Electromagnetism Physics 15b

Size: px
Start display at page:

Download "Electromagnetism Physics 15b"

Transcription

1 Electromagnetism Physics 5b Lecture #9 DC Circuits Purcell What We Did Last Time Define current and current density J J da S Charge conservation divj ρ or 0 in steady current t Carrier densities n k, velocities u k J n k q k u k J σe Ohm s Law (micro) (macro) For constant cross section A, Physics of electrical conduction R R L σ A Assuming that carrier (electron) motion is dominated by thermal fluctuation k σ n e e2 τ m e

2 Today s Goals One more resistance problem How to go between micro (resistivity) and macro (resistance) Power dissipation in a resistor Discuss direct current (DC) circuits Made of resistors, capacitors and electromotive forces Resistor arithmetic Many of you already know Kirchhoff s rules Simple and straightforward rules that help you to solve DC circuit problems systematically Gustav Kirchhoff ( ) Cylindrical Resistor A material of resistivity ρ is filled between two highlyconductive tubes of radii a and b (a < b), length Apply potential difference between tubes E and J are both pointing out At radius r, J(r) σe(r) ρ E(r)ˆr ntegrate J over a cylinder at r J(r) da 2πrLJ(r) E(r) ρj(r) ρ 2πrL ˆr cylinder ntegrate E from a to b b E(r) dr ρ b dr a 2πL ρ a r 2πL ln b a R ρ 2πL ln b a a r J b 2

3 Power Dissipation Current flows through a piece of resistive wire Every t seconds, charge Q t moves across potential difference They lose energy U Q t What happens to the energy? Current flowing downstream across dissipates power and turn it into heat P 2 R Unit: erg/sec in CGS, joule/sec watt (W) in S q q q Next: We need a source of energy to keep it going R Electromotive Force Batteries supply electricity Connect it to a resistor and we ll find and Connect it to a capacitor and we ll find and Q R Q C Q A battery is a potential-difference generator We call a battery s ability to produce a potential difference an electromotive force, or emf Unit: statvolt in CGS, volt in S Watch out! t s not a force 3

4 What is an EMF nside a battery, chemical reactions move the charges from one contact to another t s like a pump pushing water up R h Battery converts chemical energy to potential energy of charges Pump converts kinetic energy to potential energy of water nternal Resistance Connect a battery with an emf E to a resistor R The current should be E R E! True only for an ideal battery R Real batteries have internal resistance E! nternal resistance deal battery measured outside the battery is E < E R E! Loss due to internal resistance 4

5 Measuring E and nternal loss,, is proportional to the current We can measure with no current and get E! This is open-circuit voltage We can measure with current and find out E E! E! R E! R ER R Battery testers do this to determine if is too large Dead batteries have the same emf E as the fresh ones, but larger internal resistance Series/Parallel Resistors Series Parallel Current through and are the same Potential differences across and are and 2 Total potential must be 2 R equiv. Potential across and are the same Currents through and are / and 2 / Combined, they draw 2 R equiv. R equiv. R equiv. 5

6 Resistor Arithmetic For arbitrary number of resistors R n R n R equiv. i R Generally, any 2-terminal network equiv. of resistors is equivalent to a single resistor t may be easy or not so easy i Not so easy ones need a strategy R 4 Kirchhoff s Rules #) At any point in a circuit, the sum of the incoming current equals to the sum of the outgoing current in Junction Rule out #2) Around any loop in a circuit, the sum of the potential differences is zero 0 Loop Rule loop These are restatements of what we know perfectly well Electric charge is conserved d Current is divergent free J 0 ρ dv dt 0 Electric potential is conservative Potential is curl free E 0 E ds 0 C 6

7 Using Kirchhoff Let s do a simple example: Find the current through Step : Define currents One for each branch of the circuit Direction doesn t matter Pick one Step 2: Apply the junction rule Junction A 2 A B E Junction B 2 Step 3: Apply the loop rule Top loop E 0 Bottom loop What s this minus sign doing here? Loop Rule Subtlety To apply the loop rule, you must decide which direction to go around each loop Either will work, just pick one As you go around the loop, An emf counts as E if you pass through it from to A resistor counts as f the current is flowing the direction you are going f you are going this way A 2 B E E E R R 2 0 7

8 Back to the Problem We ve found so far Junctions: 2 Top loop: E 0 Bottom loop: 2 0 We introduced 3 unknown currents and found 3 equations Solve them: ( )E 2 E ( ) A 2 B E E Kirchhoff Strategy Step : Define currents One for each branch of the circuit Pick the direction of the current Step 2: Apply the junction rule Step 3: Apply the loop rule Pick the direction of the loop Pay attention to the polarity loop You ll have just the right number of equations to solve for all the currents you defined in Step The rest is straightforward (it may be tedious) R E E R 8

