2 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 an outlet is alternating voltage AC circuits are much more complicated because circuit elements can introduce lag A typical analysis of AC circuits requires Fourier techniques
3 DC Circuits A voltage difference can be created using a battery This gives rise to an electric field inside the wire Charge can not redistribute itself to cancel the field generated by a battery, because the battery maintains a constant voltage difference even as charge builds up on it.
4 Electro-motive Force For historical reasons, the voltage applied to a circuit is sometimes referred to as an electro-motive force, or emf. Note that the emf is not a force.
5 Current Current is defined as the amount of charge that moves through a crosssection of a wire per unit time: I = Δq Δt
6 Current By convention, we say that current points in the direction that positive charge flows. In most materials, the electrons move. We call the charge responsible for the current the charge carrier.
7 Current Since electrons have a negative charge, the motion of the electron is opposite the direction of the current. current
8 Current Current is a vector: Current has magnitude and direction Like a car traveling down a road, current in a wire can only point in one of two directions. Therefore, current can be thought of as a onedimensional vector. Like any one-dimensional vector, we denote the direction using a plus or minus sign
9 Current For a simple circuit, current flows from high voltage to a low voltage. +
10 Current For a simple circuit, current flows from high voltage to a low voltage. +
11 Current - Example A 12 V battery is connected to a battery charger for 5 hours. The charger carries charge from the low voltage end of the battery, back to the high voltage end of the battery. The charge moves the charge at a rate of 6 A, and the voltage across the battery remains 12 V during this time. (a) How much charge is transferred to the battery during this time? (b) How much energy is transferred to the battery?
12 I = 6 A ΔV = 12 V Δt = 5 hr Δq =? ΔPE =?
13 Ohm s Law Resistance is like friction for current in a wire. Resistance is denoted with by the letter R. The symbol for a resistor is:
14 Ohm s Law The current flowing through a wire is related to the voltage and resistance according to Ohm s Law: ΔV = I R
15 Ohm s Law We can find the units of the resistance using dimensional analysis:
16 Ohm s Law The flow of current through a circuit is analogous to the flow of water through a pipe: Current flow of water ΔV Pressure difference Resistance friction and viscosity of the water
17 Ohm s Law How does the water flow depend on the crosssectional area of the pipe? How does the water flow depend on the length of the pipe?
18 Ohm s Law In a similar manner, the resistance of most wires is related to the length and cross-sectional area of the wire, according to: R = ρ L A Where ρ is called resistivity and is a measure of how well a material conducts current.
19 Ohm s Law - Example An incandescent light bulb is made with a tungsten filament. When plugged into a 120 V outlet, 1.24 A of current flows through the bulb. If the radius of the filament is m and the resistivity of tungsten is Ω m, what is the length of the filament?
20 ΔV = 120 V I = 1.24 A r = m ρ = Ω m L =?
21 When current flows through a resistor the electrostatic energy is converted into heat. Using Power Lost in Resistors P = ΔE Δt we can write a formula for the power converted into heat in a circuit.
22 Power Lost in Resistors Combining this formula with Ohm s Law gives:
23 Power Lost in Resistors The power lost in a resistor is given by: P = I V P = I 2 R P = V2 R
24 Power Lost in Resistors The old-fashioned incandescent light bulbs can be treated like a resistor. What is the resistance of a 60 W light bulb that is designed to be plugged into a 120 V power outlet?
25 Power Lost in Resistors P = 60 W V = 120 V R =?
26 Internal Resistance Most batteries have some resistance between the positive and V term. r int R negative terminals. + V
27 Internal Resistance Some voltage is lost due to this internal resistance. We call the voltage difference between the ends of a battery the terminal voltage V term. + r int V
28 Internal Resistance There are two things to know about internal resistance: 1. The internal resistance is always in series with the objects connected to the battery 2. The internal resistance lowers the terminal voltage by an amount given by Ohm s Law V term = emf I r int
29 Internal Resistance 930 ma flow through a 10 Ω resistor when connected to a battery with a 9.5 V emf. What is the internal resistance of the battery?
