Essential idea: The majority of electricity generated throughout the world is generated by machines that were designed to operate using the principles of electromagnetic induction. Nature of science: Experimentation: In 1831 Michael Faraday, using primitive equipment, observed a minute pulse of current in one coil of wire only when the current in a second coil of wire was switched on or off but nothing while a constant current was established. Faraday’s observation of these small transient currents led him to perform experiments that led to his law of electromagnetic induction. Understandings:
• Electromotive force (emf)
• Magnetic flux and magnetic flux linkage
• Faraday’s law of induction Faraday's law simulation
• Lenz’s law Applications and skills:
• Describing the production of an induced emf by a changing magnetic flux and within a uniform magnetic field
• Solving problems involving magnetic flux, magnetic flux linkage and Faraday’s law
• Explaining Lenz’s law through the conservation of energy Guidance:
• Quantitative treatments will be expected for straight conductors moving at right angles to magnetic fields and rectangular coils moving in and out of fields and rotating in fields
• Qualitative treatments only will be expected for fixed coils in a changing magnetic field and ac generators Data Booklet reference:
• F = BA cosq
• e = -N ∆F / ∆t
• e = Bvl
• e = BvlN
• The magnetic flux is represented by F. The magnetic field strength (aka magnetic flux density) is represented by B. The A represents the area through which the B-field passes. The q represents the angle between the B-field vector and the normal to the area. The induced emf is represented with e. The change in magnetic flux is represented with ∆F and the change in time with ∆t. The l represents the length of a straight wire, the v represents the relative speed between the wire and the B-field. The N represents the number of wires or loops. Theory of knowledge:
• Terminology used in electromagnetic field theory is extensive and can confuse people who are not directly involved. What effect can lack of clarity in terminology have on communicating scientific concepts to the public? Utilization:
• Applications of electromagnetic induction can be found in many places including transformers, electromagnetic braking, geophones used in seismology, and metal detectors Aims:
• Aim 2: the simple principles of electromagnetic induction are a powerful aspect of the physicist’s or technologist’s armoury when designing systems that transfer energy from one form to another

Essential idea: Generation and transmission of alternating current (ac) electricity has transformed the world. Nature of science: Bias: In the late 19th century Edison was a proponent of direct current electrical energy transmission while Westinghouse and Tesla favoured alternating current transmission. The so called “battle of currents” had a significant impact on today’s society. Understandings:
• Alternating current (ac) generators Generator simulation
• Average power and root mean square (rms) values of current and voltage Transmission line simulation
• Transformers Power lines link to cancer...Power grid simulation
• Diode bridges
• Half-wave and full-wave rectification Applications and skills:
• Explaining the operation of a basic ac generator, including the effect of changing the generator frequency
• Solving problems involving the average power in an ac circuit
• Solving problems involving step-up and step-down transformers
• Describing the use of transformers in ac electrical power distribution
• Investigating a diode bridge rectification circuit experimentally
• Qualitatively describing the effect of adding a capacitor to a diode bridge rectifica-tion circuit Guidance:
• Calculations will be restricted to ideal transformers but students should be aware of some of the reasons why real transformers are not ideal (for example: flux leakage, joule heating, eddy current heating, magnetic hysteresis)
• Proof of the relationship between the peak and rms values will not be expected Data Booklet reference:
• Vrms = V0 / Ö2
• R = V0 / I0 = Vrms / Irms
• Pmax = I0V0
• Pavg = (1/2) I0V0
• e p / e s = Np/ Ns = Is/ Ip
• The V represents ac voltage. The rms means "root mean square" and is a way of evening out an ac quantity to find its equivalent dc value (for the purposes of calculating power usage). The V0 represents the peak voltage, and the I0 represents the peak current. The P represents the power. The e represents the emfs of the two stages of an ideal transformer (the P and the S stands for primary and secondary respectively). The N represents the number of windings in the transformer stages. The I represents the currents in the transformer stages. International-mindedness:
• The ability to maintain a reliable power grid has been the aim of all governments since the widespread use of electricity started Theory of knowledge:
• There is continued debate of the effect of electromagnetic waves on the health of humans, especially children. Is it justifiable to make use of scientific advances even if we do not know what their long-term consequences may be? Aims:
• Aim 6: experiments could include (but are not limited to): construction of a basic ac generator; investigation of variation of input and output coils on a transformer; observing Wheatstone and Wien bridge circuits
• Aim 7: construction and observation of the adjustments made in very large electricity distribution systems is best carried out using computer-modelling software and websites
• Aim 9: power transmission is modelled using perfectly efficient systems but no such system truly exists. Although the model is imperfect, it renders the maximum power transmission. Recognition and ac-counting for the differences between the “perfect” system and the practical system is one of the main functions of professional scientists

