I depicted in Figure 1. When a current of I amps (A) flows through the resistor, a voltage drop V AB volts (V) appears across the terminals A and B.

Size: px
Start display at page:

Download "I depicted in Figure 1. When a current of I amps (A) flows through the resistor, a voltage drop V AB volts (V) appears across the terminals A and B."

Transcription

1 ntroduction to DC Circuits v 0.92: September 20, 2018 Gerald ecktenwald 1 ntroduction Engineers from all disciplines need to have working knowledge of basic electrical circuits. These notes introduce the following fundamental concepts. 1. eview of Ohm s Law 2. Power dissipation 3. esisters in series 4. esistors in parallel t is important to have more than just a knowledge of the vocabulary and concepts. Engineers need to be able to work with mathematical models of DC circuits in order to predict the behavior of circuits and to choose components (resistors, capacitors, diodes, etc.) 2 Ohm s Law Ohm s law is the quantitative relationship between electrical current and voltage when the current flows through a resistor or conductor. Ohm s law applies to individual resistive elements, e.g., lengths of wire and resistors, as well as networks of resistive elements. Consider a wire or resistor with resistance ohm (Ω) depicted in Figure 1. When a current of amps (A) flows A B through the resistor, a voltage drop V AB volts (V) appears across the terminals A and B. V AB = V AB We say that V AB is a voltage drop because the voltage at A is higher than the voltage at B. Figure 1: Ohm s law for a conductor. For the resistor in the diagram, there is no ambiguity about the physical end points that correspond to the and poles. Therefore, we can simply write V =. (1) The double arrow associated with V AB in Figure 1 indicates the end points that correspond to V AB, or since in this case the end points are not ambiguous, V. The units of the terms in Ohm s Law define the relationship between the units of voltage, current and resistance. V = = 1 volt = 1 amp 1 ohm = 1 V = 1 A 1 Ω We can rearrange Ohm s law to obtain other useful formulas and see other relationships between

2 ME 120 ntroduction to DC Circuits 2 units = V 1 volt = 1 amp = 1 ohm or 1 A = 1 V 1 Ω = V = 1 ohm = 1 volt 1 amp or 1 Ω = 1 V 1 A 3 Physical Definitions of Current, Voltage and esistance Ohm s law is a fundamental relationship between voltage, current and resistance that determine the flow of electricity through a single conductor with two clearly delineated ends. But what are the fundamental definitions or properties of voltage, current and resistance? n other words, can we define those quantities in terms of more basic physical quantities that are independent of Ohm s law? The answer, of course, is yes. Current is the flow of electrons, or equivalently, the flow of electrical charge. The unit of charge is coulomb, which is given the symbol C. An amp is defined as 1 A = 1 C 1 s = 1 coulomb 1 second (2) Voltage is a measure of the work (or energy) necessary to separate opposite charges. The units of energy joule (J) and the units of charge are coulomb (C), and a volt is defined as 1 V = 1 J 1 C = 1 joule 1 coulomb esistance is a macroscopic property of a fixed amount of material. Electrical conductors have an intrinsic property called the resistivity. n other words, whereas a fixed amount of material, say a length of wire, has a value of resistance, the material that makes up that wire has a resistivity that is independent of the amount. The relationship between wire length, skinniness and intrinsic material properties are expressed by = ρl (4) A where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire. n most practical engineering situations we usually work with the macroscopic value of resistance, not the resistivity of the material. However, when comparing materials for a particular application, say in the design of a heating element, we use Equation (4). Let s compare a copper wire 0.64 mm in diameter 1 and 1 m long with a wire of the same diameter, but 2 m long. ntuitively we might guess that a greater length of wire would have a greater resistance, and we would be right. However, the diameter of the wire also has an effect. Skinnier wires have a higher resistance than fatter wires. But what about the material properties? Copper is better at conducting electricity than wood or plastic 2. 1 A 22 gage wire has diameter of 0.64 mm or inch. 2 That s why, of course, wires are made of copper. (3)

