Electric Currents. Resistors (Chapters 2728)


 Megan McCormick
 1 years ago
 Views:
Transcription
1 Electric Currents. Resistors (Chapters 2728) Electric current I Resistance R and resistors Relation between current and resistance: Ohm s Law Resistivity ρ Energy dissipated by current. Electric power Electromotive force: emf, ε Simple resistive circuits: Series and parallel circuits. Circuits reducible to simple combinations Circuits nonreducible to series and parallel: Kirchhoff Rules Resistors and capacitors combined: dc RC circuit
2 Electric Current Charge Carrier Motion in a Conductor In an electrically insulated wire, the electrons undergo thermal random motion When an potential difference is set up between the ends of a wire, the surface charge gets nonuniformly distributed, producing an electric field inside the wire, such that electrons tend to drift against the average field producing an electric current, I more positive V E E a E c a b b + E c b + E + net E + net When a circuit is completed, the electric field sets in the wires with the speed of light (of the order of 10 8 m/s), and all free electrons throughout the material move very fast; however, their motion is impeded by collisions in the material, so their drift speed, v d, is much smaller, (of the order of 10 4 m/s) Ex: The zigzag lines represent the drift against the electric field of an electron in a conductor. The drift is analog with the parabolic trajectories of a ball drifting due to gravity down a wall with pegs. The nature of the charges carrying the current depends on the nature of the material Ex: electrons in metals, electrons and ions in plasma, holes in semiconductors, etc. e ion cores E v d more negative V m g pegs
3 Electric Current Definition So, whenever electric charges of like signs drift, an electric current is said to exist In order to define it quantitatively, consider at the charge flowing through a wire perpendicular to a crosssectional surface of area A Def: The rate at which the electric charge flows through this surface, that is, the amount of charge dq flowing per unit of time dt through the surface, is called an electric current dq 1C I SI Ampere (A) 1s dt Comments: Conventional current direction: the direction of the current is the direction of the drift of positive charge: that is, in the direction of the average field, or from high potential to low potential Albeit its directionality, the current is not a vector The current across a potential difference is the same through any crosssection, that is, the carriers drift identically as long as the conductive substance is the same The colloquial short for Amperes is Amps I Order of magnitude: flashlight bulb ~1A, sensitive electronics ~μa, highpower devices (such as large electromagnets) ~ka Q A
4 Electric Current Relation to drift speed. Current density To find the relationship between the macroscopic electric current and the microscopic details of the electriccarrier drift, consider elementary charge carriers of charge e drifting with constant drift speed v d through a current carrying conductor of crosssectional area A, with the charge concentration given by: Number of carriers n Volume Then, as shown on the figure, Qe n Q neax Ax Therefore, combining with the definition of current, we find that the current is related to the drift speed v d as following: Q x I nea I neav t t d So, if the drift speed is small (many collisions), the current is small and vice versa. If the carriers are electrons (charge e), the current opposes the drift velocity. Def: The current per unit crosssectional area of a conductor is a vector called current density: J I A nq v d
5 Quiz 1: We learned that the electron drift speed is relatively small: of the order of 10 4 m/s. How come, when the circuit in the figure is closed, the bulb light up almost instantaneously? a) Actually it doesn t: in my house we wait minutes until bulbs light up b) Since the energy of the electric field is delivered to the bulb before electrons from the battery reach to it c) Because the sea of electrons fill all the circuit. When the circuit is closed, the field is set with the speed of light and electrons start to drift through each crosssection of the circuit including the bulb. Quiz 2: Both segments of the shown wire are made of the same metal. Current I 1 flows into segment 1 from the left. How does current I 1 in segment 1 compare to current I 2 in segment 2? a) I 1 > I 2 b) I 1 = I 2 c) I 1 < I 2 d) There s not enough information to compare them
