# PH 222-2C Fall Circuits. Lectures Chapter 27 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)

Size: px
Start display at page:

Download "PH 222-2C Fall Circuits. Lectures Chapter 27 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)"

Transcription

1 PH 222-2C Fall 2012 Circuits Lectures Chapter 27 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1

2 Chapter 27 Circuits In this chapter we will cover the following topics: -Electromotive force (emf) -Ideal and real emf devices -Kirchhoff s loop rule -Kirchhoff s junction rule -Multiloop circuits -Resistors in series -Resistors in parallel -RC circuits, charging and discharging of a capacitor 2

3 In order to create a current through a resistor, a potential difference must be created across its terminals. One way of doing this is to connect the resistor to a battery. A device that can maintain a potential difference between two terminals is called a "seat of an emf " or an "emf device." Here emf stands for electromotive force. Examples of emf devices are a battery, an electric generator, a solar cell, a fuel cell, etc. These devices act like "charge pumps" in the sense that they move positive charges from the low-potential (negative) terminal to the high-potential (positive) terminal. A mechanical analog is given in the figure below. pump High (+) reservoir Low (-) reservoir In this mechanical analog a water pump transfers water from the low to the high reservoir. The water returns from the high to the low reservoir through a pipe, which is the analog of the resistor. The emf (symbol ) is defined as the potential difference between the terminals of the emf device when no current flows through it. 3

4 Notation : The polarity of an emf device is indicated by an arrow with a small circle at its tail. The arrow points from the negative to the positive terminal of the device. When the emf device is connected to a circuit its internal mechanism transports positive charges from the negative to the positive terminal and sets up a charge flow (a.k.a. current) around the circuit. In doing so the emf device does work dw on a charge dq, which is given by the equation dw dq. The required energy comes from chemical reactions in the case of a battery; in the case of a generator it comes from the mechanical force that rotates the generator shaft; in the case of a solar cell it comes from the Sun. In the circuit of the figure the energy stored in emf device B changes form: It does mechanical work on the motor. It produces thermal energy on the resistor. It gets converted into chemical energy in emf device A. 4

5 Ideal and Real Emf Devices V Ideal emf device V i V ir Real emf device V An emf device is said to be ideal if the voltage V across its terminals a and b does not depend on the current i that flows through the emf device: V. An emf device is said to be real if the voltage V across its terminals a and b decreases with current i according to the equation V ir. The parameter r is known as the " internal resistance" of the emf device. i 5

6 ir 0 Current in a Single - Loop Circuit Consider the circuit shown in the figure. We assume that the emf device is ideal and that the connecting wires have negligible resistance. A current i flows through the circuit in the clockwise direction. In a time interval dt a charge dq idt passes through the circuit. The battery is doing work dw dq idt. Using energy conservation we can set this amount of work equal to the rate at which heat is generated on R: idt 2 Ri dt Ri ir 0. Kirchhoff put the equation above in the form of a rule known as Kirchhoff's loop rule (KLR for short). KLR : The algebraic sum of the changes in potential encountered in a complete traversal of any loop in a circuit is equal to zero. The rules that give us the algebraic sign of the charges in potential through a resistor and a battery are given on the next page. 6

7 i i R motion R motion V V -ir ir Resistance Rule : For a move through a resistance in the direction of the current, the change in the potential is V ir. For a move through a resistance in the direction opposite to that of the current, the change in the potential is V ir. - + motion + - motion V V - EMF Rule : For a move through an ideal emf device in the direction of the emf arrow, the change in the potential is V. For a move through an ideal emf device in a direction opposite to that of the emf arrow, the change in the potential is V. 7

8 KLR example : Consider the circuit of fig. a. The battery is real with internal resistance r. We apply KLR for this loop starting at point a and going counterclockwise: ir ir 0 i. We note that for an ideal battery, r 0 and i. R r R Note : The internal resistance r of the battery is an integral part of the battery's internal mechanism. There is no way to open the battery and remove r. In fig. b we plot the potential V of every point in the loop as we start at point a and go around in the clockwise direction. The change V in the battery is positive because we go from the negative to the positive terminal. The change V across the two resistors is negative because we chose to traverse the loop in the direction of the current. The current flows from high to low potential. 8