30 Internal Resistance V term. =? r int =? R = 10 Ω V
31 Equivalent Resistance Objects in a circuit can be connected in one of two ways: Series Parallel
32 Equivalent Resistance R 1 R 2 + The current through resistor 1 is equal to the current through resistor 2, I 1 = I 2 The total voltage drop across the two resistors is equal to the sum of the voltage drops across each resistor V
33 Equivalent Resistance Want a formula for ΔV total in terms of I, R 1, and R 2. R 1 R 2 + V
34 Equivalent Resistance The two resistors in series behave like a single resistor with resistance R 1 + R 2. We call this the equivalent resistance. R eq = R 1 + R 2 (series)
35 Equivalent Resistance In general, the equivalent resistance of N resistors in series is given by: R eq = R 1 + R 2 + R 3 + R 4 +
36 Equivalent Resistance The voltage across both resistors is the same. The total current that flows through the resistors is the sum of the currents through each resistor. R 1 R 2 + V
37 Equivalent Resistance R 1 Want a formula that relates I total to V, R 1, and R 2. R 2 + V
38 Equivalent Resistance Single Resistor: Parallel Resistors: I = V R I = V 1 R R 2 The two resistors are equivalent to a single resistor with a resistance given by:
39 Equivalent Resistance In general, the equivalent resistance of N resistors connected in parallel is given by: 1 R eq = 1 R R R R 4 +
40 Equivalent Resistance When there are only two resistors connected in parallel, the equivalent resistance can be rewritten as:
41 Equivalent Resistance Notice that, the equivalent resistance for resistors in parallel is always less than the resistance of either of the two resistors. R eq = R 1 R 2 R 1 + R 2
42 Equivalent Resistance If N identical resistors are connected in parallel, the equivalent resistance is equal to:
43 Equivalent Resistance - Example A 15 Ω toaster and a 10 Ω iron are connected in parallel to a 120 V source. A 20 A breaker is connected in series with the power source. Will using both appliances at the same time throw the breaker?
44 R T = 15 Ω R Iron = 10 Ω V = 120 V I =? Breaker R T R Iron V +
45 Equivalent Resistance - Example Using the circuit diagram below, find the: (a) Power dissipated in the circuit when the switch is open (b) equivalent resistance of the circuit when the switch is closed, and (c) power dissipated in the circuit when the switch is closed. + 9V 65Ω 96Ω
46 Equivalent Resistance - Example P open =? P closed =? R eq =? + 9V 65Ω 96Ω
47 Equivalent Resistance - Example A 60 W lamp is placed in series with a resistor and a 120 V source. If the voltage lost across the lamp is 25 V, what is the resistance of the unknown resistor, R? R lamp R + 120V
48 Equivalent Resistance - Example P = 60 W ΔV = 25V R lamp R =? + 120V
49 Complex Circuits When given a complex circuit of resistors, we use divide an conquer to find R eq : Identify a small segment of the circuit for which we can easily calculate an equivalent resistance. Replacing these segments with a single equivalent resistance. Repeat the process until there is only one equivalent resistance.
50 Find the equivalent resistance between points A and B. A Complex Circuits 2Ω 6Ω 1Ω 4Ω 3Ω 2Ω B 3Ω Which portion of the circuit should we calculate the equivalent resistance for?
51 Complex Circuits A 2Ω 6Ω 1Ω 4Ω 3Ω 2Ω B 3Ω
52 Complex Circuits A 2Ω 6Ω 4Ω 3Ω 6Ω B
53 Complex Circuits A 2Ω 6Ω 4Ω 2Ω B
54 Complex Circuits A 2Ω 4Ω 8Ω B
55 Complex Circuits A 2Ω 2.67Ω B
56 Complex Circuits 1Ω 2Ω A 7Ω 6Ω B 3Ω
57 Complex Circuits 1Ω 2Ω A 7Ω 6Ω B 3Ω
58 Complex Circuits 3Ω A 7Ω 6Ω B 3Ω
59 Complex Circuits 3Ω A 7Ω 6Ω B 3Ω
60 Complex Circuits A 7Ω 2Ω B 3Ω
61 Complex Circuits A 7Ω 2Ω B 3Ω
62 Complex Circuits A 12Ω B
63 Kirchoff s Laws While equivalent resistance is useful, it does not allow us to find the voltage drop and current flowing through each individual resistor in a circuit. For this we will need an additional set of equations.