6 Ohm s Law Statement Experiments show that in most metals the current density J depends on: the electric field E the tabulated properties of the material: resistivity ρ or conductivity σ = ρ 1 The dependency is given by Ohm s Law: In an ohmic (or linear) material at constant temperature, the resistivity and conductivity remain constant for any electric field and the current density is proportional to the field: Comments: J E E J constant Ohm s Law does not state the proportionality E ~ J, but the constancy of ρ For most metals, resistivity increases approximately linearly with temperature T, over limited Tranges: 1 T T 0 0 ρ is the resistivity at temperature T ρ 0 is the resistivity at a reference temperature T 0 (usually taken to be 20 C) is the temperature coefficient of resistivity Ex: Only some metals follow this behavior through the whole range of temperatures. The resistivity of superconductors drops sharply to zero under a critical T, while the resistivity of semiconductors decreases with increasing T ρ ρ ρ ρ 0 Slope = αρ 0 T 0 conductor T T c superconductor T T seminconductor
7 Resistance and Resistors A new element of circuit Ohm s law can be reformulated in terms of the potential difference V ab responsible for the electric field driving a current through a wire: V I L V a L A A A I ab E J Vab I Vab RI length parallel with current 1V The quantity R is termed the resistance of the conductor: R SI Ohm (Ω) 1A The elements of circuit with resistance are called resistors. Symbol: a I V V V IR V V ab a b a b R +  b E J area perpendicular on current In a resistor in circuit with a battery, the electric potential decreases in the direction of the current the resistor determines a voltage drop while the potential increases across a battery it determines a voltage raise since a battery does work on the carriers I I I Analogy: circuit of pipes with water in laminar flow L Constricted pipe resistance Flow rate current High Low V b Pump: pressure difference potential
8 Quiz 3: An ohmic material is probed for drawn current I by applying an increasing potential difference V across the sample. Which of the shown I vs. V graphs (called IVcharacteristics) represents the likely dependency of I on V? I I a) b) V V Quiz 4: What geometrical aspect of the IVcharacteristics is a measure of the resistance? a) The intercept of V axis divided by the respective current b) The slope of the graph c) The inverse of the slope of the graph Problems: 1. Temperature dependence of current: A resistor with uniform crosssection and temperature coefficient α = C 1 is heated from T 0 = 20 o C to T = 170 o C. All this time a constant potential difference is applied across the device. If the current through the resistor at T 0 is I 0 = 2.0 A what is the current at temperature T? 2. Resistance and directionality: A metallic solid parallelepiped with resistivity ρ has length L, width a and height b. Find the resistance of the object if a) a potential difference is applied on the ab crosssections b) the potential difference is applied perpendicular on L
9 Meters in a Circuit Measuring current and voltage An ammeter is used to measure current. Symbol: A It must be mounted in line with the element along which the current is measured: all the charge passing through the element must also pass through the meter In order to measure current without modifying it, the ammeter must have a very small resistance, so no potential difference across it A voltmeter is used to measure potential difference. Symbol: It must be connected to the two ends of the element In order to measure the voltage without affecting it, the voltmeter must carry no current so its resistance is very large V
10 Energy Dissipated in a Resistor Qualitative approach We ve seen that the capacitor is an element of circuit that stores electric energy. What about a resistor? What does a resistor do from an energy point of view? Consider an element of positive charge, dq, moving around a closed circuit from point a back to point a As the charge moves through the battery from a to b, the potential energy of the charge increases by Vdq (on behalf of the chemical energy of the battery) As the charge moves through the resistor R, from c to d, it looses energy in collisions with the atoms of the resistor: the energy is transferred to the internal energy ground: taken as having zero potential When the charge returns to a, the net result is that some chemical energy of the battery has been delivered to the resistor and caused its temperature to rise: we say that the energy was dissipated across the resistor Notice that as long the charge flowing around the circuit (that is, the current) looses energy in the resistor, the battery must resupply it in order to maintain the current Resistance acts like friction in a mechanics: without resistance (friction), the current would flow (charges would move) around the circuit without the need of a battery
11 Say that a circuit carries a charge dq through a difference of potential V across a resistor R that dissipates energy du = Vdq The rate at which the energy U is dissipated is the electric power of the resistor: du dq P V P IV dt dt Using Ohm s law, we can find two useful alternative forms: The unit of energy used by electric companies is the kilowatthour: defined in terms of the unit of power and the amount of time it is supplied: 1 kwh = J Quiz: Energy Dissipated in a Resistor Electric power 5. Which of the resistors on the right will draw a larger current? a) A b) B c) Both draw the same current P 2 2 V I R R 6. Which of the two resistors will get hotter? a) A b) B c) Both will get equally hot d) They don t get hot