9 Potential Difference Between Two Points : Consider the circuit shown in the figure. We wish to calculate the potential difference V V between point b and point a. b a V V sum of all potential changes V along the path from point a to point b. b a We choose a path in the loop that takes us from the initial point a to the final point b. V V sum of all potential changes V along the path. f There are two possible paths: We will try them both. Left path: Right path: i Note : V V ir b b a V V ir a The values of V V we get from the two paths are the same. b a 9

10 6. A current of 1A flows through the wire shown in Fig. What will a voltmeter read when connected from: (a) A to B (b) A to C (c) A to D 1 A 2 5 V 10V 3 A B C D a) V AB =V B -V A =IR=2V; b) V AC =V C -V A =V C -(V C -5V-2V)=7V; c) V AD =V D -V A =V D -(V D +10V-3V-5V-2V)=V D -V D - 10V+3V+5V+2V=0V 10

11 i V Equivalent Resistance Consider the combination of resistors shown in the figure. We can substitute this combination of resistors with a single resistor R that is eq "electrically equivalent" to the resistor group it substitutes. This means that if we apply the same voltage V across the resistors in fig. a and across R, the same current i is provided by the battery. eq Alternatively, if we pass the same current i through the circuit in fig. a and through the equivalent resistance R, the voltage V across them is identical. This can be stated in the following manner: If we place the resistor combination and the equivalent resistor in separate black boxes, by doing electrical measurements we cannot distinguish between the two. eq 11

12 Req R1 R2 R3 Req R1 R2... Rn Resistors in Series Consider the three resistors connected in series (one after the other) as shown in fig. a. These resistors have the same current i but different voltages V, V, and V The net voltage across the combination is the sum V V V We will apply KLR for the loop in fig. a starting at point a, and going around the loop in the clockwise direction: ir1ir2 ir3 0 i ( eq. 1) R R R We will apply KLR for the loop in fig. b starting at point a, and going around the loop in the clockwise direction: ireq 0 i ( eq. 2) R If we compare eq. 1 with eq. 2 we get: eq R R R R eq For n resistors connected in series, the equivalent resistance is: n R R R R... R eq i 1 2 i1 n 12.

13 R R R R eq Resistors in Parallel Consider the three resistors shown in the figure. "In parallel" means that the terminals of the resistors are connected together on both sides. Thus resistors in parallel have the same potential applied across them. In our circuit this potential is equal to the emf of the battery. The three resistors have different currents flowing through them. The total current is the sum of the individual currents. We apply KJR at point a: i i i i i i i R1 R2 R i (eq. 1). From fig. b we have: R1 R2 R3 i (eq. 2). If we compare equations 1 and 2 R eq we ge t:. R R R R eq

14 14

15 Multiloop Circuits Consider the circuit shown in the figure. There are three branches in it: bad, bcd, and bd. We assign currents for each branch and define the current directions arbitrarily. The method is selfcorrecting. If we have made a mistake in the direction of a particular current, the calculation will yield a negative value and thus provide us with a warning. We assign current i for branch bad, current i for branch bcd, and current i for branch bd. Consider junction d. Currents i and i arrive, while i leaves Charge is conserved, thus we have: i 1 i 3 i 2. This equation can be formulated as a more general principle known as Kirchhoff's junction rule (KJR). KJR : The sum of the currents entering any junction is equal to the sum of the currents leaving the junction. 15

16 In order to determine the currents i, i, and i in the circuit we need three equations. The first equation will come from KJR at point d: KJR/junction d: i i i ( eq. 1) The other two will come from KLR: If we traverse the left loop ( bad) starting at b and going in the counterclockwise direction we get: KLR/loop bad: i R i R 0 ( eq. 2). Now we go around the right loop ( bcd) starting at point b and going in the counterclockwise direction: KLR/loop bcd: i R i R 0 ( eq. 3) We have a system of three equations (eqs.1, 2, and 3) and three unknowns i, i, and i. If a numerical value for a particular current is negative, this means that the chosen direction for this current is wrong and that the current flows in the opposite direction. We can write a fourth equation (KLR for the outer loop not provide any new information. KLR/loop abcd: i R i R 0 ( eq. 4) abcd) but this equation does 16 3

17 !!! When calculating the potential change across a resistor we must take the product of the resistance and the net current trough the resistor. The net current is the algebraic sum of all the currents flowing through the resistor. 17