Essential idea: Capacitors can be used to store electrical energy for later use. Nature of science: Relationships: Examples of exponential growth and decay pervade the whole of science. It is a clear example of the way that scientists use mathematics to model reality. This topic can be used to create links between physics topics but also to uses in chemistry, biology, medicine and economics. Understandings:
• Capacitance
• Dielectric materials
• Capacitors in series and parallel
• Resistor-capacitor (RC) series circuits
• Time constant Applications and skills:
• Describing the effect of different dielectric materials on capacitance
• Solving problems involving parallel-plate capacitors
• Investigating combinations of capacitors in series or parallel circuits
• Determining the energy stored in a charged capacitor
• Describing the nature of the exponential discharge of a capacitor
• Solving problems involving the discharge of a capacitor through a fixed resistor
• Solving problems involving the time constant of an RC circuit for charge, voltage and current Guidance:
• Only single parallel-plate capacitors providing a uniform electric field, in series with a load, need to be considered (edge effect will be neglected)
• Problems involving the discharge of capacitors through fixed resistors need to be treated both graphically and algebraically
• Problems involving the charging of a capacitor will only be treated graphically
• Derivation of the charge, voltage and current equations as a function of time is not required Data Booklet reference:
• C = q / V
• Cparallel = C1 + C2 + …
• 1 / Cseries = 1 / C1 + 1 / C2 + …
• C = e 0 A / d
• E = ( 1 / 2 ) CV2
• t = RC
• q = q0 e-t / tau
• I = I0 e-t / tau
• V = V0 e-t / tau
• The C represents the capacitance, the q represents the charge, and the V represents the potential difference (voltage). The permittivity of free space e 0 = 8.85x10-12 C2N-1m-2, the A represents the area of one of the plates of a parallel plate capacitor, and the d represents the separation between the plates. E represents the electrical energy stored in a capacitor. The tau t
represents the time constant of a capacitor C discharging through a resistance R. The q represents the charge remaining on a discharging capacitor after a time t if it began with an initial charge q0. The I represents the current flowing through a discharging capacitor after a time t if it began with an initial current I0. The V represents the voltage on a discharging capacitor after a time t if it began with an initial voltageV0. International-mindedness:
• Lightning is a phenomenon that has fascinated physicists from Pliny through Newton to Franklin. The charged clouds form one plate of a capacitor with other clouds or Earth forming the second plate. The frequency of lightning strikes varies globally, being particularly prevalent in equatorial regions. The impact of lightning strikes is significant with many humans and animals being killed annually and huge financial costs to industry from damage to buildings, communication and power transmission systems, and delays or the need to reroute air transport. Utilization:
• The charge and discharge of capacitors obeys rules that have parallels in other branches of physics including radioactivity (see Physics sub-topic 7.1) Aims:
• Aim 3: the treatment of exponential growth and decay by graphical and algebraic methods offers both the visual and rigorous approach so often characteristic of science and technology
• Aim 6: experiments could include (but are not limited to): investigating basic RC circuits; using a capacitor in a bridge circuit; examining other types of capacitors; verifying time constant

TOPIC 11 PROBLEM SET

This is the complete problem set for Topic 11 - the same one I hand out. If you lose yours, you can download this one to replace it.

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.

