Mr. Rogers' AP Physics C: E&M (with IB Physics) Objectives

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter IB Objectives

AP Physics C E&M Standards

C. Electric circuits ..................................................................20%


1. Current, resistance, power
2. Steady-state direct current circuits with batteries and resistors only
3.Capacitors in circuits
a. Steady state
b. Transients in RC circuits *

Ohm's Law (Chap. 27 Serway)

Essential Question: Is voltage a force?

Voltage, Current, Resistance

  1. Describe the nature of the following terms:
  description unit basic units equation
voltage electrical potential per unit of charge. Note: voltage is not a force! volt
   Joule     
Coulomb
 
current flow of charge ampere
Coulomb   

sec
i =  dq  

dt
resistance tendency to restrict the flow of charge ohm

   J ∙ s   

C2
 
 

  1. Calculate resistance of a conductor: given length, resistivity, and cross sectional area.

  2. State the resistance of both an ideal ammeter and an ideal voltmeter.
  • Ideal Voltmeter Resistance = Infinity
  • Ideal Ammeter Resistance = Zero
  1. Use Ohm's law to analyze simple circuits with a resistor and DC power source.

I = V / R

Note:  V = the voltage difference across a resistor. The resistor can have a million volts on each side (voltage difference = 0) and the current is will be zero.

 

Relevance: Ohm's law is possibly the most commonly used and basic of all equations in E&M. It is used not just by engineers but also electricians, power company linemen, and all kinds of technicians.

 

Demo: Hot Dog Cooker

Demonstrate that a hot dog can be cooked by plugging it into a the wall outlet.

Questions:

  1. What do resistors do to electrical energy?
  2. From an energy standpoint, why do microwave ovens work faster than standard ovens?
  3. Can an appliance like a ceiling fan be modeled as a resistor?
  4. Do ceiling fans cool or warm up rooms?
  5. Is it useful to leave a ceiling fan on when no one is home?

 

Essential Question: What do resistors do?

Resistors and Wires

  1. Use Ohm's law and the relationship, power = V * I,  to derive two additional power equations.

  2. Solve for the heat loss in a current carrying piece of wire. A wire can be modeled as a resister and ultimately, resistors turn electrical energy into heat.

  3. Use the 3 power equations and Ohm's law to analyze various types of simple circuits with resistors and a DC power source.

 

  

 

Essential Question: How are volt and ammeters used for measuring voltages and current?

Parallel and Series Circuits

  1. Explain the difference between a parallel and series circuit.

  2. Correctly connect voltmeters and ammeters. Remember, an ideal measuring instrument will not alter the behavior of a circuit. When they are connected to a circuit it is as though they are not there.

  • Voltmeter's Connection: in parallel. Ideal voltmeters have an infinite resistance, hence, draw no current out of the circuit.
  • Ammeter's Connection: in series. Ideal ammeters have zero resistance, hence, they have no voltage drop across them.

Note: do not expect to pass this course unless you know how to use voltmeters and ammeters.

Relevance: Multi-meters containing voltmeters and ammeters are a highly useful diagnostic tool for all kinds of people including do-it-yourselfers, auto mechanics, electricians, technicians, and engineers.

  1. Find the total resistance of parallel or series circuit containing only resistors and a DC power source.
Circuit
Equation for Total Resistance
Series  RT = R1 + R2 + ... + Rn
Parallel 1 / RT = 1 / R1 + 1 / R2 + ... + 1 / Rn

 

  1. Qualitatively describe the current, power, and voltage conditions for circuits with resistors in series compared to resistors in parallel.
    • total resistance = maximum
    • current = min
    • total power = min
    • current = same for all resistance elements
  1. Qualitatively describe the current, power, and voltage conditions for circuits with resistors in parallel compared to resistors in series.
  • total resistance = minimum
  • total current = max
  • total power = max
  • voltage = same for all resistance elements

 

 

  

 

 

Bob's New Multi-Meter

Bob get's an expensive new multi-meter' as a high school graduation present (true story, names changed) and goes off to college.