9 Thévenin/Norton Equivalences Any 2-terminal circuit of emfs and resistors can be replaced with an emf and a resistor in series, or a current source and a resistor in parallel Thévenin Norton R Th E Th! No! R No They cannot be electrically distinguished from outside They have the same - relation on the terminals The equivalence theorems assume linearity (including reversibility) of the emfs and resistors Symbol for a current source Finding Equivalences Two parameters Two points on the - relation Open-circuit voltage O : potential difference between the terminals with nothing connected Short-circuit current S : current between the terminals when they are shorted O E Th, S E Th R Th for Thévenin O No R No, S No for Norton R Th E Th! Th O, No S, R Th R No O S Let s do an example No! R No 9

10 Example Thévenin/Norton Put the circuit we looked at before in a black box Open circuit : we have already solved for, 2, and R 0 3 ( E ) Short circuit : connecting A and B means adding 0Ω in parallel with Effectively this makes 0 will become S S R3 0 E A 2 E B We find: R eq R o S Equivalent Resistance Thévenin/Norton equivalent resistance turns out to be R eq R 3 One can find R eq by replacing all emfs with 0Ω and calculating the total resistance Consider the differential - relation d For a resistor d(r) R d d For an emf d d de d 0 i.e., an emf s differential resistance is 0 A 0Ω 0Ω B 0

11 Summary Power dissipation in resitors Electromotive forces (emfs) Batteries are made of an emf and an internal resistance Resistor arithmetic Kirchhoff s rules in out R series i Junction Rule P 2 R R parallel 0 loop i Loop Rule Loop rule requires attention to the polarity Tévenin and Norton equivalences Open-circuit voltage and short-circuit current R eq can be evaluated by emf 0Ω Th O No S R Th R No O S

Physics 11b Lecture #8

Physics 11b Lecture #8 Physics 11b Lecture #8 Current and Resistance S&J Chapter 27 Administravia First midterm this Thursday Covers up to and including capacitance Lectures #1 #7, textbook chapters 23 26 Five problems Problem

More information

Capacitance. A different kind of capacitor: Work must be done to charge a capacitor. Capacitors in circuits. Capacitor connected to a battery

Capacitance. A different kind of capacitor: Work must be done to charge a capacitor. Capacitors in circuits. Capacitor connected to a battery Capacitance The ratio C = Q/V is a conductor s self capacitance Units of capacitance: Coulomb/Volt = Farad A capacitor is made of two conductors with equal but opposite charge Capacitance depends on shape

More information

Chapter 28. Direct Current Circuits

Chapter 28. Direct Current Circuits Chapter 28 Direct Current Circuits Circuit Analysis Simple electric circuits may contain batteries, resistors, and capacitors in various combinations. For some circuits, analysis may consist of combining

More information

Chapter 27. Circuits

Chapter 27. Circuits Chapter 27 Circuits 1 1. Pumping Chagres We need to establish a potential difference between the ends of a device to make charge carriers follow through the device. To generate a steady flow of charges,

More information

Direct-Current Circuits. Physics 231 Lecture 6-1

Direct-Current Circuits. Physics 231 Lecture 6-1 Direct-Current Circuits Physics 231 Lecture 6-1 esistors in Series and Parallel As with capacitors, resistors are often in series and parallel configurations in circuits Series Parallel The question then

More information

Lecture Notes on DC Network Theory

Lecture Notes on DC Network Theory Federal University, Ndufu-Alike, Ikwo Department of Electrical/Electronics and Computer Engineering (ECE) Faculty of Engineering and Technology Lecture Notes on DC Network Theory Harmattan Semester by

More information

Chapter 28. Direct Current Circuits

Chapter 28. Direct Current Circuits Chapter 28 Direct Current Circuits Electromotive Force An electromotive force device, or emf device, is a source of constant potential. The emf describes the work done per unit charge and has units of

More information

Chapter 6 DIRECT CURRENT CIRCUITS. Recommended Problems: 6,9,11,13,14,15,16,19,20,21,24,25,26,28,29,30,31,33,37,68,71.

Chapter 6 DIRECT CURRENT CIRCUITS. Recommended Problems: 6,9,11,13,14,15,16,19,20,21,24,25,26,28,29,30,31,33,37,68,71. Chapter 6 DRECT CURRENT CRCUTS Recommended Problems: 6,9,,3,4,5,6,9,0,,4,5,6,8,9,30,3,33,37,68,7. RESSTORS N SERES AND N PARALLEL - N SERES When two resistors are connected together as shown we said that

More information

Version 001 CIRCUITS holland (1290) 1

Version 001 CIRCUITS holland (1290) 1 Version CIRCUITS holland (9) This print-out should have questions Multiple-choice questions may continue on the next column or page find all choices before answering AP M 99 MC points The power dissipated

