Instructor: Mr. Undieme B.S. Physics University of Illinois, M.S. Mathematics University of Central Florida

Transcription

1 AP Physics C Mechanics and AP Physics C Electricity and Magnetism Room 3-05 Text: Physics for Scientists and Engineers Serway and Jewett 6 th edition Materials: Notebooks, scientific calculator, and graph paper Instructor: Mr. Undieme B.S. Physics University of Illinois, M.S. Mathematics University of Central Florida Students: Students have had Calculus their Junior year or will be enrolled in Calculus their Senior year. Most students have had either AP Chemistry or Honors Physics their Junior year. Classroom: There are sixteen computers in my classroom and I have Vernier lab equipment (motion detectors, photogates, force sensors, pulley s, microphones, etc.) I have a multimedia projector in my classroom that is hooked up to my computer and to a DVD player. I use the projector to show applets, the Physics Cinema Classics, and demos form the web. The Course: My course is based on the College Board Curriculum for AP Physics C Mechanics and AP Physics C Electricity and Magnetism as listed on the College Board website and contains the topics listed below. Differential and Integral Calculus are used throughout the course to derive equations, solve problems, and present material. In the early chapters I give students a great deal of help solving problems in order to develop their skills as physics problem solvers. The help consists of students offering their ideas for solving the problem while I ask them questions to guide them towards the solution. Demonstrations and applets are also used to foster critical thinking and discussion by the class. Some of the labs (listed below) are inquiry based and ask students to design their own experiments. All labs are hands on. Some of the labs may require more than one class period. I keep track of the time students are doing labs to make sure that it is 0% of the contact time. If more labs are needed, I will use lab questions from previous AP C exams. Assignments and Grades: Approximately 5-5 problems are chosen as homework for each chapter (including conceptual questions). Several of the most difficult problems are chosen to challenge the students. Student grades are based on homework, labs (listed after the topic outline), and unit tests. The AP Physics C Test: The test is separated into two sections: Mechanics and Electricity & Magnetism. Students may choose to only do the Mechanics portion of the test or they may choose to do both sections. Mechanics: Section : 35 multiple choice questions NO EQUATION SHEET AND NO CALCULATOR. You will have a sheet of constants. To succeed at this section you will have to completely understand the physics concepts and be able to perform calculations without your calculator. You have 45 minutes for section. Section : Three free response questions in which you will be required to solve problems. You will have an equation sheet for this section and you may use your calculator. You may receive partial credit for portions of the solutions. You have 45 minutes for section. Section and of the test are weighted equally. Electricity &Magnetism: Section : 35 multiple choice questions NO EQUATION SHEET AND NO CALCULATOR. You will have a sheet of constants. To succeed at this section you will have to completely understand the physics concepts and be able to perform calculations without your calculator. You have 45 minutes for section. Section : Three free response questions in which you will be required to solve problems. You will have an equation sheet for this section and you may use your calculator. You may receive partial credit for