One day in the dorm, he decides to measure the voltage provided by the electrical outlet. He carefully inserts the leads into the outlet--no problem--he gets a reading 

Next Bob decides to measure the current. He again plugs the leads into the socket. Result: he blows the circuit breaker in two rooms, melts the end of the lead, and blows the multi-meter's fuse.

 Guess why.

Essential Question: How are houses wired?

Voltage, Current and Power in Houses

  1. Solve for voltage, current and power in pure series or parallel resistance circuits. Determine is a circuit breaker will trip.

  2. Solve problems with batteries in series or parallel

  • parallel - same voltage, longer battery life: example: storage for solar cells

  • series - higher voltage; example: flashlight

Homefun: Questions (page 790-791) 2-9, 17, 18, 20; Prob. (page 790-791)3, 15, 21, 25, 43, 53

Relevance: Houses are all wired with parallel circuits. All of the devices inside a house can be modeled as resistors.

Summative Assessment: Test on objectives 1-13

Practice Test

  
   
   

Formal Physics Investigation
Title Does a light bulb follow Ohm's Law?
Purpose Determine if a a light bulb follow Ohm's Law.
Models Ohm's Law.
Overview For a device following Ohm's Law, a plot of current vs. voltage drop across the device will be linear with a slope = 1 / R. Regression analysis can give us a curve of best fit for the data along with an indicator of the fit's quality (R-square). Residuals analysis can indicate whether a linear fit is or is not appropriate. If it is not then the device being tested does not follow Ohm's law. (Note: if you have not taken AP Statistics Mr. Rogers will assist you with making the statistical analysis.)
  1. Connect a variable DC power supply ammeter and voltmeter to a low voltage light bulb. Remember, the light bulb, power supply, and ammeter will be in series. The voltmeter will be connected in parallel with the light bulb. Note the power supply should be turned off and adjusted to its lowest voltage setting.
  2. Turn the power supply on and slowly adjust the voltage upward while collecting current vs. voltage data points. Stop when the light bulb is at its rated voltage and is glowing brightly.
  3. Plot a current vs. voltage drop curve for the device and perform regression analysis as well as residuals analysis.
  4. Repeat the process for a commercial resistor.

 
Safety Issues Shorting out the power supply can damage the unit and burn up wires. Remember, an ideal ammeter has a resistance = 0. If you connect it across the power supply without placing the light bulb or resistor in the circuit, the power supply will be shorted out. Putting excessive current through the resistor will overheat it and create a burn hazard.

Note: To prevent overheating of the elements in your circuit, turn the power switch off and adjust  the voltage knob on the variable power supply to its lowest setting before connecting wires. When ready to start the experiment, turn the power switch on and adjust the voltage up slowly while monitoring the temperature of the circuit.
Equipment Limitations Subjecting the light bulb to more than its rated voltage will burn it out. Remember, a light bulb glows because it reaches very high temperatures. If the bulb glows brightly and is then turned off it will take some time for it to return to its original temperature. This could affect your results.

Note: TURN THE MULTIMETER OFF WHEN FINISHED! It is battery operated.
Resources/Materials: 12 volt light bulb, a resistor designed for high power, variable DC power supply, ammeter, multimeter (voltmeter), wires

 

AP Physics C E&M Standards

A. Electrostatics .....................................................................30%


1. Charge, field, and potential
2. Coulomb's law and field and potential of point charges
3. Fields and potentials of other charge distributions

a. Planar
b. Spherical symmetry *
c. Cylindrical symmetry *

4. Gauss's law *

Electric Potential (Chap. 25 Serway)

Essential Question: Could you draw free electrical power out of the air using an antennae?

  1. State whether electric potential is a vector or scalar and give its units.

  2. Explain the difference between  negative and positive work. Positive work increases kinetic energy. Negative work decreases kinetic energy.

  3. Write the generic electric potential difference equation.

      - ∫ b  
 

ΔV

 =   E • ds
      a  
  1. Explain the negative sign in the above equation.

By convention, positive charges move from high to low voltage. Since ΔV = (Vlow - Vhigh), ΔV will be a negative number when the positive charge is gaining kinetic energy. The right hand side of the equation calculates the work done and positive work indicates an increase in kinetic energy. The negative sign on the right side is needed so that a negative ΔV yields an increase in kinetic energy.