More information

Chapter 19 Lecture Notes

Chapter 19 Lecture Notes Chapter 19 Lecture Notes Physics 2424 - Strauss Formulas: R S = R 1 + R 2 +... C P = C 1 + C 2 +... 1/R P = 1/R 1 + 1/R 2 +... 1/C S = 1/C 1 + 1/C 2 +... q = q 0 [1-e -t/(rc) ] q = q 0 e -t/(rc τ = RC

More information

52 VOLTAGE, CURRENT, RESISTANCE, AND POWER

52 VOLTAGE, CURRENT, RESISTANCE, AND POWER 52 VOLTAGE, CURRENT, RESISTANCE, AND POWER 1. What is voltage, and what are its units? 2. What are some other possible terms for voltage? 3. Batteries create a potential difference. The potential/voltage

More information

Electricity & Magnetism

Electricity & Magnetism Electricity & Magnetism D.C. Circuits Marline Kurishingal Note : This chapter includes only D.C. In AS syllabus A.C is not included. Recap... Electrical Circuit Symbols : Draw and interpret circuit diagrams

More information

Chapter 24: Electric Current

Chapter 24: Electric Current Chapter 24: Electric Current Electric current Electric current is a net flow of electric charge. Quantitatively, current is the rate at which charge crosses a given area. I = dq dt dq = q(n AL)=q(n Av

More information

Electric Currents and Circuits

Electric Currents and Circuits Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 19 Electric Currents and Circuits Marilyn Akins, PhD Broome Community College Electric Circuits The motion of charges leads to the idea of

More information

Chapter 18 Electric Currents

Chapter 18 Electric Currents Chapter 18 Electric Currents 1 The Electric Battery Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Review The resistance R of a device is given by Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 8 R =! L A ρ is resistivity of the material from which the device is constructed L is the

More information

PHY102 Electricity Course Summary

PHY102 Electricity Course Summary TOPIC 1 ELECTOSTTICS PHY1 Electricity Course Summary Coulomb s Law The magnitude of the force between two point charges is directly proportional to the product of the charges and inversely proportional

More information

Physics 1214 Chapter 19: Current, Resistance, and Direct-Current Circuits

Physics 1214 Chapter 19: Current, Resistance, and Direct-Current Circuits Physics 1214 Chapter 19: Current, Resistance, and Direct-Current Circuits 1 Current current: (also called electric current) is an motion of charge from one region of a conductor to another. Current When

More information

SPS Presents: A Cosmic Lunch!

SPS Presents: A Cosmic Lunch! SPS Presents: A Cosmic Lunch! Who: Dr. Brown will be speaking about Evolution of the Elements: from Periodic table to Standard Model and Beyond! When: October 7 th at am Where: CP 79 (by the front office)

More information

Chapter 24: Electric Current

Chapter 24: Electric Current Chapter 24: Electric Current Current Definition of current A current is any motion of charge from one region to another. Suppose a group of charges move perpendicular to surface of area A. The current

More information

AP Physics C. Electric Circuits III.C

AP Physics C. Electric Circuits III.C AP Physics C Electric Circuits III.C III.C.1 Current, Resistance and Power The direction of conventional current Suppose the cross-sectional area of the conductor changes. If a conductor has no current,

More information

Class 8. Resistivity and Resistance Circuits. Physics 106. Winter Press CTRL-L to view as a slide show. Class 8. Physics 106.

Class 8. Resistivity and Resistance Circuits. Physics 106. Winter Press CTRL-L to view as a slide show. Class 8. Physics 106. and Circuits and Winter 2018 Press CTRL-L to view as a slide show. Last time we learned about Capacitance Problems Parallel-Plate Capacitors Capacitors in Circuits Current Ohm s Law and Today we will learn

More information

4 Electric circuits. Serial and parallel resistors V 3 V 2 V Serial connection of resistors:

4 Electric circuits. Serial and parallel resistors V 3 V 2 V Serial connection of resistors: 4 lectric circuits PHY67 Spring 006 Serial and parallel resistors Serial connection of resistors: As the current I through each of serially connected resistors is the same, one can use Ohm s law and write...

More information

in series Devices connected in series will have the same amount of charge deposited on each capacitor. But different potential difference. That means

in series Devices connected in series will have the same amount of charge deposited on each capacitor. But different potential difference. That means Electric Field Electricity Lecture Series Electric Field: Field an area where any charged object will experience an electric force Kirchoff s Laws The electric field lines around a pair of point charges

More information

Chapter 25: Electric Current

Chapter 25: Electric Current Chapter 25: Electric Current Conductors and Charge Carriers Consider a conducting piece of metal: The valence electrons are weakly bound to the nuclei form a fluidlike sea of electrons that can move through

More information

Chapter 26 & 27. Electric Current and Direct- Current Circuits

Chapter 26 & 27. Electric Current and Direct- Current Circuits Chapter 26 & 27 Electric Current and Direct- Current Circuits Electric Current and Direct- Current Circuits Current and Motion of Charges Resistance and Ohm s Law Energy in Electric Circuits Combination