3 ME 120 ntroduction to DC Circuits 3 4 Work, Energy and Power We have already introduced the definitions of voltage, current and resistance. Next we turn to work, energy and power. 4.1 Definitions Although power, work and energy have everyday meanings, we need to define these terms with a precision that allows quantitative calculations. Work and Energy Work is a thermodynamic quantity with the same units as energy. Mechanical work is defined as the energy necessary to raise a weight a given distance. Figure 2 is a schematic representation of a mass m being raised through a distance d. The weight of the mass is W = mg. The amount of mechanical work done in raising the weight is Work = force distance = (mg) d. (5) The work done is equivalent to the change in potential energy 2 d 1 W W = mg Change in potential energy = mgd. (6) Figure 2: aising a weight W through a distance d. The unit of work or energy is joule 3. One joule is defined as a newton-meter 1 J = 1 N 1 m (7) The unit of force is Newton and is defined from the units of Newton s law of motion, F = ma 1 N = 1 kg 1 m s 2 (8) Work is done when a force acting on an object causes that object to move. The motion can be in any direction. For example, as depicted in Figure 3, pushing a block with a force F through a horizontal distance d does F d units of work on the block. Unlike raising a weight (see Figure 2), pushing the block horizontally does not change the potential energy of the block. The work input is dissipated by friction between the block and the table surface. f the table was frictionless, or if the block was supported by rollers having zero friction, the force necessary to move the block would be theoretically zero, and hence no work would be done. Power and Work Power is the rate at which work is done. t is also the rate at which energy is expended. The S unit of power is watt 4. 1 W = 1 J (9) 1 s 3 n honor of James Prescott Joule ( ), who, among other achievements, built an elegant experiment to show the equivalents of mechanical work and thermal energy. Although the unit of energy is named after James Prescott Joule, when joule is used as the unit of energy, it is not capitalized. The same is true for other units named after people who made important contributions to science, e.g. curie, newton, and watt. 4 Named after James Watt, a Scottish engineer, who lived from 1736 to 1819.

4 ME 120 ntroduction to DC Circuits Power Dissipation in a conductor When electrical current flows through a simple conductor, like that in Figure 1, the power dissipation is P = V (10) where P is the power (in Watt)s, V is the voltage across the conductor (in Volts), and is the current through the conductor (in Amps). f we use Ohm s law to substitute for V in Equation (10) we obtain P = () = 2 (11) Alternatively, if we rearrange Ohm s law as = V/ and substitute this expression for in Equation (10) we get ( ) V P = V (12) The three equivalent formulas for power dissipated in a single conductive element are P = V = 2 = V 2 (13) Example 1 Energy consumed by a light bulb How much energy is consumed when a 40W light bulb burns for 5 minutes? Given: Find: A 40W light bulb. Energy consumed in 5 minutes. Solution: Note: no voltage or current are given. s there enough information to solve this problem? Answer: yes. The goal is the find the amount of energy consumed. n engineering, Energy is an amount and power is the rate at which that energy is transferred. n other words, power is an amount of energy transfered in a given time interval. We start with the defintion of power as Power = rate of energy dissipation = Force F energy dissipated time d Figure 3: Pushing a block across a table does F d units of work.

5 ME 120 ntroduction to DC Circuits 5 Let E be the amount of energy consumed in time t. P = E t = E = P t. We know P and t. Therefore, the rest of the analysis amounts to substituting known values into the preceeding formula. ( (40 W) 5 min 60 s ) ( = 40 J ) (300 s) = J = 12 kj. 1 min s Therefore, E = J = 12 kj. Discussion: The analysis is a straight forward use of Ohm s law and the definition of power. Example 2 Characteristics of a light bulb A D cell battery supplies 2W of power to a small lightbulb. 1. Find the current from the battery 2. Find the resistance of the bulb Given: A D-cell connected in series with a light bulb. Find: Current consumed and electrical resistance of the bulb if the battery supplies 2W. Schematic: D 2W V b =?

6 ME 120 ntroduction to DC Circuits 6 Solution: What do we know? Battery is a D cell = V b = 1.5 V. Power dissipation is 2 W. We don t know the resistance of the light bulb. Does Ohm s law apply? Yes! V b = where is the current flowing through the bulb, and is the resistance of the bulb. Both and are unknown. Additional information is available from the power dissipation of 2W. Apply the formula for power P = V b where both the power P and the battery voltage V b are known. We can solve this equation for the unknown current, = P = 2 W V b 1.5 V = 2 3/2 A = 4 3 A. Therefore = 4 3 A Now that is known, use it in Ohm s law for the resistor Therefore V b = = = V = 1.5 V 4 3 A = Ω = 1.13 Ω. Discussion: There are two separate ways to solve this problem. We ll call these Plan A and Plan B, respectively. Plan A (used in the example) Start with P = V b where both P and V b are known. Solve for. With known (freshly computed), apply Ohm s law V b = Now that both V b and are known, we can solve for. = V b. Plan B (Equally valid procedure:) Start with an alternative definition of power. P = V b 2 where both P and V b are known. Solve for = V b 2 Now that is known (freshly computed) we can apply Ohm s law V b = and solve for = V b t is not uncommon to have multiple algebraic paths in the analysis of an problem. n this case, both approaches require the same number of steps. That is not always the case. Although there is an advantage, or an aesthetic preference, for shorter and more direct solutions, the primary