12 Types of Circuits DirectCurrent or dc circuits are traveled by currents in only one direction: the magnitude of the currents along the circuit branches may vary, but not their direction AlternatingCurrent circuits or ac circuits are traveled by currents in directions alternating with a certain periodicity Different elements of circuit behave differently in dc and ac circuits Electromotive Force Sources and internal resistance Def: An device such as a battery or generator that maintains the current in a closed circuit is said to provide an electromotive force or emf, ε Volts V SI A real battery has some internal resistance r, so some of its energy is dissipated internally Therefore, the voltage V ab across a real battery when it drives a current is not equal to the emf V V Ir ab The voltage V ab is applied to the external circuit of resistance R (called load), so r IR Ir The internal resistance can be represented as a resistor in series with the battery
13 Electromotive Force Comments Notice that the emf ε is equal to the terminal voltage when the current is zero (also called the opencircuit voltage) If the emf source is mounted across a load, a current I is driven and the difference of potential across the battery decreases by Ir The current provided by the battery depends both on the load R and the internal resistance r I R r When R r, the source is considered as ideal Ordinary batteries have a small internal resistance, such that the voltage delivered is less than the nominal voltage which is the emf The battery power is distributed both to the load and internal resistance: So, when R r, most of the power delivered by the battery is transferred to the load 2 2 I I R I r ε r IR Ir Ex: Voltage diagram The voltage V raised by the battery by ε drops both across the internal resistance r and the load R R
14 V V V s In general, for n resistors in series: s ab bc IR IR IR s 1 2 R R R 1 2 R R R R R Electric Circuits Resistors in series When two or more resistors are connected endtoend, they are said to be in series The current is the same in all resistors because any charge that flows through one resistor flows through the other: I I I 1 2 As a consequence of energy conservation around the circuit, the sum of the potential differences across the resistors is equal to the total potential difference across the combination n The series equivalent resistance is always greater than any of the individual resistors V ab V bc R s
15 Electric Circuits Resistors in parallel When two or more resistors are connected to the same two points in the circuit, they are said to be in parallel The potential difference across each resistor is the same As a consequence of charge conservation, the current, that enters into a junction must be equal to the total current leaving that junction, so, using for instance junction a, I I I 1 2 V V V Rp R1 R RR 1 2 Rp R R R R R p V V V In general, for n resistors in parallel: R R R R p 1 2 V V V 1 ab V 2 ab So, the parallel equivalent resistance is always less than the smallest resistor n R p
16 Problems: 3. Current with and without internal resistance: A battery with emf ε and internal resistance r = 2.0 Ω delivers a current I 0 = 100 ma when connected to a load R = 70 Ω. Calculate the current I through the circuit if the internal resistance of the battery were zero. 4. Analysis of combined circuit: An electric circuit contains an ideal battery with ε and four given resistors, R 1, R 2, R 3, R 4, arranged as in the figure. a) Calculate the equivalent resistance of the circuit. b) Calculate the current through resistor R 4 and the potential difference V bc across it c) Calculate the potential difference V ab across points a and b on the circuit. d) Calculate the currents I 1 and I 2 through R 1 and R 2, 3 respectively. e) Say that point c is grounded. What are the potentials in points a, b, and d with respect to this ground? What changes if the ground changes? a ε R 1 R 2 d R 3 c R 4 b
17 Kirchhoff s Rules Statements Resistors can be connected so that the circuits formed cannot be reduced to a single equivalent resistor as a combination of parallel and series arrangements These generic circuits can be analyzed that is, can be described in terms of currents carried along various branches, and potential differences between different points in the circuit using Kirchhoff s Rules: 1. Junction Rule A statement of Charge Conservation The sum of the currents entering any junction must equal the sum of the currents leaving that junction I 0 2. Loop Rule A statement of Energy Conservation The sum of the potential differences across all the elements around any closed circuit loop must be zero V 0