More information

ELECTRIC CURRENT. Ions CHAPTER Electrons. ELECTRIC CURRENT and DIRECT-CURRENT CIRCUITS

ELECTRIC CURRENT. Ions CHAPTER Electrons. ELECTRIC CURRENT and DIRECT-CURRENT CIRCUITS LCTRC CURRNT CHAPTR 25 LCTRC CURRNT and DRCTCURRNT CRCUTS Current as the motion of charges The Ampère Resistance and Ohm s Law Ohmic and nonohmic materials lectrical energy and power ons lectrons nside

More information

Chapter 21 Electric Current and Direct- Current Circuits

Chapter 21 Electric Current and Direct- Current Circuits Chapter 21 Electric Current and Direct- Current Circuits 1 Overview of Chapter 21 Electric Current and Resistance Energy and Power in Electric Circuits Resistors in Series and Parallel Kirchhoff s Rules

More information

Direct-Current Circuits

Direct-Current Circuits Direct-Current Circuits A'.3/.". 39 '- )232.-/ 32,+/" 7+3(5-.)232.-/ 7 3244)'03,.5B )*+,"- &'&./( 0-1*234 35-2567+- *7 2829*4-& )"< 35- )*+,"-= 9-4-- 3563 A0.5.C2/'-231).D')232.')2-1 < /633-">&@5-:836+-0"1464-625"-4*43"

More information

Clicker Session Currents, DC Circuits

Clicker Session Currents, DC Circuits Clicker Session Currents, DC Circuits Wires A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? 1) it decreases

More information

Physics 115. General Physics II. Session 24 Circuits Series and parallel R Meters Kirchoff s Rules

Physics 115. General Physics II. Session 24 Circuits Series and parallel R Meters Kirchoff s Rules Physics 115 General Physics II Session 24 Circuits Series and parallel R Meters Kirchoff s Rules R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 5/15/14 Phys

More information

Chapter 7 Direct-Current Circuits

Chapter 7 Direct-Current Circuits Chapter 7 Direct-Current Circuits 7. Introduction... 7. Electromotive Force... 7.3 Resistors in Series and in Parallel... 4 7.4 Kirchhoff s Circuit Rules... 6 7.5 Voltage-Current Measurements... 8 7.6

More information

Physics 7B-1 (A/B) Professor Cebra. Winter 2010 Lecture 2. Simple Circuits. Slide 1 of 20

Physics 7B-1 (A/B) Professor Cebra. Winter 2010 Lecture 2. Simple Circuits. Slide 1 of 20 Physics 7B-1 (A/B) Professor Cebra Winter 2010 Lecture 2 Simple Circuits Slide 1 of 20 Conservation of Energy Density In the First lecture, we started with energy conservation. We divided by volume (making

More information

Electric Current. Note: Current has polarity. EECS 42, Spring 2005 Week 2a 1

Electric Current. Note: Current has polarity. EECS 42, Spring 2005 Week 2a 1 Electric Current Definition: rate of positive charge flow Symbol: i Units: Coulombs per second Amperes (A) i = dq/dt where q = charge (in Coulombs), t = time (in seconds) Note: Current has polarity. EECS

More information

Electric Circuits Part 2: Kirchhoff s Rules

Electric Circuits Part 2: Kirchhoff s Rules Electric Circuits Part 2: Kirchhoff s Rules Last modified: 31/07/2018 Contents Links Complex Circuits Applying Kirchhoff s Rules Example Circuit Labelling the currents Kirchhoff s First Rule Meaning Kirchhoff

More information

ELECTRIC CURRENT INTRODUCTION. Introduction. Electric current

ELECTRIC CURRENT INTRODUCTION. Introduction. Electric current Chapter 7 ELECTRIC CURRENT Introduction Electric current Charge conservation Electric conductivity Microscopic picture Electric power Electromotive force Kirchhoff s rules Summary INTRODUCTION The first

More information

Chapter 20 Electric Circuits

Chapter 20 Electric Circuits Chapter 0 Electric Circuits Chevy olt --- Electric vehicle of the future Goals for Chapter 9 To understand the concept of current. To study resistance and Ohm s Law. To observe examples of electromotive

More information

M. C. Escher: Waterfall. 18/9/2015 [tsl425 1/29]

M. C. Escher: Waterfall. 18/9/2015 [tsl425 1/29] M. C. Escher: Waterfall 18/9/2015 [tsl425 1/29] Direct Current Circuit Consider a wire with resistance R = ρl/a connected to a battery. Resistor rule: In the direction of I across a resistor with resistance

More information

Physics 202: Lecture 5, Pg 1

Physics 202: Lecture 5, Pg 1 Resistance Resistors Series Parallel Ohm s law Electric Circuits Current Physics 132: Lecture e 15 Elements of Physics II Kirchhoff s laws Agenda for Today Physics 202: Lecture 5, Pg 1 Electric Current