7 ME 120 ntroduction to DC Circuits 7 goal is mathematical correctness. An important, but secondary, goal is clarity how well does the algebra show the logic of the analysis? n this case, both approaches are equivalent. 5 Equivalent esistance Consider the options for extending the circuit from Example 2 to circuits where the battery is connected to two light bulbs at the same time. There are two possible configurations as depicted in Figure 4. Are these configurations equivalent? For example, would you expect the brightness of the light bulbs in the two configurations to be the same? Hands-on Learning: t would be a very good idea to gather some materials to experiment with these circuits. You will need a small flashlight bulb, an AA or AAA cell battery (or two), and a piece of scrap wire. The positive terminal of a typical incandescent light bulb is the nub that protrudes from the bottom end. The negative terminal is the metallic side of the bulb. The schematics in Figure 4 attempt to suggest these features and how to connect the circuits. f you are using small flashlight bulbs and AA or AAA batteries, you can use your fingers to hold the bare ends of a small piece of wire to the battery terminals and bulbs. You could also use tape to make the connections more robust. More permanent solutions with glue or soldering are not necessary and would make it more difficult to experiment with alternate circuit configurations. What happens when you connect the battery to the bulbs with the opposite polarity (i.e., switching the positive and negative terminals) from that shown in Figure 4? How does the brightness of the individual bulbs compare for the two arrangements in Figure 4? Note that the use of incandescent light bulbs is a convenience for the purpose of demonstration. Any resistor, or more generally any load, such as a DC motor or resistive heating element, could be connected to the battery. Furthermore, the resistive elements need not be the same. We will explore the more general case of unequal resistances after discussing the simpler case of two equal resistive load elements. What thoughts go through an engineer s mind when she looks at the two possible configurations of the light bulb circuits in Figure 4? An obvious question is, Will either of these circuits work? n other words, if hook up the circuit according to either of the diagrams, will the two bulbs light up? The answer is, it depends. Try it! The two circuits in Figure 4 are correct in the sense that when the wires, batteries and bulbs are connected as shown, current will flow through the bulbs. Series circuit Parallel circuit Figure 4: Two light bulbs arranged in a series connection (left) and a parallel connection (right).

8 ME 120 ntroduction to DC Circuits 8 Despite being correct circuits, there are practical choices of bulbs and batteries that will result in no light being emitted from the bulbs. How can that be? Being able to ask and then answer that question is an example of thinking like an engineer. The light coming from the bulbs depends on the size of the battery and the size of the bulbs. We put size in quotes because that term is too vague for engineering purposes. We need to use the more precise language from the preceding section of these notes. nstead of size, we need to think of voltage, current, resistance and power. The size of the battery is specified by its rated voltage, current and power it can supply. By rated we mean the values that we expect from the label or the standard specifications for a given type of battery. The size of a light bulb is specified by its rated voltage and the amount of power the bulb can dissipate without burning out. The question of whether either or both of the light bulb circuits work is determined by how well the power supplied by the battery matches the power that the light bulb can safely handle. f the battery cannot supply enough power, then the light bulbs will be dim, or may not even appear to emit any light. f the battery can supply too much power, then the bulb (or bulbs) may burn out. The question of how well the battery and the bulbs match is also affected by whether the series or parallel circuit is used. Therefore, the engineering question of whether the circuit works depends on the configuration of the wires and the choice of components (batteries and bulbs) used in the circuit. Beyond the simple question of whether the circuit even works, are several deeper and more interesting questions: How much current will the two bulbs draw? How long will the battery last? What happens if have two batteries? And how should connect the batteries in series or parallel? For the two-bulb circuits, how does the brightness of each bulb compare to the case of only one bulb? How bright are the bulbs in each of the two-bulb configurations? n other words, for the given battery, is it better (by some definition of better ) for the bulbs to be connected in series or parallel? These are all practical questions. encourage you to directly experiment with batteries and wires and bulbs to tie your hands-on experience to these notes. Above all, be safe! Small flashlight bulbs (2W or 4W) and 1.5V alkaline batteries (AAA, AA, A, C or D cell) will be fine. Series circuit 1 V b 2 Equivalent circuit V b eq = 1 2 Figure 5: Two resistors in series (left) and the equivalent circuit (right).