18 Kirchhoff s Rules Junction rule I in I out How to use the rule: Assign symbols and directions to the currents in all branches of the circuit The directions can be arbitrary: if a direction is chosen incorrectly, the current resulting after solving the equations will be negative, with a correct magnitude Write the junction rule for as many junctions as needed as needed, as long as each time you write an equation you include in it a current that has not been used in a previous junction rule equation In general, the number of times the junction rule can be used is one fewer than the number of junction points in the circuit Ex: Hydrodynamic analog: the current entering into a junction splits into partial currents (a) as water flowing into bifurcating pipes (b)
19 Kirchhoff s Rules Loop rule How to use the rule: Vi around a loop Circuits contain loops of electric elements such as resistors and batteries Choose an arbitrary direction to travel around a circuit loop Resistors: 0 Ex: clockwise loop If the resistor is traveled in the direction of the current: V = IR (voltage drop) If the resistor is traveled opposite to the current: V = +IR (voltage raise) Batteries: If the source of emf is traveled in the direction of the emf: V = +ε (voltage raise) If the source of emf is traveled opposite to the emf: V = ε (voltage drop)
20 Kirchhoff s Rules Problem solving strategy 1. Draw the circuit diagram and assign labels and symbols to all quantities 2. Assign directions to the currents no need for the directions to be all correct; a current with an incorrectly chosen direction will eventually come out negative 3. Apply the junction rule to any junction in the circuit 4. Apply the loop rule to as many loops as are needed to solve for the unknowns 5. Solve the equations simultaneously for the unknown quantities. Check your answers Problems: a 5. Applying Kirchhoff s Rules one battery: An electric circuit contains an ideal battery with ε = 6 V and four given resistors, R 1 = 10 Ω, R 2 = 12 Ω, R 3 = 2 Ω, arranged as in the figure. Use Kirchhoff Rules to calculate the currents I, I 1, I 2 through the branches of the circuit. ε b R 1 R 2 6. Applying Kirchhoff s Rules two batteries: An electric circuit contains 4 resistors and two ideal batteries, as in the figure. Write out Kirchhoff rules for this circuit. R 4 a ε 1 R2 ε 2 c R 1 d b R 3
21 RC Circuit Functionality A more complex behavior is expected when resistors are connected in the same circuit with capacitors forming an RC dccircuit: in these circuits, currents will be unidirectional (dc), but their magnitudes will vary with time When the RC circuit is completed is series with a battery ε, the capacitor C starts to charge and the circuit is called in charging regime Due to the presence of resistance R, the flow of charge is slowed down, such that the capacitor will take time to approach its maximum charge Q = Cε The capacitor builds a potential opposing the battery, so the current i which is initially ε/r when there is no charge on the capacitor decreases until the capacitor is fully charged and the current in the circuit tends to zero Subsequently, if the battery is removed, the capacitor will enter in a discharging regime gradually releasing its charge through the resistor like a finitecharge reservoir Initially the capacitor drives the current ε/r opposite to the current in the charging regime, but the current decreases since the charge on the capacitor depletes ready for charging ready for discharging
22 RC Circuit Charging regime Using Kirchhoff rules around the circuit, one ca obtain an equation for how the charge on the capacitor increases with time exponentially, tending to Q final = Cε: q Q 1e final t RC time constant τ = RC charging Consequently, the current through resistor decreases with time from I 0 = ε/r to zero: i I e 0 t RC The constant = RC is called the time constant and represents the time required for the charge to increase from zero to 63.2% of its maximum In a circuit with a large time constant, the capacitor charges and discharges slowly
23 RC Circuit Discharging regime When the battery is removed, the capacitor discharges and it can be shown that the charge decreases exponentially with time, from Q 0 asymptotically to zero: discharging q t Q0e time constant τ The current decreases exponentially from I 0 (but in opposite direction than when charging) i t I0e I 0 V R Q RC 0 0 maximum voltage across the capacitor
24 Problems: 7. Charging an RC circuit: Demonstrate that the time dependency of the charge on the plates of a capacitor in an RCcircuit charged by a battery with emf ε is, indeed, given by 1 t RC t RC 1 f q C e Q e 8. RC circuit: An RC circuit is connected to a battery with emf ε = 10 V. The capacitance is C = 0.50 μf and the resistance is R = 4.0 MΩ. a) Calculate the current and the amount of charge accumulated in the capacitor at t = 0.20 s in the charging regime b) How long will it take until the charge reaches half of its maximum value c) If the battery is removed (discharging regime), how long will it take until the charge in the capacitor is half the maximum charge d) What is the current through the resistor at that moment?