18 in 18

19 19

20 20

21 21

22 22

23 8. 23

24 Ammeters and Voltmeters An ammeter is an instrument that measures current. In order to measure the current that flows through a conductor at a certain point we must cut the conductor at this point and connect the two ends of the conductor to the ammeter terminals so that the current can pass through the ammeter. An example is shown in the figure, where the ammeter has been inserted between points a and b. It is essential that the ammeter resistance R be much smaller than the other resistors in the circuit. In our example: R R and R R. A A 1 A 2 A voltmeter is an instrument that measures the potential difference between two points in a circuit. In the example of the figure we use a voltmeter to measure the potential across R. The voltmeter terminals are connected to the two points c and d. 1 It is essential that the voltmeter resistance R be much larger than the other resistors in the circuit. In our example: R R and R R. 24 V V 1 V 2

25 i + - RC Circuits : Charging of a Capacitor Consider the circuit shown in the figure. We assume that the capacitor is initially uncharged and that at t 0 we throw the switch S from the middle position to position a. The battery will charge the capacitor C through the resistor R. Our objective is to examine the charging process as a function of time. We will write KLR starting at point b and going in the clockwise direction: q dq dq q ir 0. The current i R 0. If we rearrange the terms C dt dt C dq q we have: R. This is an inhomogeneous, first order, linear differential dt C equation with initial condition q(0) 0. This condition expresses the fact that at t 0 the capacitor is uncharged. 25

26 dq Differential equation: dt Intitial condition: q(0) 0 t/ Solution: 1 Here: q R C qc e RC The constant is known as the "time constant" of the circuit. If we plot q versus t we see that q does not reach its terminal value C but instead increases from its initial value and reaches the terminal value at t. Do we have to wait for an eternity to charge the capacitor? In practice, no. qt ( ) qt ( 3 ) qt ( 5 ) C C C If we wait only a few time constants the charge, for all practical purposes, has reached its terminal value C. dq t/ The current i e. If we plot i versus t dt R we get a decaying exponential (see fig. b). RC 26

27 i RC Circuits : Discharging of a Capacitor Consider the circuit shown in the figure. We assume q o O q RC t + - that the capacitor at t 0 has charge q and that at t 0 we throw the switch S from the middle position to position b. The capacitor is disconnected from the battery and loses its charge through resistor R. We will write KLR starting at point b and going in q the counterclockwise direction: ir 0. C Taking into account that i dq we get: - dq R q 0. dt dt C 0 This is a homogeneous, first order, linear differential equation with initial condition q q q q e RC q t -/ t (0) 0 The solution is: 0, where. If we plot versus we get a decaying exponential. The charge becomes zero at t only have to wait a few time constants: q( ) q, q(3 ) q, q(5 ) q In practical terms we 27

### 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,

### 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

### 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

### 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

### 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

### Electromotive Force. The electromotive force (emf), ε, of a battery is the maximum possible voltage that the battery can provide between its terminals

Direct Current When the current in a circuit has a constant magnitude and direction, the current is called direct current Because the potential difference between the terminals of a battery is constant,

### 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

### 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"

### Circuits. David J. Starling Penn State Hazleton PHYS 212

Invention is the most important product of man s creative brain. The ultimate purpose is the complete mastery of mind over the material world, the harnessing of human nature to human needs. - Nikola Tesla

### 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,

### 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

### 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

### 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

### 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

### 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

### 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

### MasteringPhysics: Assignment Print View. Problem 30.50

Page 1 of 15 Assignment Display Mode: View Printable Answers phy260s08 homework 13 Due at 11:00pm on Wednesday, May 14, 2008 View Grading Details Problem 3050 Description: A 15-cm-long nichrome wire is

### 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

### 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

### 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

### 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

Superconductors A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, T C T C is called the critical temperature The graph is the same as a normal metal

### 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)

### Switch. R 5 V Capacitor. ower upply. Voltmete. Goals. Introduction

Switch Lab 9. Circuits ower upply Goals + + R 5 V Capacitor V To appreciate the capacitor as a charge storage device. To measure the voltage across a capacitor as it discharges through a resistor, and

### 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

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

### Lecture 16 - Circuit Problems

Lecture 16 - Circuit Problems A Puzzle... Crash Course in Circuits Compute the change in voltage from point A to point B (in other words, the voltage difference V B - V A ) in the following cases. Current