9 ME 120 ntroduction to DC Circuits Two esistors in Series Figure 5 shows the circuit diagram for two light bulbs (two resistors) in series. This is called a series circuit because all the current flowing from the battery goes first through one bulb and then the next. efer to the left side of Figure 4 for the cartoon version of the circuit. The light bulbs are represented by resistors 1 and 2. ncandescent bulbs are resistors, so the diagram in the left side of Figure 5 is an excellent model of two incandescent light bulbs in series. The simple circuit would not apply to fluorescent lights. LED (Light emitting diode) bulbs can be modeled as resistors, so the left side of Figure 5 would also apply to two LEDs in series. There are additional considerations with using LED lights, which we ll explore later in the course. For the circuit with two resistors in series, the current through each of the resistors is the same. n addition, the current leaving the battery is also the same as the current flowing through each resistor. = 1 = 2 (14) Apply Ohm s law to each resistor V 1 = 1 1 and V 2 = 2 2 (15) Ohm s law also applies to the equivalent circuit on the right hand side of Figure 5 V b = eq. (16) The voltage across each battery is not the same as the voltage applied across each resistor. n fact, the sum of the voltages V 1 and V 2 must add up to V b, the voltage supplied by the battery. This is a consequence of a more general principle called Kirchoff s Voltage Law, which we will discuss in detail later. For now, we can make the empirical observation that the two voltages add up to the total supplied voltage V b = V 1 V 2. (17) We say that the voltage drop across the resistors must add up to the voltage drop across the two batteries. The word drop suggests that the voltage decreases in the direction of the current flow. f we take Equation (17) as true (which it is!) then we can substitute the two forms of Ohm s law from Equation (15) and the version of Ohm s law for the equivalent circuit (Equation (16)) into Equation (17) to get eq = (18) But, we know from Equation (14) that the current from the battery is the same as the current flowing through each of the resistors. Therefore, the on the left hand side of Equation (18) is the same as both the 1 and 2 on the right hand side. Algebraically, because the, 1 and 2 are equal (for this circuit!) those values can be cancelled from Equation (18) to give Equation (19) is true for any combination of two reistors in series. 5.2 Two esistors in Parallel eq = 1 2. (19) Figure 6 shows the circuit diagram for two resistors in parallel. We say that this is a parallel circuit because the current from the battery splits and flow through each bulb separately, or in parallel. f the two bulbs have identical resistance, the current flow through each bulb will be equal. f the bulbs have unequal resistance, the current flowing will be unequal. egardless of whether the electrical

10 ME 120 ntroduction to DC Circuits 10 Parallel circuit Equivalent circuit V b V b Figure 6: Two resistors in parallel (left) and the equivalent circuit (right). currents have equal values, the electrons flowing through one bulb do not flow through the other bulb. The electrons from the battery split and flow on separate, parallel paths. efer to the right side of Figure 4 for the cartoon version of the circuit for two light bulbs wired in parallel. n the parallel circuit, the voltage across the battery is also the same as the voltage across each of the resistors V b = V 1 = V 2. (20) The relationship between the current flows is determined by Kirchoff s Current Law, which requires that the net flow of current into a node (or wire junction) be zero. n other words, the sum of the currents flowing into a node must be equal to the sum of currents flowing out of that same node. Figure 7 shows the circuit for two resistors in parallel with the current flows labelled. The right side of Figure 7 shows the current flows into each of two nodes, labeled A and B where three currents, 1 and 2 come together. For this circuit, it turns out that these nodes both give the same information, i.e., the same relationship between, 1 and 2. n more complex circuits the relationships between current flows will involve different combinations of currents. Applying Kirchoff s currently law to node A gives and applying Kirchoff s current law to node B gives = 1 2 (21) 1 2 =. (22) Algebraically, Equation (21) and (22) are equivalent. Therefore, we only need to analyze node A or node B in this simple circuit. f we rearrange Ohm s law as = V/ and apply it to each one of the terms in Equation (21) we obtain V b = V 1 V 2. (23) eq 1 2 A V b 1 1 B = A B = Figure 7: Current flows into nodes of the circuit for two resistors in parallel.

11 ME 120 ntroduction to DC Circuits 11 For the parallel circuit, all of the voltages are the same (See Equation (20).) Therefore, we can cancel the equal voltage terms in the numerators of Equation (23) to get Equation (24) is true for any combination of two reistors in parallel. 1 eq = (24) 5.3 General ules for esistors in Series and Parallel The results from the preceding sections can be summarized and extended as follows. esistors in Series V V 2 V 3 V n n 2 3 n V tot = V 1 V 2 V 3 V n or V tot = = 1 = 2 = 3 = = n eq = n or eq = n i=1 n i=1 V i i esistors in Parallel V s n n V s = V 1 = V 2 = V 3 = = V n 1 = or 1 = eq n eq n 1 i=1 i The relationship between the currents is obtained by applying Kirchoff s current law to each node. There isn t a simple or compact formula that is the same for each node in the parallel resistor circuit.