More information

CHAPTER 7 ELECTRODYNAMICS

CHAPTER 7 ELECTRODYNAMICS CHAPTER 7 ELECTRODYNAMICS Outlines 1. Electromotive Force 2. Electromagnetic Induction 3. Maxwell s Equations Michael Faraday James C. Maxwell 2 Summary of Electrostatics and Magnetostatics ρ/ε This semester,

More information

Lecture 1. Electrical Transport

Lecture 1. Electrical Transport Lecture 1. Electrical Transport 1.1 Introduction * Objectives * Requirements & Grading Policy * Other information 1.2 Basic Circuit Concepts * Electrical l quantities current, voltage & power, sign conventions

More information

2/25/2014. Circuits. Properties of a Current. Conservation of Current. Definition of a Current A. I A > I B > I C B. I B > I A C. I C D. I A E.

2/25/2014. Circuits. Properties of a Current. Conservation of Current. Definition of a Current A. I A > I B > I C B. I B > I A C. I C D. I A E. Circuits Topics: Current Conservation of current Batteries Resistance and resistivity Simple circuits 0.1 Electromotive Force and Current Conventional current is the hypothetical flow of positive charges

More information

Physics 142 Steady Currents Page 1. Steady Currents

Physics 142 Steady Currents Page 1. Steady Currents Physics 142 Steady Currents Page 1 Steady Currents If at first you don t succeed, try, try again. Then quit. No sense being a damn fool about it. W.C. Fields Electric current: the slow average drift of

More information

Chapter 16. Current and Drift Speed. Electric Current, cont. Current and Drift Speed, cont. Current and Drift Speed, final

Chapter 16. Current and Drift Speed. Electric Current, cont. Current and Drift Speed, cont. Current and Drift Speed, final Chapter 6 Current, esistance, and Direct Current Circuits Electric Current Whenever electric charges of like signs move, an electric current is said to exist The current is the rate at which the charge

More information

Series/Parallel Circuit Simplification: Kirchoff, Thevenin & Norton

Series/Parallel Circuit Simplification: Kirchoff, Thevenin & Norton Series/Parallel Circuit Simplification: Kirchoff, Thevenin & Norton Session 1d of Basic Electricity A Fairfield University E-Course Powered by LearnLinc Basic Electricity Two Parts Electron Flow and Resistance

More information

Lecture 14 Current Density Ohm s Law in Differential Form

Lecture 14 Current Density Ohm s Law in Differential Form Lecture 14 Current Density Ohm s Law in Differential Form Sections: 5.1, 5.2, 5.3 Homework: See homework file Direct Electric Current Review DC is the flow of charge under electrostatic forces in conductors

More information

Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson

Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson Chapter 2 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 2 Objectives Understand symbols and behavior of the following circuit elements: Independent voltage and current sources; Dependent voltage and

More information

Lecture #3. Review: Power

Lecture #3. Review: Power Lecture #3 OUTLINE Power calculations Circuit elements Voltage and current sources Electrical resistance (Ohm s law) Kirchhoff s laws Reading Chapter 2 Lecture 3, Slide 1 Review: Power If an element is

More information

Chapter 18. Direct Current Circuits -II

Chapter 18. Direct Current Circuits -II Chapter 18 Direct Current Circuits -II So far A circuit consists of three-four elements: Electromotive force/power supply/battery capacitors, resistors inductors Analyzed circuits with capacitors or resistors

More information

Topic 5.2 Heating Effect of Electric Currents

Topic 5.2 Heating Effect of Electric Currents Topic 5.2 Heating Effect of Electric Currents Kari Eloranta 2017 Jyväskylän Lyseon lukio International Baccalaureate February 14, 2017 Topic 5.2 Heating Effect of Electric Currents In subtopic 5.2 we study

More information

Power lines. Why do birds sitting on a high-voltage power line survive?

Power lines. Why do birds sitting on a high-voltage power line survive? Power lines At large distances, the resistance of power lines becomes significant. To transmit maximum power, is it better to transmit high V, low I or high I, low V? (a) high V, low I (b) low V, high

More information

Lecture Outline Chapter 21. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 21. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 21 Physics, 4 th Edition James S. Walker Chapter 21 Electric Current and Direct- Current Circuits Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power

More information

Chapter 19. Electric Current, Resistance, and DC Circuit Analysis

Chapter 19. Electric Current, Resistance, and DC Circuit Analysis Chapter 19 Electric Current, Resistance, and DC Circuit Analysis I = dq/dt Current is charge per time SI Units: Coulombs/Second = Amps Direction of Electron Flow _ + Direction of Conventional Current:

More information

EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1

EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit

More information

Monday July 14. Capacitance demo slide 19 Capacitors in series and parallel slide 33 Elmo example

Monday July 14. Capacitance demo slide 19 Capacitors in series and parallel slide 33 Elmo example Monday July 14 Lecture 5 Capacitance demo slide 19 Capacitors in series and parallel slide 33 Elmo example Lecture 6 Currents and esistance Lecture 9 Circuits Wear Microphone 1 3 Lecture 6 Current and

More information

1) Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits.

1) Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits. 1) Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits. a. The two bulbs are first connected in parallel to a 120 V source. i. Determine the

More information

DC Circuit Analysis + 1 R 3 = 1 R R 2

DC Circuit Analysis + 1 R 3 = 1 R R 2 DC Circuit Analysis In analyzing circuits, it is generally the current that is of interest. You have seen how Ohm s Law can be used to analyze very simple circuits consisting of an EMF and single resistance.

More information

AC vs. DC Circuits. Constant voltage circuits. The voltage from an outlet is alternating voltage

AC vs. DC Circuits. Constant voltage circuits. The voltage from an outlet is alternating voltage Circuits AC vs. DC Circuits Constant voltage circuits Typically referred to as direct current or DC Computers, logic circuits, and battery operated devices are examples of DC circuits The voltage from

More information

Introduction to AC Circuits (Capacitors and Inductors)

Introduction to AC Circuits (Capacitors and Inductors) Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More information

Current and Resistance. February 12, 2014 Physics for Scientists & Engineers 2, Chapter 25 1

Current and Resistance. February 12, 2014 Physics for Scientists & Engineers 2, Chapter 25 1 Current and Resistance February 12, 2014 Physics for Scientists & Engineers 2, Chapter 25 1 Helproom hours! Strosacker learning center, BPS 1248! Mo: 10am noon, 1pm 9pm! Tue: noon 6pm! We: noon 2pm! Th:

More information

BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING

BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING Introduction Ismail Mohd Khairuddin, Zulkifil Md Yusof Faculty of Manufacturing Engineering Universiti Malaysia Pahang Introduction BFF1303 ELECTRICAL/ELECTRONICS

More information

Lecture 19: WED 07 OCT

Lecture 19: WED 07 OCT b Physics 2113 a Jonathan Dowling Lecture 19: WED 07 OCT Circuits I 27.2: Pumping Charges: In order to produce a steady flow of charge through a resistor, one needs a charge pump, a device that by doing

More information

Physics 1302W.400 Lecture 21 Introductory Physics for Scientists and Engineering II

Physics 1302W.400 Lecture 21 Introductory Physics for Scientists and Engineering II Physics 1302W.400 Lecture 21 Introductory Physics for Scientists and Engineering II In today s lecture, we will learn to: Calculate the resistance of a conductor depending on the material and shape Apply

More information

Direct Current Circuits. February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1

Direct Current Circuits. February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1 Direct Current Circuits February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1 Kirchhoff s Junction Rule! The sum of the currents entering a junction must equal the sum of the currents leaving

More information

Electric Currents. Resistors (Chapters 27-28)

Electric Currents. Resistors (Chapters 27-28) Electric Currents. Resistors (Chapters 27-28) Electric current I Resistance R and resistors Relation between current and resistance: Ohm s Law Resistivity ρ Energy dissipated by current. Electric power

More information

Today in Physics 217: circuits

Today in Physics 217: circuits Today in Physics 217: circuits! Review of DC circuits: Kirchhoff s rules! Solving equations from Kirchhoff s rules for simple DC circuits 2 December 2002 Physics 217, Fall 2002 1 Lumped circuit elements:

More information

Chapter 33 - Electric Fields and Potential. Chapter 34 - Electric Current

Chapter 33 - Electric Fields and Potential. Chapter 34 - Electric Current Chapter 33 - Electric Fields and Potential Chapter 34 - Electric Current Electric Force acts through a field An electric field surrounds every electric charge. It exerts a force that causes electric charges

More information

Capacitance, Resistance, DC Circuits

Capacitance, Resistance, DC Circuits This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple

More information

Engineering Fundamentals and Problem Solving, 6e

Engineering Fundamentals and Problem Solving, 6e Engineering Fundamentals and Problem Solving, 6e Chapter 17 Electrical Circuits Chapter Objectives Compute the equivalent resistance of resistors in series and in parallel Apply Ohm s law to a resistive

More information

PHYS 375: Introduction

PHYS 375: Introduction PHYS 375: Introduction Some general remarks Note on labs Today s lecture: Storing electric energy Voltage, Current, Power Conductivity, Ohm s law Resistor Kirchoff s laws Series and parallel circuits Thevenin

More information

Parallel Resistors (32.6)

Parallel Resistors (32.6) Parallel Resistors (32.6) Resistors connected at both ends are called parallel resistors The important thing to note is that: the two left ends of the resistors are at the same potential. Also, the two

More information

Agenda for Today. Elements of Physics II. Resistance Resistors Series Parallel Ohm s law Electric Circuits. Current Kirchoff s laws