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 informationChapter 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 informationElectric Current. Chapter 17. Electric Current, cont QUICK QUIZ Current and Resistance. Sections: 1, 3, 4, 6, 7, 9
Electric Current Chapter 17 Current and Resistance Sections: 1, 3, 4, 6, 7, 9 Whenever electric charges of like signs move, an electric current is said to exist The current is the rate at which the charge
More informationChapter 17. Current and Resistance. Sections: 1, 3, 4, 6, 7, 9
Chapter 17 Current and Resistance Sections: 1, 3, 4, 6, 7, 9 Equations: 2 2 1 e r q q F = k 2 e o r Q k q F E = = I R V = A L R ρ = )] ( 1 [ o o T T + = α ρ ρ V I V t Q P = = R V R I P 2 2 ) ( = = C Q
More informationLecture 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 informationAP 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 crosssectional area of the conductor changes. If a conductor has no current,
More informationChapter 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 informationChapter 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 informationChapter 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 informationElectromotive 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,
More informationChapter 7 DirectCurrent Circuits
Chapter 7 DirectCurrent Circuits 7. Introduction... 7. Electromotive Force... 7.3 Resistors in Series and in Parallel... 4 7.4 Kirchhoff s Circuit Rules... 6 7.5 VoltageCurrent Measurements... 8 7.6
More informationChapter 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
More informationCurrent and Resistance
Current and Resistance 1 Define the current. Understand the microscopic description of current. Discuss the rat at which the power transfer to a device in an electric current. 2 21 Electric current 22
More informationElectric 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 informationPhysics 1214 Chapter 19: Current, Resistance, and DirectCurrent Circuits
Physics 1214 Chapter 19: Current, Resistance, and DirectCurrent Circuits 1 Current current: (also called electric current) is an motion of charge from one region of a conductor to another. Current When
More informationSuperconductors 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
More informationAC 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 informationAP Physics C  E & M
AP Physics C  E & M Current and Circuits 20170712 www.njctl.org Electric Current Resistance and Resistivity Electromotive Force (EMF) Energy and Power Resistors in Series and in Parallel Kirchoff's
More informationPhysics 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 informationChapter 3: Electric Current and DirectCurrent Circuit
Chapter 3: Electric Current and DirectCurrent Circuit n this chapter, we are going to discuss both the microscopic aspect and macroscopic aspect of electric current. Directcurrent is current that flows
More informationChapter 3: Electric Current And DirectCurrent Circuits
Chapter 3: Electric Current And DirectCurrent Circuits 3.1 Electric Conduction 3.1.1 Describe the microscopic model of current Mechanism of Electric Conduction in Metals Before applying electric field
More informationChapter 26 DirectCurrent and Circuits.  Resistors in Series and Parallel  Kirchhoff s Rules  Electric Measuring Instruments  RC Circuits
Chapter 26 DirectCurrent 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
More informationChapter 27. Current and Resistance
Chapter 27 Current and Resistance Electric Current Most practical applications of electricity deal with electric currents. The electric charges move through some region of space. The resistor is a new
More informationPhysics 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 informationDirectCurrent Circuits. Physics 231 Lecture 61
DirectCurrent Circuits Physics 231 Lecture 61 esistors in Series and Parallel As with capacitors, resistors are often in series and parallel configurations in circuits Series Parallel The question then
More informationChapter 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 informationDC 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 informationChapter 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
More informationChapter 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 informationELECTRIC CURRENT. Ions CHAPTER Electrons. ELECTRIC CURRENT and DIRECTCURRENT 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 informationCapacitance. 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 informationChapter 26 DirectCurrent Circuits
Chapter 26 DirectCurrent 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 informationCapacitance, 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 informationChapter 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 informationChapter 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 informationChapter 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 informationCHAPTER 1 ELECTRICITY
CHAPTER 1 ELECTRICITY Electric Current: The amount of charge flowing through a particular area in unit time. In other words, it is the rate of flow of electric charges. Electric Circuit: Electric circuit
More informationEXPERIMENT 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 informationClass 8. Resistivity and Resistance Circuits. Physics 106. Winter Press CTRLL to view as a slide show. Class 8. Physics 106.