12 ME 120 ntroduction to DC Circuits 12 6 Summary 1. Ohm s Law relates the flow of current to the voltage drop across a resistor. V = where V is the voltage (in volts, V ), is the current (in amp, A) and is the resistance (in ohm, Ω). Notes: V is used for both a voltage value and the units of volts. A resistor can be any element that conducts electricity, e.g.,, a length of wire, a resistor in a circuit, or the filament of an incandescent light bulb. 2. At a basic physical level, current is defined as a flow of electrons where coulomb is the unit of charge. 1 A = 1 C 1 s = 1 coulomb 1 second At a basic physical level, voltage is the amount of energy associated with the separation of opposite charges 1 V = 1 J 1 C = 1 joule 1 coulomb n terms of resistivity, an intrinsic property of conductors, the macroscopic resistance of a wire (or any long and relatively skinny conductor) is = ρl A where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire. 3. Work and energy are amounts. Power is a rate Work and energy can be defined in terms of raising a mass of material against the acceleration of gravity. The amount of mechanical work done in raising a mass, m, by a distance, d, is Work = force distance = mgd. where g is the acceleration of gravity. The work done is equivalent to the change in potential energy of the mass Change in potential energy = mgd. Power is the rate at which work is done. Power = work time = energy time. aising the mass m through a distance d always takes the same amount of work. However, raising it quickly takes more power than raising it slowly.

13 ME 120 ntroduction to DC Circuits Power dissipated in a resistor can be computed by three equivalent formulas P = V, P = 2, P = V 2. We usually write these separate formulas in a single line as P = V = 2 = V The equivalent resistance of two resistors in series is Two resistors in series: eq = 1 2. The equivalent resistance of two resistors in parallel is Two resistors in parallel: 1 eq = efer to Section 5.3 for cases involving more than two resistors.

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

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

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

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

Brian Blais Quick Homemade Guide to Circuits

Brian Blais Quick Homemade Guide to Circuits 1 Initial Equations and Concepts Current, I. Units:amps rate of flow of charge: I = Q/ t Potential difference, V. Units: volts esistance,. Units:ohms Ohm s

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

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

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

Closed 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

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

Electric 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

Note on Posted Slides. Flow of Charge. Electricity/Water Analogy: Continuing the Analogy. Electric Current

Note on Posted Slides These are the slides that I intended to show in class on Tue. Mar. 18, 2014. They contain important ideas and questions from your reading. Due to time constraints, I was probably

LESSON 5: ELECTRICITY II

LESSON 5: ELECTRICITY II The first two points are a review of the previous lesson 1.1.ELECTRIC CHARGE - Electric charge is a property of all objects and is responsible for electrical phenomena. -All matter

Chapter 21 Electric Current and Circuits

Chapter 21 Electric Current and Circuits 1 As an introduction to this chapter you should view the following movie. If you cannot click on the link, then copy it and paste it into your web browser. http://www.ionaphysics.org/movies/vir.mp4

Chapter 27: Current and Resistance

Chapter 7: Current and esistance In this section of the course we will be studying the flow of electric charge, current, in a circuit. We have already seen electric current when we first discussed 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

MEP 382: Design of Applied Measurement Systems Lecture 3: DC & AC Circuit Analysis

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

ELECTRICITY. Electric Circuit. What do you already know about it? Do Smarty Demo 5/30/2010. Electric Current. Voltage? Resistance? Current?

ELECTRICITY What do you already know about it? Voltage? Resistance? Current? Do Smarty Demo 1 Electric Circuit A path over which electrons travel, out through the negative terminal, through the conductor,

670 Intro Physics Notes: Electric Current and Circuits

Name: Electric Current Date: / / 670 Intro Physics Notes: Electric Current and Circuits 1. Previously, we learned about static electricity. Static electricity deals with charges that are at rest. 2. Now

CHARGE AND ELECTRIC CURRENT:

ELECTRICITY: CHARGE AND ELECTRIC CURRENT ELECTRIC CHARGE ELECTRIC CURRENT ELECTRIC CIRCUIT DEFINITION AND COMPONENTS EFFECTS OF ELECTRIC CURRENT TYPES OF CIRCUITS ELECTRIC QUANTITIES VOLTAGE CURRENT RESISTANCE

52 VOLTAGE, CURRENT, RESISTANCE, AND POWER

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

b) What is its position when its velocity (magnitude) is largest? When it is at x=0 all the energy is kinetic.

Question 1. The electrostatic force between two charges, Q 1 and F 1 /4 Q 2 a separated by a distance D, is F 1. What is the force between them after they are moved to a distance 2D apart? (Give in terms

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

Notebook Circuits With Metering. 22 February July 2009

Title: Original: Revision: Authors: Appropriate Level: Abstract: Time Required: NY Standards Met: 22 February 2007 14 July 2009 Notebook Circuits With Metering Jim Overhiser, Monica Plisch, and Julie Nucci

Electricity. Prepared by Juan Blázquez, Alissa Gildemann. Electric charge is a property of all objects. It is responsible for electrical phenomena.