Agenda for Today. Elements of Physics II. Resistance Resistors Series Parallel Ohm s law Electric Circuits. Current Kirchoff s laws Resistance Resistors Series Parallel Ohm s law Electric Circuits Physics 132: Lecture e 17 Elements of Physics II Current Kirchoff s laws Agenda for Today Physics 201: Lecture 1, Pg 1 Clicker Question

More information

physics 4/7/2016 Chapter 31 Lecture Chapter 31 Fundamentals of Circuits Chapter 31 Preview a strategic approach THIRD EDITION

physics 4/7/2016 Chapter 31 Lecture Chapter 31 Fundamentals of Circuits Chapter 31 Preview a strategic approach THIRD EDITION Chapter 31 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 31 Fundamentals of Circuits Chapter Goal: To understand the fundamental physical principles

More information

Parallel Resistors (32.6)

Parallel Resistors (32.6) Parallel Resistors (32.6) Resistors connected at both ends are called parallel resistors Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring 2010 1 / 1 Parallel Resistors (32.6)

More information

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3 Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/3 Summary of last lecture Equipotential surfaces: Surfaces where the potential is the same everywhere, e.g. the

More information

POWER B. Terms: EMF, terminal voltage, internal resistance, load resistance. How to add up resistors in series and parallel: light bulb problems.

POWER B. Terms: EMF, terminal voltage, internal resistance, load resistance. How to add up resistors in series and parallel: light bulb problems. iclicker Quiz (1) I have completed at least 50% of the reading and study-guide assignments associated with the lecture, as indicated on the course schedule. A. True B. False Hint: this is a good time to

More information

Chapter 25 Current, Resistance, and Electromotive Force

Chapter 25 Current, Resistance, and Electromotive Force Chapter 25 Current, Resistance, and Electromotive Force Lecture by Dr. Hebin Li Goals for Chapter 25 To understand current and how charges move in a conductor To understand resistivity and conductivity

More information

ANNOUNCEMENT ANNOUNCEMENT

ANNOUNCEMENT ANNOUNCEMENT ANNOUNCEMENT Exam : Tuesday September 25, 208, 8 PM - 0 PM Location: Elliott Hall of Music (see seating chart) Covers all readings, lectures, homework from Chapters 2 through 23 Multiple choice (5-8 questions)

More information

Chapter 3: Electric Current and Direct-Current Circuit

Chapter 3: Electric Current and Direct-Current Circuit Chapter 3: Electric Current and Direct-Current Circuit n this chapter, we are going to discuss both the microscopic aspect and macroscopic aspect of electric current. Direct-current is current that flows

More information

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS 1.0 Kirchoff s Law Kirchoff s Current Law (KCL) states at any junction in an electric circuit the total current flowing towards that junction is equal

More information

Electric Current & DC Circuits

Electric Current & DC Circuits Electric Current & DC Circuits Circuits Click on the topic to go to that section Conductors Resistivity and Resistance Circuit Diagrams Measurement EMF & Terminal Voltage Kirchhoff's Rules Capacitors*

More information

EXPERIMENT 12 OHM S LAW

EXPERIMENT 12 OHM S LAW EXPERIMENT 12 OHM S LAW INTRODUCTION: We will study electricity as a flow of electric charge, sometimes making analogies to the flow of water through a pipe. In order for electric charge to flow a complete

More information

DC CIRCUIT ANALYSIS. Loop Equations

DC CIRCUIT ANALYSIS. Loop Equations All of the rules governing DC circuits that have been discussed so far can now be applied to analyze complex DC circuits. To apply these rules effectively, loop equations, node equations, and equivalent

More information

DC Circuits. Electromotive Force Resistor Circuits. Kirchoff s Rules. RC Circuits. Connections in parallel and series. Complex circuits made easy

DC Circuits. Electromotive Force Resistor Circuits. Kirchoff s Rules. RC Circuits. Connections in parallel and series. Complex circuits made easy DC Circuits Electromotive Force esistor Circuits Connections in parallel and series Kirchoff s ules Complex circuits made easy C Circuits Charging and discharging Electromotive Force (EMF) EMF, E, is the

More information

Chapter 25 Current Resistance, and Electromotive Force

Chapter 25 Current Resistance, and Electromotive Force Chapter 25 Current Resistance, and Electromotive Force 1 Current In previous chapters we investigated the properties of charges at rest. In this chapter we want to investigate the properties of charges

More information

Look over Chapter 26 sections 1-7 Examples 3, 7. Look over Chapter 18 sections 1-5, 8 over examples 1, 2, 5, 8, 9,

Look over Chapter 26 sections 1-7 Examples 3, 7. Look over Chapter 18 sections 1-5, 8 over examples 1, 2, 5, 8, 9, Look over Chapter 26 sections 1-7 Examples 3, 7 Look over Chapter 18 sections 1-5, 8 over examples 1, 2, 5, 8, 9, 1)How to find a current in a wire. 2)What the Current Density and Draft Speed are. 3)What

More information

KIRCHHOFF S LAWS. Learn how to analyze more complicated circuits with more than one voltage source and numerous resistors.