  1. Calculate potential differences by moving a charge to different locations in a uniform electric field.
       
 

ΔV

= E • x
       

Homefun (formative summative assessment): p.714-716 1, 3 13

Essential Question: How is the E-field around a point charge similar to the gravity field around a planet?
  1. Calculate the electric potential due to a point charge. By convention the voltage is considered to be zero at infinity.
     

- ∫

 r  
 

(Vr - 0)

 =

 

(kQ / r2 ) • dr
      ∞  

  1. Calculate the electric potential from more than one point charges. (Note: voltages are not vectors. the positive and negative sign on them does not have anything to do with spatial direction. Positive charges generate positive voltages, negative charges negative voltages.)

  2. Relate the electric field to electric potential mathematically and conceptually. Be sure to add the minus sign. Remembering this fact can sometimes make a difference.

E = - dV / ds

  1. Given electric field lines sketch equipotential lines.

Electric field lines are always perpendicular to equipotential surfaces or lines

Why?

dV = - E ∙ ds 

This is a dot product, so for  E ≠ 0, dV can only be zero if E is perpendicular to ds. Therefore, if ds is the displacement along an equipotential surface, E must be perpendicular to it because dV = 0 along an equipotential surface.

Homefun (formative summative assessment): p.731: 1, 3, 11,12, 33

  1. Draw analogies between topographical maps and electric potential and field lines. A topographical map is essentially a map of gravitational potential energy. Remember (PE) = (mg)h, so, multiply the elevation on the map by (mg) and you have gravitational potential energy.

Homefun (formative summative assessment): page 717-738; 27, 32, 43

 

 

Electric Potential Fun with Fuzzy and Non-fuzzy Spheres and Cylinders

(Fuzzy stuff dejavu, yippy!)

Essential Question: Why can a bird land on a high voltage wire and not be electrocuted ?
  1. Derive an expression for the electric potential of a uniformly charged:

  1. Be aware that current, if there is any, will always flow in the direction of the E-field or from high voltage to low voltage.. For E = 0, The voltage could be anything as long as it is constant.

  2. Derive an expression for the electric potential inside and outside various types of spheres with radius = R.

outside: v = kQ / r

inside: Note: the voltage does not equal zero at the center of the sphere for any of the cases shown below.

  1. Calculate the charge distribution when a charged conductive sphere is connected to an uncharged one. Note: the charge stops flowing when the the voltage is the same on both spheres.

 

Homefun (formative summative assessment): page 717-738; 55, 57

Summative Assessment: Test on objectives 1-16

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Analysis of Circuits with Resistors in Parallel and Series
Overview
  1. Determine if the equations for calculating the total resistance of series an parallel circuits actually work.
  2. Configure 3 resistors in series and measure the total resistance of the circuit.
  3. Configure 3 resistors in parallel and measure the total resistance of the circuit.
  4. Configure two different  combination parallel and series circuit with a minimum of 5 resistors in each circuit. Measure the total resistance of the circuit.

Be sure to record a drawing of each circuit.

Note: use the color code to select resistors, keeping in mind that you will not be able to measure total resistance if the resistance is too high or too low. However, measure the resistance of each with the multimeter and use this number in your calculations.

Note: TURN THE MULTIMETER OFF WHEN FINISHED! It's battery operated.
Data, Calculations Calculate a total resistance for each circuit configuration and a % difference from the measured value
Questions, Conclusions
  1. Why is it better to use the measured values for each resistor when calculating the total resistance rather than using the official manufacture's values?
  2. Why would we use the term "% differences" rather than "% error" ?
  3. What assumptions are implicit in the models you used to calculate the total resistance?
  4. What additional experimental errors did you introduce when using the multimeter?
Resources/Materials: multimeter, various resistors, solderless breadboard

 

AP Physics C E&M Standards

C. Electric circuits (continued)..................................................................20%


1. Current, resistance, power
2. Steady-state direct current circuits with batteries and resistors only
3.Capacitors in circuits

a. Steady state
b. Transients in RC circuits *

DC Resistance Circuits (Chap. 28 Serway)

Essential Question: How do various common circuit components compare to mechanical components?
 