### 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

### Tactics Box 23.1 Using Kirchhoff's Loop Law

PH203 Chapter 23 solutions Tactics Box 231 Using Kirchhoff's Loop Law Description: Knight/Jones/Field Tactics Box 231 Using Kirchhoff s loop law is illustrated Learning Goal: To practice Tactics Box 231

### Inductance, RL Circuits, LC Circuits, RLC Circuits

Inductance, R Circuits, C Circuits, RC Circuits Inductance What happens when we close the switch? The current flows What does the current look like as a function of time? Does it look like this? I t Inductance

### Physics 102: Lecture 06 Kirchhoff s Laws

Physics 102: Lecture 06 Kirchhoff s Laws Physics 102: Lecture 6, Slide 1 Today Last Lecture Last Time Resistors in series: R eq = R 1 R 2 R 3 Current through each is same; Voltage drop is IR i Resistors

### 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

### Electric Current & DC Circuits How to Use this File Electric Current & DC Circuits Click on the topic to go to that section Circuits

Slide 1 / 127 Slide 2 / 127 Electric Current & DC Circuits www.njctl.org Slide 3 / 127 How to Use this File Slide 4 / 127 Electric Current & DC Circuits Each topic is composed of brief direct instruction

### Circuits. Electric Current & DC Circuits. Slide 1 / 127. Slide 2 / 127. Slide 3 / 127. Slide 4 / 127. Slide 5 / 127. Slide 6 / 127

Slide 1 / 127 Slide 2 / 127 New Jersey Center for Teaching and Learning Electric Current & DC Circuits www.njctl.org Progressive Science Initiative This material is made freely available at www.njctl.org

### 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

### 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

### 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

### 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

### 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*

### 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

### 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

### 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

### 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

### 2005 AP PHYSICS C: ELECTRICITY AND MAGNETISM FREE-RESPONSE QUESTIONS

2005 AP PHYSICS C: ELECTRICITY AND MAGNETISM In the circuit shown above, resistors 1 and 2 of resistance R 1 and R 2, respectively, and an inductor of inductance L are connected to a battery of emf e and

### Lecture 12 Chapter 28 RC Circuits Course website:

Lecture 12 Chapter 28 RC Circuits Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 28: Section 28.9 RC circuits Steady current Time-varying

### 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

### Physics 2135 Exam 2 October 20, 2015

Exam Total / 200 Physics 2135 Exam 2 October 20, 2015 Printed Name: Rec. Sec. Letter: Five multiple choice questions, 8 points each. Choose the best or most nearly correct answer. 1. A straight wire segment

### 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)

### 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

### A positive value is obtained, so the current is counterclockwise around the circuit.

Chapter 7. (a) Let i be the current in the circuit and take it to be positive if it is to the left in. We use Kirchhoff s loop rule: ε i i ε 0. We solve for i: i ε ε + 6. 0 050.. 4.0Ω+ 80. Ω positive value

### 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

### The RC Time Constant

The RC Time Constant Objectives When a direct-current source of emf is suddenly placed in series with a capacitor and a resistor, there is current in the circuit for whatever time it takes to fully charge

### Problem Solving 8: Circuits

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics OBJECTIVES Problem Solving 8: Circuits 1. To gain intuition for the behavior of DC circuits with both resistors and capacitors or inductors.

### Chapter 3: Electric Current And Direct-Current Circuits

Chapter 3: Electric Current And Direct-Current Circuits 3.1 Electric Conduction 3.1.1 Describe the microscopic model of current Mechanism of Electric Conduction in Metals Before applying electric field

### RC Circuits. Lecture 13. Chapter 31. Physics II. Course website:

Lecture 13 Chapter 31 Physics II RC Circuits Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html Steady current

### 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

### Physics 212 Midterm 2 Form A

1. A wire contains a steady current of 2 A. The charge that passes a cross section in 2 s is: A. 3.2 10-19 C B. 6.4 10-19 C C. 1 C D. 2 C E. 4 C 2. In a Physics 212 lab, Jane measures the current versus

### Laboratory 7: Charging and Discharging a Capacitor Prelab

Phys 132L Fall 2018 Laboratory 7: Charging and Discharging a Capacitor Prelab Consider a capacitor with capacitance C connected in series to a resistor with resistance R as shown in Fig. 1. Theory predicts