KIRCHHOFF S LAWS. Learn how to analyze more complicated circuits with more than one voltage source and numerous resistors. KIRCHHOFF S LAWS Lab Goals: Learn how to analyze more complicated circuits with more than one voltage source and numerous resistors. Lab Notebooks: Write descriptions of all of your experiments in your

More information

AP Physics C - E & M

AP Physics C - E & M AP Physics C - E & M Current and Circuits 2017-07-12 www.njctl.org Electric Current Resistance and Resistivity Electromotive Force (EMF) Energy and Power Resistors in Series and in Parallel Kirchoff's

More information

Chapter 26 Examples : DC Circuits Key concepts:

Chapter 26 Examples : DC Circuits Key concepts: Chapter 26 Examples : DC Circuits Key concepts: Internal resistance : battery consists of some idealized source of voltage (called the electromotive force, or EMF, which uses the symbol ξ) and an effective

More information

A free web support in Education. Internal resistance of the battery, r = 3 Ω. Maximum current drawn from the battery = I According to Ohm s law,

A free web support in Education. Internal resistance of the battery, r = 3 Ω. Maximum current drawn from the battery = I According to Ohm s law, Exercises Question 3.1: The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery? Answer 3.1: Emf

More information

2. Basic Components and Electrical Circuits

2. Basic Components and Electrical Circuits 1 2. Basic Components and Electrical Circuits 2.1 Units and Scales The International System of Units (SI) defines 6 principal units from which the units of all other physical quantities can be derived

More information

Physics 102: Lecture 05 Circuits and Ohm s Law

Physics 102: Lecture 05 Circuits and Ohm s Law Physics 102: Lecture 05 Circuits and Ohm s Law Physics 102: Lecture 5, Slide 1 Summary of Last Time Capacitors Physical C = ke 0 A/d C=Q/V Series 1/C eq = 1/C 1 + 1/C 2 Parallel C eq = C 1 + C 2 Energy

More information

Physics 2B: Review for Celebration #2. Chapter 22: Current and Resistance

Physics 2B: Review for Celebration #2. Chapter 22: Current and Resistance Physics 2: eview for Celebration #2 Chapter 22: Current and esistance Current: q Current: I [I] amps (A) 1 A 1 C/s t Current flows because a potential difference across a conductor creates an electric

More information

PHYSICS 171. Experiment 3. Kirchhoff's Laws. Three resistors (Nominally: 1 Kilohm, 2 Kilohm, 3 Kilohm).

PHYSICS 171. Experiment 3. Kirchhoff's Laws. Three resistors (Nominally: 1 Kilohm, 2 Kilohm, 3 Kilohm). PHYSICS 171 Experiment 3 Kirchhoff's Laws Equipment: Supplies: Digital Multimeter, Power Supply (0-20 V.). Three resistors (Nominally: 1 Kilohm, 2 Kilohm, 3 Kilohm). A. Kirchhoff's Loop Law Suppose that

More information

Lecture 6 Current and Resistance Ch. 26

Lecture 6 Current and Resistance Ch. 26 Lecture 6 Current and esistance Ch. 6 Cartoon -nvention of the battery and Voltaic Cell Warm-up problem Topics What is current? Current density Conservation of Current esistance Temperature dependence

More information

physics for you February 11 Page 68

physics for you February 11 Page 68 urrent Electricity Passage 1 4. f the resistance of a 1 m length of a given wire t is observed that good conductors of heat are also is 8.13 10 3 W, and it carried a current 1, the good conductors of electricity.

More information

Direct Currents. We will now start to consider charges that are moving through a circuit, currents. Sunday, February 16, 2014

Direct Currents. We will now start to consider charges that are moving through a circuit, currents. Sunday, February 16, 2014 Direct Currents We will now start to consider charges that are moving through a circuit, currents. 1 Direct Current Current usually consists of mobile electrons traveling in conducting materials Direct

More information

Chapter 26 Direct-Current Circuits

Chapter 26 Direct-Current Circuits Chapter 26 Direct-Current Circuits 1 Resistors in Series and Parallel In this chapter we introduce the reduction of resistor networks into an equivalent resistor R eq. We also develop a method for analyzing

More information

General Physics (PHY 2140)

General Physics (PHY 2140) General Physics (PHY 140) Lecture 6 lectrodynamics Direct current circuits parallel and series connections Kirchhoff s rules circuits Hours of operation: Monday and Tuesday Wednesday and Thursday Friday,

More information

Review. Spring Semester /21/14. Physics for Scientists & Engineers 2 1

Review. Spring Semester /21/14. Physics for Scientists & Engineers 2 1 Review Spring Semester 2014 Physics for Scientists & Engineers 2 1 Notes! Homework set 13 extended to Tuesday, 4/22! Remember to fill out SIRS form: https://sirsonline.msu.edu Physics for Scientists &

More information