64 Kirchoff s Laws Junction Rule Charge can not be created or destroyed. Therefore, the current flowing into the junction must equal the current flowing out of the junction.
65 Kirchoff s Laws Junction Rule For example: 5 A 3 A I =?
66 Kirchoff s Laws Loop Rule When an electron, starting at point A, goes around a loop in the circuit, and returns to point A, it must have the same voltage that it started with. R V A
67 Kirchoff s Laws Loop Rule Because voltage decreases when current flows through a resistor, the voltage is higher on the side that the current flows in and lower on the side the current flows out. A I B V A > V B
68 Kirchoff s Laws Together these two rules are called Kirchoff s Laws: The current flowing into a junction must equal the current flowing out of the junction The total voltage change around any closed loop must always equal zero volts.
69 Kirchoff s Laws - Example Find I 1, I 2, I 3, and V AB in the circuit below. I 1 A 10 A 10 Ω 14 Ω 8 Ω B I 3 I 2
70 Kirchoff s Laws - Example Use Kirchoff s Laws to solve for all the currents in the circuit below: I 1 5 Ω 12 V I 2 I 3 5 Ω 10 Ω
71 Kirchoff s Laws - Example Use Kirchoff s Laws to solve for all the currents in the circuit below: I 1 4 Ω 2 V 4 Ω 10 V I 2 I 3 3 Ω 2 Ω
72 Making Measurements Measurements in circuits are commonly made using a multi-meter. Which is capable of measuring current, voltage, and resistance.
73 V Making Measurements Ammeters measure current An ammeter must be connected in series, so that the current flows through the ammeter. A + R +
74 V Making Measurements To prevent the ammeter from effecting the circuit, the ammeter has almost no resistance through it. A + R +
75 Making Measurements Voltmeters must be connected in parallel, so that it can measure the voltage difference between two points in the circuit. + V +
76 Making Measurements The voltage between two points can be measured by combining an ammeter and Ohm s Law. By placing a known resistance inside an ammeter, and measuring the current, an ammeter can measure voltage.
77 Capacitors A capacitor is made by placing two metal plates close to each other. When connected to a battery, the plates become oppositely charged.
78 Capacitors Using Gauss s Law, we can calculate the electric field between two oppositely charged parallel plates
79 Capacitors We can split the region up into three sections. Between the two plates the electric fields from the plates add. Outside the plates the electric fields cancel I II III
80 Capacitors Suppose the plates are infinitely long, and have charge per unit area, σ. Consider the following Gaussian Surface:
81 Capacitors The only flux comes through one end of the cylindrical Gaussian Surface. Therefore: Φ = q enc E A = ε 0 σ A ε E E = σ ε 0 A + + +
82 Voltage Across a Capacitor To find the voltage across the capacitor we use: ΔV = E Δx,E
83 Voltage Across a Capacitor The voltage across a capacitor is given by: ΔV = q d A ε 0
84 Voltage Across a Capacitor Notice that the voltage across the capacitor is proportional to the charge on it: ΔV = q d A ε 0 d Also, notice that describes the design of the A ε 0 two plates, and has nothing to do with voltage or charge.
85 Voltage Across a Capacitor Capacitance is a quantity which describes the plates ability to hold charge (think capacity). We define capacitance according to the formula: q = V C
86 Voltage Across a Capacitor If we rearrange: ΔV = q d A ε 0 to solve for q, and compare this with: q = V C We can write a formula for the capacitance of two parallel plates.
87 Voltage Across a Capacitor Two parallel plates of area A and separated by a distance d, have a capacitance of: C = ε 0 A d This is known as a parallel plate capacitor.
88 Voltage Across a Capacitor We can find the units of capacitance using dimensional analysis We call the quantity C a Farad in honor of Michael V Faraday who discovered elecro-magnetic induction.