  1. Calculate the total resistance of circuits containing a mixture of parallel and series resistors.

  2. Compare capacitors, inductors, and resistors to each other.

    Resistor - dissipates electrical energy from the circuit as heat, similar to the way viscous drag forces in a damper or dashpot (such as a shock absorber in a car) dissipates mechanical energy as heat.

    Capacitor - stores electrical energy in a circuit, similar to the way a spring stores mechanical energy.

Inductor - stores electrical energy in a circuit when current is flowing, similar to the way an inertia or mass stores kinetic energy when it is moving.
    Component
    Stored Energy
    Capacitor
    E = 1/2 Ce2
    Spring
    E = 1/2 kx2
    Inductor
    E = 1/2 Li2
    Mass
    E = 1/2 mv2

     

  1. Calculate the total capacitance of circuits containing a mixture of parallel and series capacitors. Hint: the equations for total capacitance are the opposite of the same type equations for resistors.
Circuit
Equation for Total Capacitance
Equation for Total Resistance
Series
1/CT = 1/C1 + 1/C 2+ ... + 1 Cn 
 RT = R1 + R2 + ... + Rn
Parallel
CT = C1 + C2 + ... + Cn
1/RT = 1/R1 + 1/R2+ ... + 1/Rn

 

  1. Solve circuit problems by understanding how a capacitor behaves at time = 0 and infinity.

    @ t = 0: a capacitor acts like a wire

    @ t = infinity: a capacitor acts like an open circuit

  2. Solve circuit problems by understanding how an inductor behaves at time = 0 and infinity.

    @ t = 0: an inductor acts like an open circuit

    @ t = infinity: an inductor acts like a wire

  3. Analyze DC resistance circuits containing only a batteries and resistors using Ohm's and Kirchoff's laws. (These are based on conservation of energy and conservation of charge laws.)

    at a junction, current in = current out

    the sum of voltages around a closed loop = 0

 

Homefun (formative summative assessment): 8 (will be formally graded), 9, 15, 21, 23, 31, 33, 55 p. 800-805

 

  

Demo: Capacitor Demo

 Charge the large sized capacitor and use it to light a light bulb.

Questions:

  1. Could large capacitors be used as a substitute for batteries in electric cars or electric hybrids?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Investigation of Kirchoff's law
Purpose Determine if the sum of the voltage drops around a closed loop = zero
Overview Set up a circuit with a power supply and 3 loops in it, one big overall loop and 2 small ones (similar to a "B"). Place a known resistor in each segment of each loop. Measure the voltage drops around each segment for each loop to see if the voltage drops do indeed add up to zero.

Be careful not to short out the power supply.
Data, Calculations Collect the information for all 3 loops.
Questions, Conclusions
  1. Can you calculate a % error for the sum of the voltages?
  2. What assumption are you making about the voltmeter which will cause an error?
Resources/Materials: multimeter, various resistors, solderless breadboard, variable power supply

 

 AP Physics C E&M Standards

D. Magnetostatics.................................................................20%

1. Forces on moving charges in magnetic fields
2. Forces

D. Magnetostatics.................................................................20%

1. Forces on moving charges in magnetic fields
2. Forces on current-carrying wires in magnetic fields
3. Fields of long current-carrying wires
4. Biot-Savart and Ampere's law *
 

Magnetic Field (Chap 29 Serway)

Essential Question: Is the North Pole the North Pole?

How Can We Describe a Magnetic Field?

  1. Draw the magnetic field lines on a bar magnet. Arrows go from N to S pole

  2. Explain what the magnetic field lines indicate. The force on the N pole of a magnet

  3. Describe the important differences between magnetic field lines and electric field lines.

    • Magnetic field lines are closed loops. E-field lines are not.

    • The net magnetic flux though a closed Guassian surface is always zero, whether the magnet is inside or outside of the closed surface.

  4. Calculate the magnitude of the force on a moving charge given its velocity and the strength of the magnetic field.

F = q ( v x B )

F = q v B sin q

  1. Using the right hand thumb rule state the direction of the force. The direction of the force is always perpendicular to the plane containing the velocity and B-field vectors. Memory hint: have you taken your v-to-Bs today?