and Circuits and Winter 2018 Press CTRLL to view as a slide show. Last time we learned about Capacitance Problems ParallelPlate Capacitors Capacitors in Circuits Current Ohm s Law and Today we will learn
More informationChapter 27. Current And Resistance
Chapter 27 Current And Resistance Electric Current Electric current is the rate of flow of charge through some region of space The SI unit of current is the ampere (A) 1 A = 1 C / s The symbol for electric
More informationPhysics 7B1 (A/B) Professor Cebra. Winter 2010 Lecture 2. Simple Circuits. Slide 1 of 20
Physics 7B1 (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 informationFlow 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
More informationCurrent. source charges. test charg. 1. Charges in motion
Current 1. Charges in motion 1. Cause of motion 2. Where is it going? 3. Let's keep this going. 2. Current 1. Flow of particles in pipes. 2. A constant problem 3. Conservation Laws 4. Microscopic motion
More informationClosed loop of moving charges (electrons move  flow of negative charges; positive ions move  flow of positive charges. Nucleus not moving)
Unit 2: Electricity and Magnetism Lesson 3: Simple Circuits Electric circuits transfer energy. Electrical energy is converted into light, heat, sound, mechanical work, etc. The byproduct of any circuit
More informationElectromagnetic Induction (Chapters 3132)
Electromagnetic Induction (Chapters 313) The laws of emf induction: Faraday s and Lenz s laws Inductance Mutual inductance M Self inductance L. Inductors Magnetic field energy Simple inductive circuits
More informationELECTRIC CURRENTS D R M A R T A S T A S I A K D E P A R T M E N T O F C Y T O B I O L O G Y A N D P R O T E O M I C S
ELECTRIC CURRENTS D R M A R T A S T A S I A K D E P A R T M E N T O F C Y T O B I O L O G Y A N D P R O T E O M I C S lecture based on 2016 Pearson Education, Ltd. The Electric Battery Electric Current
More informationChapter 27. Current And Resistance
Chapter 27 Current And Resistance Electric Current Electric current is the rate of flow of charge through some region of space The SI unit of current is the ampere (A) 1 A = 1 C / s The symbol for electric
More informationVersion 001 CIRCUITS holland (1290) 1
Version CIRCUITS holland (9) This printout should have questions Multiplechoice questions may continue on the next column or page find all choices before answering AP M 99 MC points The power dissipated
More informationElectric charge is conserved the arithmetic sum of the total charge cannot change in any interaction.
Electrostatics Electric charge is conserved the arithmetic sum of the total charge cannot change in any interaction. Electric Charge in the Atom Atom: Nucleus (small, massive, positive charge) Electron
More informationPHY102 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 informationInsulators Nonmetals are very good insulators; their electrons are very tightly bonded and cannot move.
SESSION 11: ELECTRIC CIRCUITS Key Concepts Resistance and Ohm s laws Ohmic and nonohmic conductors Series and parallel connection Energy in an electric circuit Xplanation 1. CONDUCTORS AND INSULATORS
More informationphysics 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 informationAP Physics C  E & M
Slide 1 / 27 Slide 2 / 27 AP Physics C  E & M Current, Resistance & Electromotive Force 20151205 www.njctl.org Slide 3 / 27 Electric Current Electric Current is defined as the movement of charge from
More informationCurrent and Resistance
Chapter 26 Current and Resistance Copyright 261 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
More informationResistivity and Temperature Coefficients (at 20 C)
Homework # 4 Resistivity and Temperature Coefficients (at 0 C) Substance Resistivity, Temperature ( m) Coefficient, (C )  Conductors Silver.59 x 00.006 Copper.6 x 00.006 Aluminum.65 x 00.0049 Tungsten
More informationChapter 18. Direct Current Circuits II
Chapter 18 Direct Current Circuits II So far A circuit consists of threefour elements: Electromotive force/power supply/battery capacitors, resistors inductors Analyzed circuits with capacitors or resistors
More information10/14/2018. Current. Current. QuickCheck 30.3
Current If QCurrent is the total amount of charge that has moved past a point in a wire, we define the current I in the wire to be the rate of charge flow: The SI unit for current is the coulomb per second,
More informationElectricity
Electricity Electric Charge There are two fundamental charges in the universe. Positive (proton) has a charge of +1.60 x 1019 C Negative (electron) has a charge of 1.60 x 1019 C There is one general
More informationRead Chapter 7; pages:
Forces Read Chapter 7; pages: 191221 Objectives:  Describe how electrical charges exert forces on each other; Compare the strengths of electric and gravitational forces; Distinguish between conductors
More informationChapter 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 informationPhys 2025, First Test. September 20, minutes Name:
Phys 05, First Test. September 0, 011 50 minutes Name: Show all work for maximum credit. Each problem is worth 10 points. Work 10 of the 11 problems. k = 9.0 x 10 9 N m / C ε 0 = 8.85 x 101 C / N m e
More informationBy Mir Mohammed Abbas II PCMB 'A' CHAPTER FORMULAS & NOTES. 1. Current through a given area of a conductor is the net charge passing
Formulae For u CURRENT ELECTRICITY 1 By Mir Mohammed Abbas II PCMB 'A' 1 Important Terms, Definitions & Formulae CHAPTER FORMULAS & NOTES 1. Current through a given area of a conductor is the net charge
More informationDirectCurrent Circuits
DirectCurrent Circuits A'.3/.". 39 ' )232./ 32,+/" 7+3(5.)232./ 7 3244)'03,.5B )*+," &'&./( 01*234 352567+ *7 2829*4& )"< 35 )*+,"= 94 3563 A0.5.C2/'231).D')232.')21 < /633">&@5:836+0"1464625"4*43"
More informationPHYS 202 Notes, Week 6
PHYS 202 Notes, Week 6 Greg Christian February 23 & 25, 2016 Last updated: 02/25/2016 at 12:36:40 This week we learn about electromagnetic induction. Magnetic Induction This section deals with magnetic
More informationphysics 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 informationDirect Current (DC) Circuits
Direct Current (DC) Circuits NOTE: There are short answer analysis questions in the Participation section the informal lab report. emember to include these answers in your lab notebook as they will be
More informationPhysics 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 informationPhysics 1B Electricity & Magnetism. Frank Wuerthwein (Prof) Edward Ronan (TA) UCSD
Physics 1B Electricity & Magnetism Frank Wuerthwein (Prof) Edward Ronan (TA) UCSD Quiz 1 Quiz 1A and it s answer key is online at course web site. http://hepuser.ucsd.edu/twiki2/bin/view/ UCSDTier2/Physics1BWinter2012
More informationA Review of Circuitry
1 A Review of Circuitry There is an attractive force between a positive and a negative charge. In order to separate these charges, a force at least equal to the attractive force must be applied to one
More informationPhysics 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 informationChapter 18. Direct Current Circuits
Chapter 18 Direct Current Circuits Sources of emf The source that maintains the current in a closed circuit is called a source of emf Any devices that increase the potential energy of charges circulating
More informationPH 2222C Fall Circuits. Lectures Chapter 27 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 2222C Fall 2012 Circuits Lectures 1112 Chapter 27 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 27 Circuits In this chapter we will cover the following topics: Electromotive
More informationChapters 24/25: Current, Circuits & Ohm s law Thursday September 29 th **Register your iclickers**
Chapters 24/25: Current, Circuits & Ohm s law Thursday September 29 th **Register your iclickers** Conductors under dynamic conditions Current, current density, drift velocity Ohm s law Types of conductor
More informationChapter 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 informationPHYSICS. Chapter 27 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 27 Lecture RANDALL D. KNIGHT Chapter 27 Current and Resistance IN THIS CHAPTER, you will learn how and why charge moves through a wire
More informationChapter 27. Current and Resistance
Chapter 27 Current and Resistance Electric Current Most practical applications of electricity deal with electric currents. The electric charges move through some region of space. The resistor is a new
More informationPhysics 169. Luis anchordoqui. Kitt Peak National Observatory. Wednesday, March 8, 17
Physics 169 Kitt Peak National Observatory Luis anchordoqui 1 5.1 Ohm s Law and Resistance ELECTRIC CURRENT is defined as flow of electric charge through a crosssectional area Convention i = dq dt Unit
More informationfehmibardak.cbu.tr Temporary Office 348, Mühendislik Fakültesi B Blok
fehmibardak.cbu.tr Temporary Office 348, Mühendislik Fakültesi B Blok 1 Course Progress Introductory level Electrostatic, Coulomb s Law Electric Field, Gauss Law Magnetic field, Maxwell s Equations Current,
More informationPhysicsAndMathsTutor.com
Electricity May 02 1. The graphs show the variation with potential difference V of the current I for three circuit elements. PhysicsAndMathsTutor.com When the four lamps are connected as shown in diagram
More informationElectric Charge. Electric Charge ( q ) unbalanced charges positive and negative charges. n Units Coulombs (C)
Electric Charge Electric Charge ( q ) unbalanced charges positive and negative charges n Units Coulombs (C) Electric Charge How do objects become charged? Types of materials Conductors materials in which
More informationDirect 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 information1 Written and composed by: Prof. Muhammad Ali Malik (M. Phil. Physics), Govt. Degree College, Naushera
CURRENT ELECTRICITY Q # 1. What do you know about electric current? Ans. Electric Current The amount of electric charge that flows through a cross section of a conductor per unit time is known as electric
More informationQuestion 3: How is the electric potential difference between the two points defined? State its S.I. unit.