89 Voltage Across a Capacitor A parallel plate capacitor is connected to a 9V battery. After the capacitor is charged, you remove the capacitor from the battery without removing the charge from the plates of the capacitor. You pull on the plates of the parallel plate capacitor so that the distance between the plates is doubled. What is the new voltage across the capacitor?
90 V 0 = 9 V q f = q 0 d f = 2 d 0 V f =?
91 Energy Stored In a Capacitor When a capacitor is connected to a battery, the battery moves electrons from one plate of the capacitor to the other plate. This process continues until the voltage across the capacitor equals the voltage supplied by the battery. To calculate the energy stored in the capacitor consider the work done by the battery.
92 Energy Stored In a Capacitor As charge is moved from one plate to the other, it becomes more difficult to move the charges.
93 Energy Stored In a Capacitor The total energy stored in the capacitor is the sum of the ΔPE for each charge moved from one plate to the other. The energy required to move a charge Δq across a capacitor with a charge q is: ΔPE = Δq V = q C Δq
94 Energy Stored In a Capacitor Taking the sum of these potential energies PE total = PE In the limit that Δq 0: = Δq q C U = 0 Q q C dq = Q2 2 C
95 Energy Stored In a Capacitor Using V = q C voltage: we can rewrite this in terms of U = q2 2 C = V C 2 2 C = 1 2 C V2
96 Energy Stored In a Capacitor We can also get rid of the capacitance and write it in terms of voltage and charge U = 1 2 = 1 2 C V2 q V V2 = 1 2 q V
97 Energy Stored In a Capacitor We have three formulas for the energy stored inside a capacitor: U = q2 2 C U = 1 2 C V2 U = 1 2 q V
98 Equivalent Capacitance Recall that: A capacitor can be created by placing two conducting surfaces close to each other When a voltage is applied to the plates of a capacitor, charge from one plate moves to the other plate The charge on the capacitor is equal to: q = VC
99 Equivalent Capacitance Just like resistors, capacitors can be connected in series or in parallel Once again, we want to find the equivalent capacitance in each of these scenarios
100 Equivalent Capacitance The charge on capacitors in series is always the same: This is because the charge on the capacitor plates comes from moving charge from another plate.
101 Equivalent Capacitance Since the total voltage across the two plates is equal to the sum of the voltages across each plate: V = V 1 + V 2 = q C 1 + q C 2 = q 1 C C 2 = q C eq Therefore, 1 C eq = 1 C C 2
102 Equivalent Capacitance In general, the equivalent capacitance of many capacitors in series is: 1 C eq = 1 C n = 1 C C C 3 +
103 Equivalent Capacitance Like resistors, the voltage across capacitors in parallel is the same. The total charge on the capacitors is equal to the sum of the charges on each. q = q 1 + q 2 = VC 1 + VC 2 = V(C 1 + C 2 ) = VC eq
104 Equivalent Capacitance Therefore, the equivalent capacitance for capacitors in parallel is: C eq = C n = C 1 + C 2 + C 3 +
105 Equivalent Capacitance - Example Suppose two capacitors are in parallel. Show that the sum of the energy stored in the capacitors is equal to the energy that would be sored in an equivalent capacitor. In other words, demonstrate that: U 1 + U 2 = U eq.
106 Equivalent Capacitance - Example We want to relate U 1 + U 2 to U eq. The energy stored in a capacitor is given by: Therefore, U = q2 2C U 1 + U 2 = q q 2 2 2C 1 2C 2 However, this is not very useful because q 1 q 2.
107 Equivalent Capacitance - Example Using q = VC, we can rewrite this formula in terms of V U 1 + U 2 = q q 2 2 2C 1 2C 2 What quantity is the same for capacitors connected in parallel? U 1 + U 2 = V C V C 2 2C 1 2C 2 = V2 2 C 1 + C 2 = V2 C eq 2 2
108 Equivalent Capacitance - Example A 7 μf and 3 μf capacitor are connected in series across a 24 V battery. What voltage is required to store the same amount of energy is the capacitors were connected in parallel?