2 portions of the solutions. equally You have 45 minutes for section. Section and of the test are weighted Grade Determination: Homework: 0% of your semester grade. NO LATE HOMEWORK. First do your homework on scrap paper. It may take you several attempts to correctly solve some of the problems. When first solving problems your work may tend to be messy and disorganized. It can be very difficult to read and understand later when you are studying for a test. After you feel you have correctly solved a problem, rewrite it. Organize your thoughts. Write as if you are explaining to someone how to solve each problem. Later when you are studying for a test, you will be reading what you wrote. Always put a great deal of thought and effort into your homework before asking for help from classmates or me. Solving problems in groups is helpful, but only if you have first given it your best attempt you will not be taking your tests with the help of a group. Labs: 0% of your semester grade. Some labs will given to you, others will be labs you design yourself. Students will keep a lab notebook where they record their data, show sample calculations, and calculate experimental error. Their lab reports include a list of materials, an explanation of the procedure, a table of measured and calculated quantities (including percent difference), sample calculations, and a discussion of experimental error. In the early part of the first semester labs will be done out of the Vernier Lab book. They are asked to do preliminary questions before the lab. As the students become more familiar with the equipment many labs will be inquiry based. (Safety information is given to the students at the beginning of the year and before each lab). Unit Tests: 50% of your semester grade.. Tests will be similar to the AP test format. Tests will be graded similar to the AP test no partial credit for multiple choice, partial credit for free response. Semester Exam: 0% of your semester grade.. This will be a comprehensive test given during the assigned dates for semester tests.. The effort you put into doing and writing up your homework and taking good class notes will make studying for your semester exam much easier. Mechanics: I) Preliminaries A) Importance of Units (Disasters Air Canada, etc.) B) Dimensional Analysis C) Vectors ) Vectors and Scalars ) Adding Vectors Graphically (Applet) 3) Components 4) Notation: i, j, k 5) Adding Vectors Analytically 6) Dot Product 7) Cross Product (i) Sin Method (a) Line of Action Method (first vector perpendicular to line of action of second) (b) Tangential Component Method (tangential component of second vector wrt first) (ii) i, j, k Method (iii) Determinants (iv) RHR

3 II) Kinematics A) Motion in One Dimension ) Definitions: Displacement, Velocity, Acceleration ) Average vs. Instantaneous: The Derivative 3) Position vs. Time, Velocity vs. Time, and Acceleration vs. Time Graphs (i) Applets (ii) Graphs on Screen of Students Moving in front of Motion Detector 4) Equations for Constant Acceleration (i) Derivation Calculus (ii) Solving Physics Problems 5) Acceleration as a Function of Velocity (i) a( t) g kv example (ii) Other Examples 6) Free Fall (i) Equations - Problems (ii) Graphs B) Motion in Two Dimensions ) Independence of x-y Motion Walking North Won t Get You East (Shooting Steel Ball and Dropping Steel Ball Demo) ) Position, Velocity, and Acceleration Vectors in Two Dimensions 3) Given x(t) and y(t), Find v and a. 4) Kinematics in -D (Constant x and y acceleration) 5) Projectile Motion III) Newton s Laws and Forces A) Newton s Three Laws and Examples (car crash, untied piano in moving truck, ) B) Given F(t)=ma(t), Calculate v by Separation of Variables C) The Force of Gravity, Mass and Weight D) Weight in an Elevator E) The Force of Friction F) F kx Spring Force G) Newton s Third Law and the Normal Force H) Free Body Diagrams I) F net ma Linear examples J) F net ma Two Dimensions ( Fx ma x Fy ma y ) K) Equilibrium L) Incline Planes M) Equilibrium Problems ( F 0 F 0 ) Simultaneous Equations x N) Pulleys: Atwood, One Mass on Table (with and without Friction), Incline Plane. O) The Drag Force IV) Uniform Circular Motion A) Centripetal Acceleration r V T y a c v r B) Centripetal Force (Rubber Stopper on a string Demo, v, a, and F directions) C) Net Force Towards the Center ) Rubber Stopper on String - Vertical Circle ) Car Cresting Hill, Motorcycle in Loop, etc. 3) Satellites (Circular Orbits) (i) Setting Gravitational Force Equal to Centripetal Force to Get Speed (ii) Setting Circumference over Period = Velocity to Get Period (iii) NASA 3-D J tracker website