EXERCISE (8 A) Question : Define the term current and state its S.I unit. Solution : Current is defined as the rate of flow of charge. I = Q/t Its S.I. unit is Ampere. Question 2: Define the term electric
More informationElectric Currents & Resistance
Electric Currents & Resistance Electric Battery A battery produces electricity by transforming chemical energy into electrical energy. The simplest battery contains two plates or rods made of dissimilar
More information52 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 information3 Electric current, resistance, energy and power
3 3.1 Introduction Having looked at static charges, we will now look at moving charges in the form of electric current. We will examine how current passes through conductors and the nature of resistance
More informationPEP 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
More informationTactics 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
More informationand in a simple circuit Part 2
Current, Resistance, and Voltage in a simple circuit Part 2 Electric Current Whenever electric charges of like signs move, an electric current is said to exist. Look at the charges flowing perpendicularly
More informationCOPYRIGHTED MATERIAL. DC Review and PreTest. Current Flow CHAPTER
Kybett c0.tex V303/3/2008 8:44pm Page CHAPTER DC Review and PreTest Electronics cannot be studied without first understanding the basics of electricity. This chapter is a review and pretest on those
More informationChapter 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 informationREVISED HIGHER PHYSICS REVISION BOOKLET ELECTRONS AND ENERGY
REVSED HGHER PHYSCS REVSON BOOKLET ELECTRONS AND ENERGY Kinross High School Monitoring and measuring a.c. Alternating current: Mains supply a.c.; batteries/cells supply d.c. Electrons moving back and forth,
More information5. In parallel V 1 = V 2. Q 1 = C 1 V 1 and Q 2 = C 2 V 2 so Q 1 /Q 2 = C 1 /C 2 = 1.5 D
NSWRS  P Physics Multiple hoice Practice ircuits Solution nswer 1. The resistances are as follows: I:, II: 4, III: 1, IV:. The total resistance of the 3 and 6 in parallel is making the total circuit resistance
More informationUNIT II CURRENT ELECTRICITY
UNIT II CUENT ELECTICITY Weightage : 07 Marks Electric current; flow of electric charges in a metllic conductor, drift velocity, mobility and their relation with electric current. Ohm s law electrical
More informationBasic Electricity. Unit 2 Basic Instrumentation
Basic Electricity Unit 2 Basic Instrumentation Outlines Terms related to basic electricitydefinitions of EMF, Current, Potential Difference, Power, Energy and Efficiency Definition: Resistance, resistivity
More information3/17/2009 PHYS202 SPRING Lecture notes Electric Circuits
PHYS202 SPRING 2009 Lecture notes Electric Circuits 1 Batteries A battery is a device that provides a potential difference to two terminals. Different metals in an electrolyte will create a potential difference,
More informationSection 1 Electric Charge and Force
CHAPTER OUTLINE Section 1 Electric Charge and Force Key Idea questions > What are the different kinds of electric charge? > How do materials become charged when rubbed together? > What force is responsible
More informationElectric 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 informationMonday 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 informationChapter 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