  2. State why a B-field cannot do work on a moving charge. The displacement is always perpendicular to the force.

  3. State the relationship of the magnetic field strength units Teslas to gausses and to basic SI units.

1 Tesla = (kg) / (C ∙ s)

1 Tesla = 10,000 gauss

 

 

  

 

Demo: PVC Arrows and Lorentz Force Demonstrator

Use the arrows made out of PVC pipe to  illustrate how forces are created on moving charged particles.

Use the Lorentz Force Demonstrator to actually show the effect on a moving stream of electrons.

Essential Question: If a magnetic field cannot do work on a moving charge how can an electric motor do work, considering that it depends on the force created on moving charges by a magnetic field ?

How to Design an Electric Motor/Generator

  1. Calculate the force on a current carrying wire in a B-field.

F = ( B ) x ( i L )

F = B i L sin q

  1. Explain why the net force on a current carrying loop in a B-field is zero.

  2. Calculate the torque and direction of rotation on a current carrying loop of wire in a B-field. This is the simplest form of electric motor. However, to rotate in a single direction, the loop has to have a means of reversing the current flow every half turn.

 

 

  

Essential Question: How can E&M be used for identifying unknown compounds?

How to Design a Mass Spectrometer

Mass spectrometers are considered one of the most sensitive and accurate ways to identify unknown substances or to measure very tiny amounts of a known substance, such as in air pollution monitoring.

  1. Determine the motion of a charged particle traveling at constant velocity in a uniform magnetic field. This combines centripetal force equations with magnetic force on a moving charge equations.

  2. Solve problems with charged particles moving in both magnetic and electric fields. Called a velocity selector. In it the the E-field force must be equal in magnitude but opposite in direction to the force from the B-field.

 

Homefun (formative summative assessment): 5, 6, 13, 15, page 856

 

 

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Investigation of a simple DC Electric Motor
Purpose Determine how to fabricate the coil on a simple DC electric motor so that it rotates when supplied with a voltage source.
Overview Wind the enamel coated copper wire around the mandrel to make a coil as shown in the handout provided. This coil will be placed in the holder provided and become the rotor for a simple electric motor.

Correctly scrape off the enamel coating on the coils electrical contact points. Remember, for a DC motor to work, Either the current must be reversed every half turn or the current must be turned on for only half a turn. Otherwise the torque will flip-flop and prevent the motor from rotating. The simple motor will turn the current on for half a turn. This is accomplished by scraping off the enamel coating on half of the circumference of the wire that makes contact with the electric power supply posts. Do this wrong and the motor will not turn.

Place the the coil in its rack, connect the battery and give the coil a slight push to get it spinning.

Watch the motor spin and be amazed.

Hold a second magnet above the fixed one in the motor's base an record your observations (see the questions below). Be careful not to hit the rotating coil while holding the second magnet.
Data, Calculations There are no calculations. However, If your motor does not spin you will receive an "F". Every time you have to remake the coil, you grade will decline by one letter. The message: THINK carefully about how the motor woks before you scrape off the enamel to form contacts so that current can flow in the coil.
Questions, Conclusions
  1. Did the direction you pointed the magnet (with respect to the magnet's north pole) affect the motor's motion? Explain your answer.
  2. Did you feel a sideways force on the magnet? If so, describe and explain it.
Resources/Materials: multimeter, various resistors, solderless breadboard, variable power supply

 

Essential Question: How are properties like temperature, pressure, etc. actually measured?

Using E&M Principles in Measuring Instruments

  1. Describe the conditions needed to make a charged particle move in a spiral pattern inside a magnetic field.

  2. Describe the hall effect. This effect is used in many forms of transducers (measuring devices) including magnetic field measuring devices.

  3. Describe the effects of moving a conductor in a magnetic field.

 

Homefun (formative summative assessment): 17, 21, 25, 29, page 857-8

 

 

Essential Question: How can I make an "A" on the test?