## Electromagnetic induction

## 16 hours

## 11.1 – Electromagnetic induction

Essential idea:The majority of electricity generated throughout the world is generated by machines that were designed to operate using the principles of electromagnetic induction.Nature of science:Experimentation: In 1831 Michael Faraday, using primitive equipment, observed a minute pulse of current in one coil of wire only when the current in a second coil of wire was switched on or off but nothing while a constant current was established. Faraday’s observation of these small transient currents led him to perform experiments that led to his law of electromagnetic induction.Understandings:• Electromotive force (emf)

• Magnetic flux and magnetic flux linkage

• Faraday’s law of induction Faraday's law simulation

• Lenz’s law

Applications and skills:• Describing the production of an induced emf by a changing magnetic flux and within a uniform magnetic field

• Solving problems involving magnetic flux, magnetic flux linkage and Faraday’s law

• Explaining Lenz’s law through the conservation of energy

Guidance:• Quantitative treatments will be expected for straight conductors moving at right angles to magnetic fields and rectangular coils moving in and out of fields and rotating in fields

• Qualitative treatments only will be expected for fixed coils in a changing magnetic field and ac generators

Data Booklet reference:• F =

BAcosq•

e= -N∆F / ∆t•

e=Bvl•

e=BvlN• The

magnetic fluxis represented by F. Themagnetic field strength(akamagnetic flux density) is represented byB. TheArepresents the area through which the B-field passes. Theqrepresents the angle between the B-field vector and the normal to the area. Theinduced emfis represented withe. The change in magnetic flux is represented with ∆F and the change in time with ∆t. The l represents the length of a straight wire, thevrepresents the relative speed between the wire and the B-field. TheNrepresents the number of wires or loops.Theory of knowledge:• Terminology used in electromagnetic field theory is extensive and can confuse people who are not directly involved. What effect can lack of clarity in terminology have on communicating scientific concepts to the public?

Utilization:• Applications of electromagnetic induction can be found in many places including transformers, electromagnetic braking, geophones used in seismology, and metal detectors

Aims:•

Aim 2:the simple principles of electromagnetic induction are a powerful aspect of the physicist’s or technologist’s armoury when designing systems that transfer energy from one form to another## 11.2 – Power generation and transmission

Essential idea:Generation and transmission of alternating current (ac) electricity has transformed the world.Nature of science:Bias: In the late 19th century Edison was a proponent of direct current electrical energy transmission while Westinghouse and Tesla favoured alternating current transmission. The so called “battle of currents” had a significant impact on today’s society.Understandings:• Alternating current (ac) generators Generator simulation

• Average power and root mean square (rms) values of current and voltage Transmission line simulation

• Transformers Power lines link to cancer... Power grid simulation

• Diode bridges

• Half-wave and full-wave rectification

Applications and skills:• Explaining the operation of a basic ac generator, including the effect of changing the generator frequency

• Solving problems involving the average power in an ac circuit

• Solving problems involving step-up and step-down transformers

• Describing the use of transformers in ac electrical power distribution

• Investigating a diode bridge rectification circuit experimentally

• Qualitatively describing the effect of adding a capacitor to a diode bridge rectifica-tion circuit

Guidance:• Calculations will be restricted to ideal transformers but students should be aware of some of the reasons why real transformers are not ideal (for example: flux leakage, joule heating, eddy current heating, magnetic hysteresis)

• Proof of the relationship between the peak and rms values will not be expected

Data Booklet reference:•

Vrms =V0 / Ö2•

R=V0 /I0 =Vrms /Irms•

Pmax =I0V0•

Pavg = (1/2)I0V0•

ep /es =Np/ Ns =Is/ Ip• The

Vrepresents ac voltage. Thermsmeans "root mean square" and is a way of evening out an ac quantity to find its equivalent dc value (for the purposes of calculating power usage). TheV0 represents the peak voltage, and theI0 represents the peak current. ThePrepresents the power. Theerepresents the emfs of the two stages of an ideal transformer (the P and the S stands forprimaryandsecondaryrespectively). TheNrepresents the number of windings in the transformer stages. TheIrepresents the currents in the transformer stages.International-mindedness:• The ability to maintain a reliable power grid has been the aim of all governments since the widespread use of electricity started

Theory of knowledge:• There is continued debate of the effect of electromagnetic waves on the health of humans, especially children. Is it justifiable to make use of scientific advances even if we do not know what their long-term consequences may be?