Unit 11 Electricity 1. Electric charge Electric charge is a property of all objects. It is responsible for electrical phenomena. Electrical phenomena are caused by the forces of attraction and repulsion.

Physics 1402: Lecture 10 Today s Agenda

Physics 1402: Lecture 10 Today s Agenda Announcements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW assignments, solutions etc. Homework #3: On Masterphysics : due Friday at 8:00 AM Go to masteringphysics.com

Direct 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

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

Notes: Ohm s Law and Electric Power

Name: Date: / / 644 Intro Physics Notes: Ohm s Law and Electric Power Ohm s Law: Important Terms Term Symbol Units Definition 1. current I amps flow of electric charges through a conductor 2. voltage V

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

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

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

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

CHAPTER INTRODUCTION TO ELECTRIC CIRCUITS. C h a p t e r INTRODUCTION

C h a p t e r CHAPTE NTODUCTON TO ELECTC CCUTS.0 NTODUCTON This chapter is explaining about the basic principle of electric circuits and its connections. The learning outcome for this chapter are the students

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*

Circuits. Electric Current & DC Circuits Circuits. Unit 6. April Electric Current. Electric Current. Electric Current. ΔQ Δt

Electric Current & DC Circuits Electric Current & DC Circuits Circuits Conductors esistivity and esistance Click on the topic to go to that section Circuit Diagrams Measurement Electric Current Circuits

Notes on Electricity (Circuits)

A circuit is defined to be a collection of energy-givers (batteries) and energy-takers (resistors, light bulbs, radios, etc.) that form a closed path (or complete path) through which electrical current

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

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

Lesson Plan: Electric Circuits (~130 minutes) Concepts

Lesson Plan: Electric Circuits (~130 minutes) Concepts 1. Electricity is the flow of electric charge (electrons). 2. Electric Charge is a property of subatomic particles. 3. Current is the movement of

Relating Voltage, Current and Resistance

Relating Voltage, Current and Resistance Using Ohm s Law in a simple circuit. A Simple Circuit Consists of:! A voltage source often a battery! A load such as a bulb! Conductors arranged to complete a circuit

Electric Currents and Simple Circuits

-1 Electric Currents and Simple Circuits Electrons can flow along inside a metal wire if there is an E-field present to push them along ( F= qe). The flow of electrons in a wire is similar to the flow

ELECTRICITY. Chapter ELECTRIC CHARGE & FORCE

ELECTRICITY Chapter 17 17.1 ELECTRIC CHARGE & FORCE Essential Questions: What are the different kinds of electric charge? How do materials become charged when rubbed together? What force is responsible

Unit 1 Lesson 1.2 Energy Sources

Unit Lesson. Energy Sources ntroduction to Electricity 0 Electricity Movement of electrons nvisible force that provides light, heat, sound, motion... Elements he simplest form of matter Atoms Smallest

E40M Charge, Current, Voltage and Electrical Circuits KCL, KVL, Power & Energy Flow. M. Horowitz, J. Plummer, R. Howe 1

E40M Charge, Current, Voltage and Electrical Circuits KCL, KVL, Power & Energy Flow M. Horowitz, J. Plummer, R. Howe 1 Reading For Topics In These Slides Chapter 1 in the course reader OR A&L 1.6-1.7 -

An Introduction to Electricity and Circuits

An Introduction to Electricity and Circuits Materials prepared by Daniel Duke 4 th Sept 2013. This document may be copied and edited freely with attribution. This course has been designed to introduce

What is dynamic electricity?

Dynamic Electricity What is dynamic electricity? Has to do with charges in motion So we re talking about moving electrons Think about any electronic device Dynamic electricity Think back to properties

(b) State the relation between work, charge and potential difference for an electric circuit.

Question Bank on Ch-Electricity 1. (a) Define the S.I unit of potential difference. (b) State the relation between work, charge and potential difference for an electric circuit. Calculate the potential

What is an Electric Current?