109 Equivalent Capacitance - Example C 1 = 7 μf V s = 24 V C 2 = 3 μf To determine the voltage required for a parallel connection, we first need to find the energy stored in a series connection. Just like in the previous example, we can substitute C eq into the energy formula.
110 Equivalent Capacitance - Example C 1 = 7 μf V s = 24 V For capacitors in series: 1 C 2 = 3 μf C eq = 1 C C 2 or C eq = C 1C 2 C 1 +C 2 Therefore, C eq = (7 μf)(3 μf) (7 μf + 3 μf) = 2.1 μf
111 Equivalent Capacitance - Example C 1 = 7 μf V S = 24 V For capacitors in parallel: C 2 = 3 μf C series = 2.1 μf C eq = C 1 + C 2 Therefore, C eq = 3 μf + 7 μf = 10 μf
112 Equivalent Capacitance - Example C 1 = 7 μf V s = 24 V C 2 = 3 μf Since we are not given the charge on the capacitors, we must combine: U = q2 2C To get: and q = VC U = 1 2 C V2
113 Equivalent Capacitance - Example C s = 2.1 μf V s = 24 V Setting the energies equal to each other, and solving for V parallel gives: U series = U parallel 1 2 C s V s 2 = 1 2 C p V p 2 V P 2 = V P C s C p V s 2 = 11 V C p = 10 μf
114 RC Circuits When a capacitor is connected to battery, the battery causes charge to move from one plate of a capacitor to the other. However, as charge builds up on the plates, the repulsive electrostatic force caused by this charge makes it more and more difficult to add additional charge to the capacitor. As a result, the rate that charge builds up on the capacitor slows.
115 RC Circuits Consider applying the loop rule to the following circuit: We get: V = IR + q C
116 The current through the resistor is equal to the rate that the charge on the capacitors changes: I = dq dt RC Circuits Plugging this into the loop rule gives: V = dq dt R + q C
117 RC Circuits V = dq dt R + q C This is called a differential equation. We want to find q t that satisfies this equation. First, lets rewrite this slightly: dq dt = V R q R C
118 RC Circuits dq dt = V R q R C Recall that d dx ex = e x, Therefore, the solution to: dq dt = q RC Is: q = e t RC
119 RC Circuits dq dt = V R q R C Taking the V R term into account gives: q t = q f 1 e t RC
120 RC Circuits A graph of q t = q f 1 e t RC looks like:
121 RC Circuits Notice that time is divided by RC: q t = q f 1 e t RC This means that the product RC tells us how fast the capacitor in a circuit will charge We call this number the time-constant: τ = RC
122 RC Circuit - Example Find the time constant of the circuit shown in the diagram below:
123 RC Circuit - Example The time constant is simply τ = R eq C eq R eq = = R 1 R 2 R 1 + R 2 4 kω 2 kω 4 kω + 2 kω = 1.3 kω
124 RC Circuit - Example The time constant is simply τ = R eq C eq C eq = C 1 + C 2 = 3 μf + 6 μf = 9 μf
125 RC Circuit - Example The time constant is simply τ = R eq C eq τ = R eq C eq = s
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,
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 115 General Physics II Session 24 Circuits Series and parallel R Meters Kirchoff s Rules R. J. Wilkes Email: firstname.lastname@example.org Home page: http://courses.washington.edu/phy115a/ 5/15/14 Phys
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
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
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
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
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
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
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
1 Part 2: Electric Potential 2.1: Potential (Voltage) & Potential Energy q 2 Potential Energy of Point Charges Symbol U mks units [Joules = J] q 1 r Two point charges share an electric potential energy
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
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
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
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
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
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,
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
Electricity Refers to the generation of or the possession of electric charge. There are two kinds of electricity: 1. Static Electricity the electric charges are "still" or static 2. Current Electricity
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 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
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
+ 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
ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations Op-Amp Integrator and Op-Amp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces
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
Exam Total /200 PHYS 2135 Exam II March 20, 2018 Name: Recitation Section: Five multiple choice questions, 8 points each. Choose the best or most nearly correct answer. For questions 6-9, solutions must
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
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
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
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
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 2, March 5th, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations 1 CAPACITANCE AND INDUCTANCE Introduces two passive, energy storing devices: Capacitors
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
SIMPLE D.C. CICUITS AND MEASUEMENTSBackground This unit will discuss simple D.C. (direct current current in only one direction) circuits: The elements in them, the simple arrangements of these elements,
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
Electromagnetic Induction (Chapters 31-3) 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
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.