4 V) Work and Energy A) Definition of Work ) Dot Product ) Positive, Negative, and Zero Work rf x f 3) W F dr ri xi Fdx B) Kinetic Energy C) W KE D) Potential Energy Gravitational and Spring E) Conservative Nonconservative Forces x f F) U F( x) dx W xi / Area under Force vs. Position Graph G) Conservation of Energy ) Example Problems: Skier, Projectile Motion, Pendulum, Ball rolling in Bowl, etc ) Find the Angle at Which a Person Sliding Down a Semi-Circular Frictionless Surface Will Lose Contact with the Surface H) Energy Approach to Pulleys I) Conservation of Energy Friction, air resistance du J) F( x), dx ) Spring ) Gravity 3) U vs. x Graphs K) Power/Efficiency VI) Linear Momentum A) Center of Mass ) System of Particles ) Solid Body B) Newton s Second Law for a System of Particles C) Derivation of Conservation of Momentum D) Playing Catch in Space (Conservation of Momentum and Newton s 3 rd Law) E) Conservation of Linear Momentum ) Elastic Collisions ) Inelastic Collisions 3) Two Objects Pushed Apart by Spring 4) Lab vs. Center of Mass Reference Frame F) The Ballistic Pendulum G) Impulse-Momentum Theorem ) Ft p ) F( t) p 3) Force vs. Time Graphs H) -D Conservation of Momentum

5 VII) Rotation (For Each Rotation Equation Stress the Counterpart for Translation) A) Rotational Kinematics of a Rigid Body ) Angular Position s (i) radians r (ii) All Points Rotate Same (iii) Note is Not a Vector, Order Matters When Adding Angular Displacement ) Angular Velocity d (i) (ii) All points Rotate with Same. (iii) RHR 3) Angular Acceleration d (i) (ii) All Points Rotate with Same. (iii) RHR 4) Derive Relationships Between Linear and Angular Variables (Including Centripetal and Radial Acceleration) 5) Calculate Radial and Tangential Acceleration of a Point on a Rotating Rigid Body 6) Correction to g due to Earth s Rotation 7) Coriolis Effect 8) Equations of Constant Angular Acceleration 9) Rotational Inertia (i) The Kinetic Energy of Four Discrete Masses Rotating ( KE miri I ) i (ii) Rotational Inertia of Ridged Continuous Body (a) I r dm r dv (b) Surface Mass Density, Linear Mass Density (c) Calculating I of Hoop, Rod, Cylinder, etc. (d) Parallel Axis Theorem B) Torque ) Examples of Torque ) Different ways to calculate r F (i) Moment Arm Line of Action of F (ii) Tangential (to r) Component of F (iii) i, j, k (iv) Counter Clockwise + Clockwise (v) RHR 3) I net (i) Sphere Floating in Space with Several Applied Torques (a) Find Net Torque (b) Find, Find and After Some Time t. (ii) Rotating Rod Pivoted at One End (iii) Mass Attached to Massive Pulley with String Acceleration and Tension (iv) Atwood s Machine for Pulley s with Non-Negligible Mass

6 C) Rotational Kinetic Energy and Work ) W d f, i W (For Constant Torque) f i ) KE I I W rot dw 3) P 4) Conservation Energy (i) Rotating Rod (ii) Atwood s Machine (iii) Rolling Without Slipping Down an Incline Plane (a) Derive the Equation for the v cm (b) Derive the Equation for the a cm (c) Compare Spheres, Shells, Cylinders, etc. (Note All Spheres Have Same a cm, etc.) D) Angular Momentum dp dp dr ) r F r 0 r ) Particle Traveling in a Straight Line wrt Some Origin 3) Particle Traveling in a Circle 4) System of Particles 5) Rotating Solid Object About Fixed Axis: L I d r p p (i) L for Rotating Sphere at Some (ii) L for Rotating Spherical Shell of Same Radius, Mass, and. dl dl v cm and (iii) Use net to Find Net Torque to Rotate above Objects from Rest to the Given Value. dl di d 6) I I 7) Pulley Example (P. 34) 8) The See-Saw Example (P. 344) 9) Have Students Choose an Object to Calculate Net Torque E) Conservation of Angular Momentum 0 L Constant I I ) i i f f ) Student on Rotating Stool Demos (i) Student Initially at Rest Holding Weight (a) Student Slowly Moves Outstretched Weight in One Direction Then the Other (b) Student Quickly Moves Outstretched Weight on One Direction Then the Other (ii) Student Initially Rotating with Outstretched Weights then Pulls Arms In (iii) Student Sitting on Stool with Spinning Bicycle Wheel Then Inverting Wheel (iv) Physics Cinema Classics 3) Example Problems (i) Satellites (ii) Ballistic Pendulum (iii) Person Running on Merry-Go-Round F) Equilibrium