Electric Circuits NTODUCTON: Electrical circuits are part of everyday human life. e.g. Electric toasters, electric kettle, electric stoves All electrical devices need electric current to operate. n this

ΔV of battery. = ε - Ir or εmf = I(R+r) (for this particular series circuit) March 04, Emf and internal resistance. Emf and internal resistance

Emf and internal resistance Emf and internal resistance ΔV of battery = ε - Ir or εmf = I(R+r) (for this particular series circuit) As the current in the circuit increases the voltage, supplied to the

Gas discharges. Current flow of electric charge. Electric current (symbol I) L 26 Electricity and Magnetism [3] examples of electrical discharges

L 26 Electricity and Magnetism [3] Electric circuits what conducts electricity what doesn t t conduct electricity Current voltage and resistance Ohm s s Law Heat in a resistor power loss Making simple

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

Electromagnetism Checklist

Electromagnetism Checklist Elementary Charge and Conservation of Charge 4.1.1A Convert from elementary charge to charge in coulombs What is the charge in coulombs on an object with an elementary charge

Now let s look at some devices that don t have a constant resistance.

Lab #3 Now let s look at some devices that don t have a constant resistance. This is the same circuit you built last time. But now, in place of the resistor first build the circuit with a light bulb, then

Greek Letter Omega Ω = Ohm (Volts per Ampere)

) 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

Circuits-Ohm's Law. 1. Which graph best represents the relationship between the electrical power and the current in a resistor that obeys Ohm s Law?

1. Which graph best represents the relationship between the electrical power and the current in a resistor that obeys Ohm s Law? 2. A potential drop of 50 volts is measured across a 250- ohm resistor.

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

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

Section 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

A 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

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

Electron Theory of Charge. Electricity. 1. Matter is made of atoms. Refers to the generation of or the possession of electric charge.

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

In this unit, we will examine the movement of electrons, which we call CURRENT ELECTRICITY.

Recall: Chemistry and the Atom! What are the 3 subatomic Where are they found in the particles? atom? What electric charges do they have? How was a positive ion created? How was a negative ion created?

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

ELECTRICITY & MAGNETISM CHAPTER 8

ELECTRICITY & MAGNETISM CHAPTER 8 E & M - Focus Electric Charge & Force Magnetism Current, Voltage & Power Electromagnetism Simple Electrical Circuits Voltage & Current Transformation Electric Charge &

- Memorize the terms voltage, current, resistance, and power. - Know the equations Ohm s Law and the Electric Power formula

E: Know Circuit Vocabulary (Short Answer) Level 2 Prerequisites: Know Circuit Vocabulary (Short Answer); Recognize Insulators and Conductors Objectives: - Memorize the terms voltage, current, resistance,

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

Name Date Time to Complete. NOTE: The multimeter s 10 AMP range, instead of the 300 ma range, should be used for all current measurements.

Name Date Time to Complete h m Partner Course/ Section / Grade Complex Circuits In this laboratory you will continue your exploration of dc electric circuits with a steady current. The circuits will be

Protons = Charge Electrons = Charge Neutrons = Charge. When Protons = Electrons, atoms are said to be ELECTRICALLY NEUTRAL (no net charge)

QUICK WRITE: For 2 minutes, write the three parts of an atom and what their charges are. Explain what creates an electric charge (positive or negative) on something. Rules - You MUST write for the entire

Test Review Electricity

Name: Date: 1. An operating television set draws 0.71 ampere of current when connected to a 120-volt outlet. Calculate the time it takes the television to consume 3.0 10 5 joules of electric energy. [Show

Physics Module Form 5 Chapter 2- Electricity GCKL 2011 CHARGE AND ELECTRIC CURRENT

2.1 CHARGE AND ELECTRIC CURRENT Van de Graaf 1. What is a Van de Graaff generator? Fill in each of the boxes the name of the part shown. A device that produces and store electric charges at high voltage

Physics Module Form 5 Chapter 2- Electricity GCKL 2011 CHARGE AND ELECTRIC CURRENT

2.1 CHARGE AND ELECTRIC CURRENT Van de Graaf 1. What is a Van de Graaff generator? Fill in each of the boxes the name of the part shown. A device that... and... at high voltage on its dome. dome 2. You

Electricity Review completed.notebook. June 13, 2013

Which particle in an atom has no electric charge associated with it? a. proton c. neutron b. electron d. nucleus Jun 12 9:28 PM The electrons in a metal sphere can be made to move by touching it with a

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

10/14/2018. 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,

Notes on Electricity (Circuits)

A circuit is defined to be a collection of energy-givers (active elements) and energy-takers (passive elements) that form a closed path (or complete path) through which electrical current can flow. The

2. In words, what is electrical current? 3. Try measuring the current at various points of the circuit using an ammeter.

PS 12b Lab 1a Fun with Circuits Lab 1a Learning Goal: familiarize students with the concepts of current, voltage, and their measurement. Warm Up: A.) Given a light bulb, a battery, and single copper wire,

ES250: Electrical Science. HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws

ES250: Electrical Science HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws Introduction Engineers use electric circuits to solve problems that are important to modern society, such as: 1.