Aims:•

Aim 6:experiments could include (but are not limited to): construction of a basic ac generator; investigation of variation of input and output coils on a transformer; observing Wheatstone and Wien bridge circuits•

Aim 7:construction and observation of the adjustments made in very large electricity distribution systems is best carried out using computer-modelling software and websites•

Aim 9:power transmission is modelled using perfectly efficient systems but no such system truly exists. Although the model is imperfect, it renders the maximum power transmission. Recognition and ac-counting for the differences between the “perfect” system and the practical system is one of the main functions of professional scientists## 11.3 – Capacitance

Essential idea:Capacitors can be used to store electrical energy for later use.Nature of science:Relationships: Examples of exponential growth and decay pervade the whole of science. It is a clear example of the way that scientists use mathematics to model reality. This topic can be used to create links between physics topics but also to uses in chemistry, biology, medicine and economics.Understandings:• Capacitance

• Dielectric materials

• Capacitors in series and parallel

• Resistor-capacitor (RC) series circuits

• Time constant

Applications and skills:• Describing the effect of different dielectric materials on capacitance

• Solving problems involving parallel-plate capacitors

• Investigating combinations of capacitors in series or parallel circuits

• Determining the energy stored in a charged capacitor

• Describing the nature of the exponential discharge of a capacitor

• Solving problems involving the discharge of a capacitor through a fixed resistor

• Solving problems involving the time constant of an RC circuit for charge, voltage and current

Guidance:• Only single parallel-plate capacitors providing a uniform electric field, in series with a load, need to be considered (edge effect will be neglected)

• Problems involving the discharge of capacitors through fixed resistors need to be treated both graphically and algebraically

• Problems involving the charging of a capacitor will only be treated graphically

• Derivation of the charge, voltage and current equations as a function of time is not required

Data Booklet reference:•

C=q / V• Cparallel =

C1 +C2 + …• 1

/ Cseries = 1/ C1 + 1/ C2 + …•

C=e0A / d•

E= ( 1 / 2 )CV2• t =

RC•

q=q0e-t/ tau•

I=I0e-t/ tau•

V=V0e-t/ tau• The

Crepresents the capacitance, theqrepresents the charge, and theVrepresents the potential difference (voltage). The permittivity of free spacee0 = 8.85x10-12 C2N-1m-2, theArepresents the area of one of the plates of a parallel plate capacitor, and thedrepresents the separation between the plates.Erepresents the electrical energy stored in a capacitor. The tau trepresents the

time constantof a capacitorCdischarging through a resistanceR. Theqrepresents the charge remaining on a discharging capacitor after a timetif it began with an initial chargeq0. TheIrepresents the current flowing through a discharging capacitor after a timetif it began with an initial currentI0. TheVrepresents the voltage on a discharging capacitor after a timetif it began with an initial voltageV0.International-mindedness:• Lightning is a phenomenon that has fascinated physicists from Pliny through Newton to Franklin. The charged clouds form one plate of a capacitor with other clouds or Earth forming the second plate. The frequency of lightning strikes varies globally, being particularly prevalent in equatorial regions. The impact of lightning strikes is significant with many humans and animals being killed annually and huge financial costs to industry from damage to buildings, communication and power transmission systems, and delays or the need to reroute air transport.

Utilization:• The charge and discharge of capacitors obeys rules that have parallels in other branches of physics including radioactivity (see

Physicssub-topic7.1)Aims:•

Aim 3:the treatment of exponential growth and decay by graphical and algebraic methods offers both the visual and rigorous approach so often characteristic of science and technology•

Aim 6:experiments could include (but are not limited to): investigating basic RC circuits; using a capacitor in a bridge circuit; examining other types of capacitors; verifying time constant## TOPIC 11 PROBLEM SET

This is the complete problem set for Topic 11 - the same one I hand out. If you lose yours, you can download this one to replace it.## TOPIC 11 FORMATIVE ASSESSMENTS

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.## TOPIC 11 PROJECTS

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.## EXTENSION NOTES FOR ENRICHMENT