7 VIII) Simple Harmonic Motion A) Mass on Spring ) Recall F=-kx ) Hang Mass on Spring from Ceiling 3) Show Reference Circle Applet IX) 4) Define Period,, Frequency, Amplitude, and Phase ( f ) T 5) Derive x Asin ft from Reference Circle 6) Energy 7) Vertical - Horizontal 8) Students Do Lab to try and Identify Variables That Effect the Period and Equation for Period 9) Derive and Discuss Period with Mass Hanging form Ceiling 0) Take Derivatives to Get Velocity and Acceleration for SHM ) Differential Equation for SHM B) Pendulum d g L ) sin ) Sin for Small Angles (Have Students try on Calculator) 3) Students Try to Figure Out Period Equation in Lab 4) Resonance (Tacoma) 5) Torsional Pendulum 6) Physical Pendulum Gravitation A) Newton s Law of Gravitation ) Superposition ) Ask Students How They Would Calculate the Time it Takes Two Bodies Starting at Rest to Come Together. Discuss Two Body Problem 3) Measuring G 4) mg GM R p m R = Distance from Center of Planet 5) Average Density of Earth 6) Gravitational Force Inside and Outside Uniform Sphere B) Gravitational Field C) Gravitational Potential Energy GMm ) U g r ) Derivation 3) Conservation of Energy Problems 4) Energy of Satellites 5) Escape Speed D) Keplar s Laws

8 Electricity and Magnetism X) Electrostatics A) Charge ) Quantization-Milliken ) Inductors-Conductors- Semiconductors 3) Induction 4) Demos Electroscope, Van de Graaff, Bending Water Stream B) Coulombs Law ) Resultant Force ) Relative size of Electric Force (penny example) ) Charges in line, triangle, square C) Electric Field ) Definition-test charge Field Lines ) Discreet Charge Distributions (Applethttp:// 3) Continuous Charge Distributions i) Charged Rod ii) Charged Ring iii) Charged Disc 4) Electric Dipole D) Gauss s Law ) Definition and Examples of Electric Flux qin ) E E d A o 3) Using Gauss s Law to Calculate the E-Field for Various Charge Distributions i) Point Charge ii) Solid Insulating Sphere (Inside and Out) iii) Thin Spherical Shell (Inside and Out) iv) Infinite Line of Charge v) Infinite Plane of Charge (Ask Students to make sense of result) vi) Parallel Plates E) Electric Potential and Electric Potential Energy ) Not Vectors ) Mathematical Equivalence Of Coulomb s Force and Newton s Gravitational Force ii) Conservative iii) Work iv) Potential Energy 3) V U q E ; U V q 4) Setting U=0 at infinity. E 5) Conservation of Energy Problems with U E qv kq 6) Calculating V for a Collection of Point Charges r dq 7) Calculating V k for Continuous Charge Distributions r 8) Calculating the Electric Potential Energy of a Group of Point Charges 9) Equipotential Surfaces and E-Field Lines (Applet)