### Discussion Question 6A

Discussion Question 6 P212, Week 6 Two Methods for Circuit nalysis Method 1: Progressive collapsing of circuit elements In last week s discussion, we learned how to analyse circuits involving batteries

### Current and Resistance

Chapter 26 Current and Resistance Copyright 26-1 Electric Current As Fig. (a) reminds us, any isolated conducting loop regardless of whether it has an excess charge is all at the same potential. No electric

### 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

### COPYRIGHTED MATERIAL. DC Review and Pre-Test. Current Flow CHAPTER

Kybett c0.tex V3-03/3/2008 8:44pm Page CHAPTER DC Review and Pre-Test Electronics cannot be studied without first understanding the basics of electricity. This chapter is a review and pre-test on those

### 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

### 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

### R R V I R. Conventional Current. Ohms Law V = IR

DC Circuits opics EMF and erminal oltage esistors in Series and in Parallel Kirchhoff s ules EMFs in Series and in Parallel Capacitors in Series and in Parallel Ammeters and oltmeters Conventional Current

### Circuits. 1. The Schematic

+ ircuits 1. The Schematic 2. Power in circuits 3. The Battery 1. eal Battery vs. Ideal Battery 4. Basic ircuit nalysis 1. oltage Drop 2. Kirchoff s Junction Law 3. Series & Parallel 5. Measurement Tools

### Chapter 28 Solutions

Chapter 8 Solutions 8.1 (a) P ( V) R becomes 0.0 W (11.6 V) R so R 6.73 Ω (b) V IR so 11.6 V I (6.73 Ω) and I 1.7 A ε IR + Ir so 15.0 V 11.6 V + (1.7 A)r r 1.97 Ω Figure for Goal Solution Goal Solution

### PHYS 1444 Section 003 Lecture #12

PHYS 1444 Section 003 Lecture #12 Monday, Oct. 10, 2005 EMF and Terminal Voltage Resisters in series and parallel Kirchhoff s Rules EMFs in series and parallel RC Circuits Today s homework is homework

### Electricity & Optics

Physics 241 Electricity & Optics Lecture 12 Chapter 25 sec. 6, 26 sec. 1 Fall 217 Semester Professor Koltick Circuits With Capacitors C Q = C V V = Q C + V R C, Q Kirchhoff s Loop Rule: V I R V = V I R

### Physics 2135 Exam 2 March 22, 2016

Exam Total Physics 2135 Exam 2 March 22, 2016 Key Printed Name: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points each. Choose the best or most nearly correct answer. B 1. An air-filled

### Physics 212. Lecture 11. RC Circuits. Change in schedule Exam 2 will be on Thursday, July 12 from 8 9:30 AM. Physics 212 Lecture 11, Slide 1

Physics 212 Lecture 11 ircuits hange in schedule Exam 2 will be on Thursday, July 12 from 8 9:30 AM. Physics 212 Lecture 11, Slide 1 ircuit harging apacitor uncharged, switch is moved to position a Kirchoff

### Circuits. PHY2054: Chapter 18 1

Circuits PHY2054: Chapter 18 1 What You Already Know Microscopic nature of current Drift speed and current Ohm s law Resistivity Calculating resistance from resistivity Power in electric circuits PHY2054:

### On the axes of Fig. 4.1, carefully sketch a graph to show how the potential difference V across the capacitor varies with time t. Label this graph L.

1 (a) A charged capacitor is connected across the ends of a negative temperature coefficient (NTC) thermistor kept at a fixed temperature. The capacitor discharges through the thermistor. The potential

### AP Physics C - E & M

Slide 1 / 27 Slide 2 / 27 AP Physics C - E & M Current, Resistance & Electromotive Force 2015-12-05 www.njctl.org Slide 3 / 27 Electric Current Electric Current is defined as the movement of charge from

### Chapter 21 Electric Current and Direct- Current Circuits

Chapter 21 Electric Current and Direct- Current Circuits Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power in Electric Circuits Resistors in Series and Parallel Kirchhoff s

University of Rhode Island DigitalCommons@URI PHY 204: Elementary Physics II Physics Course Materials 2015 10. Resistors II Gerhard Müller University of Rhode Island, gmuller@uri.edu Creative Commons License