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
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
General Physics (PHY 2140) Lecture 10 6/12/2007 Electricity and Magnetism Induced voltages and induction Self-Inductance RL Circuits Energy in magnetic fields AC circuits and EM waves Resistors, capacitors
Faculty of Engineering MEP 38: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis Outline oltage and Current Ohm s Law Kirchoff s laws esistors Series and Parallel oltage Dividers
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,
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
Mansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance First Six-Weeks Second Six-Weeks Third Six-Weeks Lab safety Lab practices and ethical practices Math and Calculus
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
Conductor- Insulator: Materia Materials through which electric current cannot pass are called insulators. Electric Circuit: A continuous a CLASS X- ELECTRICITY als through which electric current can pass
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 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
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
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
IMP 113: 2 nd test (Union College: Spring 2010) Instructions: 1. Read all directions. 2. In keeping with the Union College policy on academic honesty, you should neither accept nor provide unauthorized
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
CLSS-10 1. Explain how electron flow causes electric current with Lorentz-Drude theory of electrons?. Drude and Lorentz, proposed that conductors like metals contain a large number of free electrons while
Danger High Voltage! Your friend starts to climb on this... You shout Get away! That s High Voltage!!! After you save his life, your friend asks: What is Voltage anyway? Voltage... Is the energy (U, in
Announcements l Help room hours (1248 BPS) Ian La Valley(TA) Mon 4-6 PM Tues 12-3 PM note this Tues only 12-4 PM Wed 6-9 PM note this Wed only 10-noon Fri 10 AM-noon l LON-CAPA #6 due Oct. 18 l Final Exam
Physics 150 Electric current and circuits Chapter 18 Electric current Let s imagine a conductor with a potendal difference between its ends - - - - NegaDve (lower) potendal V a E! + + + + PosiDve (higher)
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
1 Handout 10: Inductance Self-Inductance and inductors In Fig. 1, electric current is present in an isolate circuit, setting up magnetic field that causes a magnetic flux through the circuit itself. This
Basic Electronics Introductory Lecture Course for Technology and Instrumentation in Particle Physics 2011 Chicago, Illinois June 9-14, 2011 Presented By Gary Drake Argonne National Laboratory email@example.com
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 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
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
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
Announcements l LON-CAPA #7 and Mastering Physics (to be posted) due Tuesday March 11 Resistance l l l The amount of current that flows in a circuit depends not only on the voltage but also on the electrical
This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 00 0.0 points A coil has an inductance of 4.5 mh, and the current
ENERGY AND TIME CONSTANTS IN RC CIRCUITS By: Iwana Loveu Student No. 416 614 5543 Lab Section: 0003 Date: February 8, 2004 Abstract: Two charged conductors consisting of equal and opposite charges forms
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
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
) What is electric current? Flow of Electric Charge 2) What is the unit we use for electric current? Amperes (Coulombs per Second) 3) What is electrical resistance? Resistance to Electric Current 4) What
AP Physics C Magnetism - Term 4 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the world
Last time Ampere's Law Faraday s law 1 Faraday s Law of Induction (More Quantitative) The magnitude of the induced EMF in conducting loop is equal to the rate at which the magnetic flux through the surface
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
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
Name Date INSTRUCTIONS PH 102 Exam I 1. nswer all questions below. ll problems have equal weight. 2. Clearly mark the answer you choose by filling in the adjacent circle. 3. There will be no partial credit
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 cross-sectional area Convention i = dq dt Unit
AP Physics C Electricity - Term 3 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the
Physics 1502: Lecture 8 Today s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Homework #3: On Masterphysics today: due next Friday Go to masteringphysics.com
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,