9 XI) Circuits A) Current dq ) I ) Drift Speed 3) I J d A B) Resistance L ) R A ) Ohm s Law C) Power D) Series ) I I I 3 VT V V V3 RT R R R3 ) Calculate 3 Resistor Circuit on Board Current, Voltages meaning of Ground and Kirchoff s Loop Rule E) Parallel ) V V V 3 I T I I I 3 R T R R R ) Calculate and Show all Currents on Board in 3 Resistor Parallel Circuit Show Kirchoff s Junction Rule 3) Have Students Build circuits on Electronic Workbench on Computers F) Series-Parallel ) Calculating Equivalent Resistance ) Calculating Voltages and Currents for Each Resistor G) Multiple Battery Circuits and Kirchoff s Rules H) Ammeters, Voltmeters and the Internal Resistance of Batteries XII) Capacitors A) Parallel Plate ) Charging of Capacitor ) The Farad q k A 3) C C 0 (Derive with Gauss s Law and V V d Eds 4) Dielectrics 5) Energy Stored in a Capacitor 6) Electron Accelerated with a Potential Difference and then Fired between the Plates of a Capacitor B) Spherical and Cylindrical Capacitors - Derivation of E, V and C. C) Capacitors in Series ) q q q 3 V T V V V 3 C T C C 3 C ) Calculate Charges and Voltages of 3 Capacitors in Series on Board 3

10 D) Capacitors in Parallel ) V V V3 qt q q q3 CT C C C3 ) Calculate Charges and Voltages of 3 Capacitors in Parallel on Board E) RC Circuits ) Derive Charging Equation Kirchoff s Loop Rule and Differential Equation ) Derive Discharging Equation - Kirchoff s Loop Rule and Differential Equation 3) Graph - Time Constant 4) Charge.0 F Capacitor and Measure Voltage Two Weeks Later Calculate Internal Resistance 5) Steady State XIII) Magnetism/ Electromagnetism A) Magnetic Fields ) Moving Charge Creates Magnetic Fields Current Carrying Wire and Compass ) Domains 3) Magnetic Field Lines 4) Magnetic Monopole B) Force on a Moving Charge: F B qv B ) Ways to Get Zero Force ) RHR 3) Path (applet) 4) Work=0 5) FB FC 6) Velocity Selector, Mass Spectrometer, Bubble Chambers F F for a Net Force of Zero 7) When E B C) Force on a Current-Carrying Wire ) F B I L B ) RHR 3) Curved Wire 4) Loop of Wire in B-Field F net 0 5) Torque on Loop (Rectangle Example) 6) Hall Effect D) B-Field Due to a Long Straight Current-Carrying Wire 0I ) B R ) RHR 3) Field Due to Two or More Wires 4) Force of Attraction or Repulsion Between Two Wires 5) Coil E) The Biot-Savart Law ) d B 4 r 0 Id s rˆ 0I ) Using Biot-Savart Law to derive B for a Long Straight Wire R 3) Using Biot-Savart Law to derive B-field on the Axis of a Circular Current Loop F) Amperes Law ) d s I B 0 ) Using Amperes Law to Derive B-Fields of Highly Symmetric Wires (i) Long Wire Inside and Out

11 (ii) Torroid (iii) Infinite Sheet G) Magnetic Flux ) B d A B d ) 3) Examples of Magnetic Flux and Changing Magnetic Flux 4) B d A 0 H) Induction ) Coil, Moving Neodymium Magnet, Galvanometer Demo ) Faraday s Law 3) Bar Traveling Through B-Field RHR Induced Voltage 4) Bar with Resistor Attached 5) Lenz Law Fighting the Change I) LR and LC Circuits ) Self-Induced EMF = di L ) RL Circuit Kirchoff s Loop Rule and Differential Equation 3) Time Constant 4) LC and LCR Circuits : Deriving Differential Equation with Energy Considerations 5) Analogy with Simple Harmonic Oscillator J) Maxwell s Equations AP C Labs: Many of my AP C students are taking physics for the first time. The first few labs will familiarize them with the lab equipment. Students keep a lab notebook where they record their data, show sample calculations, and calculate experimental error. Their lab reports include a list of materials, an explanation of the procedure, a table of measured and calculated quantities, sample calculations, error analysis, and a discussion of experimental error. In the early part of the first semester labs will be done out of the Vernier Lab book. They are asked to do preliminary questions before the lab. As the students become more familiar with the equipment some labs will be inquiry based. I do a mix of labs from handouts (the Vernier lab book: Physics with Computers) and inquiry based - design your own lab experiments. I give the students practice at both following instructions on setting up lab equipment and analyzing graphs and data and the more creative design your own experiment (inquiry based) labs. (Safety information is given to the students at the beginning of the year and before each lab). All labs are hands-on (except for the portion of Circuits Labs where they build the circuits on the Electronics Workbench software they also build the circuits on breadboards). Mechanics Labs:. Graph Matching Lab: Using the Vernier motion detector and computers the students move in front of the motion detectors to try and match the given position vs time, velocity vs. time and acceleration vs. time graphs. The students answer analysis questions and draw their own graphs to match. (Vernier lab book experiment #).. Ball toss lab. Students toss basketballs vertically in the air above motion detectors and analyze the resulting graphs Before starting the lab the students are asked to predict the position vs. time, velocity vs. time, and acceleration vs. time graphs. They compare the actual graphs with their predictions. They also use the software to determine best fit equations and the average acceleration during free-fall. (Vernier lab book experiment #)