### Chapter 26 Direct-Current and Circuits. - Resistors in Series and Parallel - Kirchhoff s Rules - Electric Measuring Instruments - R-C Circuits

Chapter 26 Direct-Current and Circuits - esistors in Series and Parallel - Kirchhoff s ules - Electric Measuring Instruments - -C Circuits . esistors in Series and Parallel esistors in Series: V ax I V

### 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

### 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

### Flow Rate is the NET amount of water passing through a surface per unit time

Electric Current An Analogy Water Flow in a Pipe H 2 0 gallons/minute Flow Rate is the NET amount of water passing through a surface per unit time Individual molecules are bouncing around with speeds of

### Physics 6B Summer 2007 Final

Physics 6B Summer 2007 Final Question 1 An electron passes through two rectangular regions that contain uniform magnetic fields, B 1 and B 2. The field B 1 is stronger than the field B 2. Each field fills

### Multi-loop Circuits and Kirchoff's Rules

1 of 8 01/21/2013 12:50 PM Multi-loop Circuits and Kirchoff's Rules 7-13-99 Before talking about what a multi-loop circuit is, it is helpful to define two terms, junction and branch. A junction is a point

### 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 &

### 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

### Physics 102 Lab 4: Circuit Algebra and Effective Resistance Dr. Timothy C. Black Spring, 2005

Physics 02 Lab 4: Circuit Algebra and Effective Resistance Dr. Timothy C. Black Spring, 2005 Theoretical Discussion The Junction Rule: Since charge is conserved, charge is neither created or destroyed

### 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

Science Olympiad Circuit Lab Key Concepts Circuit Lab Overview Circuit Elements & Tools Basic Relationships (I, V, R, P) Resistor Network Configurations (Series & Parallel) Kirchhoff s Laws Examples Glossary

### Switch. R 5 V Capacitor. ower upply. Voltmete. Goals. Introduction

Switch Lab 6. Circuits ower upply Goals + + R 5 V Capacitor V To appreciate the capacitor as a charge storage device. To measure the voltage across a capacitor as it discharges through a resistor, and

### PEP 2017 Assignment 12

of the filament?.16.. Aductile metal wire has resistance. What will be the resistance of this wire in terms of if it is stretched to three times its original length, assuming that the density and resistivity

### Review of Ohm's Law: The potential drop across a resistor is given by Ohm's Law: V= IR where I is the current and R is the resistance.

DC Circuits Objectives The objectives of this lab are: 1) to construct an Ohmmeter (a device that measures resistance) using our knowledge of Ohm's Law. 2) to determine an unknown resistance using our

### Lab 6. RC Circuits. Switch R 5 V. ower upply. Voltmete. Capacitor. Goals. Introduction

Switch ower upply Lab 6. RC Circuits + + R 5 V Goals Capacitor V To appreciate the capacitor as a charge storage device. To measure the voltage across a capacitor as it discharges through a resistor, and

### Switch + R. ower upply. Voltmete. Capacitor. Goals. Introduction

Lab 6. Switch RC Circuits ower upply Goals To appreciate the capacitor as a charge storage device. To measure the voltage across a capacitor as it discharges through a resistor, and to compare + the result

### Switch. R 5 V Capacitor. ower upply. Voltmete. Goals. Introduction

Switch Lab 6. Circuits ower upply Goals + + R 5 V Capacitor V To appreciate the capacitor as a charge storage device. To measure the voltage across a capacitor as it discharges through a resistor, and

### Chapter 23 Revision problem. While we are waiting, please try problem 14 You have a collection of six 1kOhm resistors.

Chapter 23 Revision problem While we are waiting, please try problem 14 You have a collection of six 1kOhm resistors. 1 Electric Circuits Elements of a circuit Circuit topology Kirchhoff s law for voltage

### 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

### Induction and inductance

PH -C Fall 01 Induction and inductance Lecture 15 Chapter 30 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th etion) 1 Chapter 30 Induction and Inductance In this chapter we will study the following

### The next two questions pertain to the situation described below. Consider a parallel plate capacitor with separation d:

PHYS 102 Exams Exam 2 PRINT (A) The next two questions pertain to the situation described below. Consider a parallel plate capacitor with separation d: It is connected to a battery with constant emf V.

### 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