2. Basic Components and Electrical Circuits

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

Physics 2020 Lab 5 Intro to Circuits

Physics 2020 Lab 5 Intro to Circuits Name Section Tues Wed Thu 8am 10am 12pm 2pm 4pm Introduction In this lab, we will be using The Circuit Construction Kit (CCK). CCK is a computer simulation that allows

Chapter 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

Introduction to Electricity

Introduction to Electricity Principles of Engineering 2012 Project Lead The Way, Inc. Electricity Movement of electrons Invisible force that provides light, heat, sound, motion... Electricity at the Atomic

Electricity. From the word Elektron Greek for amber

Electricity From the word Elektron Greek for amber Electrical systems have two main objectives: To gather, store, process, transport information & Energy To distribute and convert energy Electrical Engineering

E40M Charge, Current, Voltage and Electrical Circuits. M. Horowitz, J. Plummer, R. Howe 1

E40M Charge, Current, Voltage and Electrical Circuits M. Horowitz, J. Plummer, R. Howe 1 Understanding the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage and power behave in

Name Date Time to Complete

Name Date Time to Complete h m Partner Course/ Section / Grade Complex Circuits In this laboratory you will connect electric lamps together in a variety of circuits. The purpose of these exercises is to

CLASS X- ELECTRICITY

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

STUDY GUIDE CHAPTER 5 ELECTRICITY AND MAGNETISM 1) ASSOCIATE ELEMENTARY PARTICLES WITH THEIR ELECTRICAL CHARGE

Name Date STUDY GUIDE CHAPTER 5 ELECTRICITY AND MAGNETISM 1) ASSOCIATE ELEMENTARY PARTICLES WITH THEIR ELECTRICAL CHARGE Scientists now know that an atom is composed of even smaller particles of matter:

CHAPTER 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

Materials Needed 1 D-Cell battery 6 6-inch pieces of wire 3 flashlight light bulbs 3 light bulb holders (optional)

Experiment Module 3 Electric Circuits Objective/Introduction This experiment explores building simple circuits and testing Ohm s Law. Students will start lighting a simple light bulb. Then they will explore

Continuous flow of electric charges. Current Electricity

Continuous flow of electric charges Current Electricity Did You Know? The voltage across a muscle cell in your body is about 70 millivolts. A millivolt (mv) is one thousandth of a volt. AC and DC DC Direct

Electricity Mock Exam

Name: Class: _ Date: _ ID: A Electricity Mock Exam Multiple Choice Identify the letter of the choice that best completes the statement or answers the question.. What happens when a rubber rod is rubbed

11. ELECTRIC CURRENT. Questions and Answers between the forces F e and F c. 3. Write the difference between potential difference and emf. A.

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

Gr. 11 Physics Electricity

Gr. 11 Physics Electricity This chart contains a complete list of the lessons and homework for Gr. 11 Physics. Please complete all the worksheets and problems listed under Homework before the next class.

Electricity Worksheet (p.1) All questions should be answered on your own paper.

Electricity Worksheet (p.1) 1. In terms of attraction and repulsion, how do negative particles affect negative particles? How do negatives affect positives? 2. What happens to electrons in any charging

1 of 23. Boardworks Ltd Electrical Power

1 of 23 Boardworks Ltd 2016 Electrical Power Electrical Power 2 of 23 Boardworks Ltd 2016 What is electrical power? 3 of 23 Boardworks Ltd 2016 Electrical power is the rate at which energy is transferred

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

Electric Current, Resistance and Resistivity. Brief otes

Electric current, resistance and restivity Electric Current, esistance and esistivity In This small e-book we will learn all we need to know about current electricity but in short and then we ll have some

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

University of Maryland Department of Physics

Spring 3 University of Maryland Department of Physics Laura Lising Physics 1 March 6, 3 Exam #1 nswer all questions on these sheets. Please write clearly and neatly: We can only give you credit for what

DC circuits, Kirchhoff s Laws

DC circuits, Kirchhoff s Laws Alternating Current (AC), Direct Current (DC) DC Circuits Resistors Kirchhoff s Laws CHM6158C - Lecture 2 1 Electric current Movement of electrons in a conductor Examples

Electricity and Electromagnetism SOL review Scan for a brief video. A. Law of electric charges.

A. Law of electric charges. Electricity and Electromagnetism SOL review Scan for a brief video The law of electric charges states that like charges repel and opposite charges attract. Because protons and

ELECTRICAL FORCE UNIT NOTES

ELECTRICAL FORCE UNIT NOTES Property that causes electrical force is called Charge Opposite charges Attract Like charges Repel Charge comes from the atoms. Electrons are negative, protons are positive.