12 3. Projectile Motion Lab. Using photogates students measure the initial velocity of steel balls launched horizontally from tables. Carbon paper is used to mark where the balls lands. Students measure the horizontal distance that the ball lands from the edge of the table and then compare this value to their calculated value. (Vernier lab book #8) 4. Force/Vector Lab: Students use spring scales and then force sensors attached to a ring. They construct a scaled free body diagram. They then rearrange those vectors to add them together graphically and mathematically to illustrate vector addition with a zero (or nearly zero) resultant. 5. Static and Kinetic Friction Lab: Given a block, several masses, string, and a scale measure the coefficient of static and kinetic friction between the block and various surfaces. Investigate whether adding weight to the block changes the force of friction or the coefficient of friction. Using an incline plane, measure the angle that causes the block to start to slide at a constant velocity. Take the Tangent of this angle and compare it to the coefficient of friction for the block and surface. Can you derive this equation? 6. Acceleration Down an Incline Plane: Using a motion detector measure the acceleration of a block sliding down an incline plane. Draw a free-body diagram and derive the equation for the acceleration of the block and compare it to your measured values. 7. The Coffee Filter and Air Resistance Lab: This lab is from the AP Physics Lab Guide 8. Atwood s Machine: Derive the equation for the Acceleration of the Atwood s machine using a freebody diagram. Using some string, hanging masses, vernier super pulley, and photogates measure the acceleration and compare this to your calculated value. Now use a mass hanging from a pulley to accelerate an object (book or block) across a horizontal surface with friction. Derive the equation for the acceleration of the block from a free-body diagram. 9. Energy of a Tossed Ball: Students will measure the changes in kinetic and potential energies while the ball is in free-fall. Students will measure the total energy while the ball is in free-fall. (Vernier lab #6) 0. The Turning Point Lab: This lab is from the AP Physics Lab Guide. Elastic Collisions: This lab is from the AP Physics Lab Guide. Collisions and F vs. t Graphs: Using a force sensor, photogates and a cart, design a lab to show that the area under the F vs. t graph is equal to the change in momentum of the carts. 3. The Conical Pendulum Lab: Description given at: 4. The Physical Pendulum Lab: Description given at: 5. Rolling Down an Incline Plane(without slipping): Using several hollow cylinders of various sizes, solid cylinders of various sizes, hollow spheres of various sizes, and solid spheres of various sizes, students will predict which objects will roll down the incline with the largest acceleration (We will do this before we cover rolling motion). They will explain their justification. Students will then design the experiment to test their hypothesis. After covering rolling motion in class, students will derive all of the accelerations of their objects (after making necessary measurements to calculate the I s). They will write up the derivations in their lab report.

