΟΝΤΩΝ ΠΟΥ ΕΠΗΡΕΑΖΟΥΝ ΤΗΝ ΠΑΡΑΓΟΜΕΝΗ ΙΣΧΥ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία "Η ΣΗΜΑΝΤΙΚΟΤΗΤΑ ΤΟΥ ΜΗΤΡΙΚΟΥ ΘΗΛΑΣΜΟΥ ΣΤΗ ΠΡΟΛΗΨΗ ΤΗΣ ΠΑΙΔΙΚΗΣ ΠΑΧΥΣΑΡΚΙΑΣ" Ειρήνη Σωτηρίου Λεμεσός 2014 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ
Paper Reference. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced. Thursday 11 June 2009 Morning Time: 1 hour 30 minutes
Centre No. Candidate No. Paper Reference(s) 6665/01 Edexcel GCE Core Mathematics C3 Advanced Thursday 11 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Mathematical Formulae
Smaller. 6.3 to 100 After 1 minute's application of rated voltage at 20 C, leakage current is. not more than 0.03CV or 4 (µa), whichever is greater.
Low Impedance, For Switching Power Supplies Low impedance and high reliability withstanding 5000 hours load life at +05 C (3000 / 2000 hours for smaller case sizes as specified below). Capacitance ranges
The challenges of non-stable predicates
The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates
Core Mathematics C12
Write your name here Surname Other names Pearson Edexcel International Advanced Level Centre Number Candidate Number Core Mathematics C12 Advanced Subsidiary Wednesday 25 May 2016 Morning Time: 2 hours
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΜΗΧΑΝΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ. Πτυχιακή εργασία ΟΛΙΣΘΗΡΟΤΗΤΑ ΚΑΙ ΜΑΚΡΟΥΦΗ ΤΩΝ ΟΔΟΔΤΡΩΜΑΤΩΝ ΚΥΚΛΟΦΟΡΙΑΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΜΗΧΑΝΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ Πτυχιακή εργασία ΟΛΙΣΘΗΡΟΤΗΤΑ ΚΑΙ ΜΑΚΡΟΥΦΗ ΤΩΝ ΟΔΟΔΤΡΩΜΑΤΩΝ ΚΥΚΛΟΦΟΡΙΑΣ Χριστοδούλου Αντρέας Λεμεσός 2014 2 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level * 0 5 1 0 3 4 8 7 8 5 * MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June 2013 Candidates answer on the
Συντακτικές λειτουργίες
2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.
This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail.
This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Chasandra, Mary; Tsiaousi, Louisa; Zisi, Vasiliki; Karatzaferi,
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ
ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται
*H31123A0228* 1. (a) Find the value of at the point where x = 2 on the curve with equation. y = x 2 (5x 1). (6)
C3 past papers 009 to 01 physicsandmathstutor.comthis paper: January 009 If you don't find enough space in this booklet for your working for a question, then pleasecuse some loose-leaf paper and glue it
Lecture 26: Circular domains
Introductory lecture notes on Partial Differential Equations - c Anthony Peirce. Not to be copied, used, or revised without eplicit written permission from the copyright owner. 1 Lecture 6: Circular domains
Instruction Execution Times
1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables
G482. PHYSICS A Electrons, Waves and Photons ADVANCED SUBSIDIARY GCE. Monday 6 June 2011 Afternoon. Duration: 1 hour 45 minutes
ADVANCED SUBSIDIARY GCE PHYSICS A Electrons, Waves and Photons G482 *OCE/23932* Candidates answer on the question paper. OCR Supplied Materials: Data, Formulae and Relationships Booklet Other Materials
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level *423892 8 1 3 4* PHYSICS 5054/22 Paper 2 Theory May/June 2010 1 hour 45 minutes Candidates answer on the
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Τέλος Ενότητας Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί
PRESENTATION TITLE PRESENTATION SUBTITLE
COURSE TUTORS : Advanced Materials Processing : D. Mataras, C. Galiotis PRESENTATION TITLE PRESENTATION SUBTITLE A. Student Outline 2 What is my material and why is it interesting? My Application Detailed