Chapter 29 Magnetics Review

  1. Work the practice test.
  2. Review the objectives.

Summative Assessment: Test on objectives 1-15

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Investigation of Magnetic Fields with a Hall Effect Transducer
Purpose Measure various magnetic fields with a Hall effect transducer.
Overview
  1. Connect a hall effect transducer to the Labpro computer system.
  2. Hold the probe vertically and slowly rotate it while having the computer graph the probe's output.
  3. Connect a light bulb to the power supply and make the bulb glow brightly. Place the hall effect probe in close proximity to the one of the current carrying wires and measure the direction of the magnetic field around the wire.
Data, Calculations
  1. Retain the plot from step 2
  2. Sketch the magnetic field around the wire as indicated by the Hall effect probe.
Questions, Conclusions
  1. Why does the plot from step 2 in the overview look like a sine wave (assuming you rotated the probe at constant rotational velocity)?
  2. Did the magnetic field around the current carrying wire match with expectations?
Resources/Materials: light bulb, computer system set up with Vernier LabPro software and Lab Pro units, variable power supply

 

 

Formal Physics Investigation
Title Measurement of the Mass to Charge ratio of an Electron
Purpose Measure the mass to charge ratio of an electron using a Lorentz Force Demonstrator (looks like a giant light bulb).
Models Various
Overview In the Lorentz Force Demonstrator a stream of electrons are accelerated across a known voltage difference into a magnetic field perpendicular to the electron stream so that the electrons travel in a circular path. The magnetic field is provided by a pair of coils as follows:

Radius = 280 mm

Number of loops in each coil = 140

Distance between coil = 140 mm

Measure the radius of the circulating electrons and calculate the charge to mass ratio of an electron.

Have the teacher tilt the magnetic field so that it is no longer perpendicular to the electron's inlet velocity. Obsearver, record, and explain the effects as part of the lab write up.
Safety Issues

Note: The equipment is extremely expensive and  extremely fragile do not move it from the position where it was placed by the teacher. Be careful not to stumble over the extension cord.
Equipment Limitations The equipment is designed to operate for no more than an hour continuous.
Resources/Materials: Lorentz Force Demonstrator (looks like a giant light bulb).

 

 

AP Physics C E&M Standards

D. Magnetostatics (continued)................................................................20%


1. Forces on moving charges in magnetic fields
2. Forces on current-carrying wires in magnetic fields
3. Fields of long current-carrying wires
4. Biot-Savart and Ampere's law *

Sources of Magnetic Fields (Chap30 Serway)

Essential Question: Can the electric power lines interfere with the telephone transmissions through the wires hung on the same poles?

  1. Describe the magnetic field around a long thin current carrying wire.

  2. Calculate the magnetic field around a long thin current carrying wire.

 

B =

     mo I
 

2pr
Where:  I = current
             r = radial distance from the wire
             mo = permeability of free space
  1. Describe and calculate the forces on two parallel long thin current carrying wires.
  1. Explain the Biot Savort law.

dB = km I ds x (r-hat) / r^2

  1. Relate km to mo the permeability of free space.

km = mo / 4p

  1. Use the Biot Savort law to derive the magnetic field:
 

B =

  
mo I a2
 

2 (a2 + x2)3/2

Relevance: Biot Savort law is the basis for many types of derivations and is the basis for 2 of the right hand thumb rules.

  1. Solve for the conditions needed to levitate a current carrying wire above two other current carrying wires.

  2. Solve for the forces on a rectangular current carrying loop of wire next to a long thin current carrying wire in the same plane as the loop.

  3. Apply all three right hand thumb rules.

 

Homefun (formative summative assessment): problems 10 (will be formally graded), 1, 3, 5, 17 p.859-860

 

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)
Title Investigation of "Twiddler's Delight"
Purpose Determine the mechanism that accounts for the behavior of the "Twiddler's Delight"
Overview A Twiddler's Delight looks like a cylinder with a movable shaft protruding from each end. Twist one shaft and something happens to the other.

Start by simply playing with the Twiddler's Delight and developing a hypothesis for how the device works.

Next devise a simple experiments to test your hypothesis. Briefly record your procedure, what you observed, and what you learned from each experiment The rules are that you can do nothing invasive. For example, you can't remove parts, drill holes, or in any way disect or modify the device.
Data, Calculations See above.
Questions, Conclusions Record you conclusion about how the device works.
Resources/Materials:  "Twiddler's Delights"
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