13 6. Measuring the Coefficient of Friction of a Wall Equilibrium: Attach paper to the wall and to the end of the meter stick. Using string, a meter stick, and hanging weights calculate the coefficient of friction between the wall (paper on paper) and meter stick by using F Cover a the bottom of a box and the surface of the lab table x F y with paper. Measure Compare this to the coefficient of friction by sliding a box with paper on the bottom 7. Measure k of Several Springs: Given a ring stand, spring and meter stick measure k for various springs by hanging various masses and graphing (by hand) distance stretched vs. mass (Use these Springs in the SHM lab). 8. SHM: Given a mass, spring, ring stand and stop watch determine which variables effect the period of the oscillation. Construct data tables that test each variable. See if you can determine the equation that determines period from the relevant variables. After Students have made their attempt at discovering the equation, they will graph T vs. m and use the slope to get k. 9. Pendulums: Given a mass, string, ring stand, and stop watch which variables effect the period of the oscillation. Construct data tables that test each variable. See if you can derive the equation that determines period from the relevant variables. After Students have made their attempt at discovering the equation, they will graph T vs. L and use the slope to get g. 0. Energy in Simple Harmonic Motion: Students will use the motion detector to obtain the energy graphs of SHM. They will then analyze these graphs. (Vernier Lab #7).. Hooke s Law and Harmonic Motion: This lab is from the AP Physics Lab Guide. Review Lab: Measure g in as many ways as you can. List the equipment used for each method. Give a detailed description of your procedures and measurements taken (include diagrams), show equations used and sample calculations, arrange your data in tables and/or graphs. Compare your value of g to the accepted value at our location: g = ( + A sin L - B sin L) H m s -. Discuss error analysis for each of your methods. where A = B = L = latitude H = height in meters above sea level Electricity and Magnetism Labs: (Several of the Labs require more than one class period) 3. Electroscope Lab: 4. Van De Graph Lab: Qualitative lab where students explain in detail demos I perform with the Van De Graph generator. Students then try and design and perform their own demos. 5. Electric Field Mapping: Electric fields and potentials around various shaped conductors parallel plates, dipole and ring.

14 6. Ohm s Law: This lab is from the AP Physics Lab Guide 7. Resistance - Series, Parallel and Series-Parallel: Given several resistors, a breadboard, and a multimeter students will connect resistors in both series and parallel and try and discover the equations for total resistance. Then they will then connect the resistors in various Series-Parallel arrangements of their choosing and try and calculate the total resistance. They will then check their calculation by measuring with the multimeter. 8. Series and Parallel: Students build series, parallel, and series-parallel circuits both on breadboards and the electronics workbench program. They will calculate all of the currents and voltages and then measure them with a digital multimeter. 9. Kirchoff s Rules: Students will solve a loop circuit using Kirchoff s laws. They will then build the circuit and verify Kirchoff s Rules. 30. Building your own Capacitor: Students will design and build several capacitors. They will then calculate the capacitance and compare it to the measured capacitance. 3. RC Time Constants: This lab is from the AP Physics Lab Guide. 3. Calculating Leakage Resistance of F capacitor: Students will charge a F capacitor and then measure the voltage several weeks later. The students will then derive the differential equation describing the discharge and then use it to solve for the leakage resistance. 33. Magnetic Fields: This lab is form the AP Physics Lab Guide. 34. Lenz s Law: Using a coil, Neodymium magnets and a galvanometer qualitatively verify Lenz s Law. 35. LC and LCR Circuits: Students attempt to derive and solve the differential equation for LC circuits, after I check their attempt I direct them to to correct their work. After reading the website they explain the similarities between an LC circuit and a mass oscillating on a spring. They then build the circuit and observe the oscillations on the oscilloscope. The students then add a resistor to the circuit and explain the behavior. Extra Labs after AP Exam if time: 36. Measuring the Speed of Sound: Using a tuning fork, a PVC tube, and very large plastic graduated cylinder students will measure the speed of sound and compare it to the accepted value (V = T). 37. Lens Lab: Given a candle, several lenses, lens holders, a meter stick, and note card, verify the lens equation for various object distances. 38. The Diffraction Grating: This lab is from the AP Physics Lab Guide