Lesson Plan Electric Energy, Power, Circuits, and Transmission

Mahdi Ibrahim Maynard H. Jackson High School Atlanta, GA. Faculty Advisor: Dr. Kristin Shepperd School of Physics Research Group: Prof. Edward Conrad School of Physics Program Director: Dr. Leyla Conrad Director, Outreach Electrical & Computer Engineering

Georgia Institute of Technology STEP UP 2011

Lesson Plan Title:

Electric Energy, Power and Transmission

Overview/Abstract In this lesson the students will experimentally determine Ohm’s law. Then use Ohm’s law to experimentally determine the effective resistance of resistors connected in series as well as those connected in parallel. Once they experimentally formulated the effective resistance of resistors connected in series and parallel, they will mathematically relate the total voltage of the circuit to the voltages of individual resistors or loads in both series and parallel circuit using experimental data. Likewise, they will also formulate the relationship between the total current in the circuit to the current through individual loads in both series and parallel circuits from the data. They will also determine electrical power, work, and calculate the electric energy consumption, and approximately predict their respective the electric bills. A brief note and lab on principles and practices of electric power generation and transmission from a power generator to home will be introduced with emphasis on the use of step up and step down transformers to deal with high power loss that results from a large current and high resistance due to the length and cross sectional area of the transmission line.

Problems  From experimental results, formulate mathematically – Ohm’s Law – Effective or total resistance in relation to individual resistances connected in series, and in parallel circuits – Total current through the circuit in relations to currents through individual resistors in both series and parallel circuits. – Total voltage across the circuit in relations to voltage drop across individual resistors in both series and parallel circuits.  Calculate home electric energy usage, and approximately verify validity of the monthly electric bill.  Explain how electric power is generated, and transmitted to customer.

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Objectives  The students will measure p.d, resistance, and current of these elements connected in series and parallel and determine the mathematical representation of – Ohm’s Law – Equivalent resistance of several resistors connected in a. Series b. Parallel Relate the total voltage across the circuit to the potential drop across each of the several resistors connected in a. Series b. Parallel Relate the total current through the circuit to the current through each of the several resistors connected in a. Series b. Parallel  Relate the electrical work, and power to overcome the resistor(s) of the circuit, potential difference across resistor(s) in the circuit, current through resistor(s) in the circuit, and calculate electric energy consumption, and cost as per Georgia Power’s published energy rates.  Explain how electric power is generated and transported over the transmission lines from the power generation facility to homes.

Alignment with the Standards:  Georgia (GPS)  SP5. Students will evaluate relationships between electrical and magnetic forces.  a. Describe the transformation of mechanical energy into electrical energy and the transmission of electrical energy.  b. Determine the relationship among potential difference, current, and resistance in a direct current circuit.  c. Determine equivalent resistances in series and parallel circuits.  d. Determine the relationship between moving electric charges and magnetic fields.

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AP Physics B Standards      

Competency Goal 4: The learner will build an understanding of electricity and magnetism. Objectives: 4.03 Analyze and investigate electric circuits. Current, resistance, and power. Steady-state direct current circuits with batteries and resistors only.

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4.04 Study and evaluate magneto-statics. Forces on moving charges in magnetic fields. Forces on current-carrying wires in magnetic fields. Fields of long current-carrying wires.

 4.05 Measure and analyze electromagnetism.  Electromagnetic induction (including Faraday's law and Lenz's law). AP Physics C  Unit Six: Electricity (Standards One, Two, and Three)  II. Topics Covered:  D. Electric fields, electric potential, and electric potential energy, G. Electric current and resistance, H. Ohm’s law, I. Electric circuits: series vs. parallel, J. Kirchhoff’s laws  K. Electric power               

III. Objectives: Students will … D. Apply the relationship that exists between electric potential and Electric potential energy. L. Analyze series and or parallel combinations of capacitors. N. Analyze problems involving electric current, current density, Resistance and resistivity. O. Apply Ohm’s law. P. Calculate the electric power consumption and production in a circuit. Q. Determine the current and potential differences in a single-loop circuit or combinations of series/parallel resistor circuits. R. Correctly connect digital voltmeters, ammeters, and ohmmeters to measure electrical properties of devices in a circuit. S. Apply Kirchhoff’s laws to determine unknown electrical parameters in a multi-loop circuit. .

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ENDURING UNDERSTANDING:  Ohm’s Law relates the p.d. across each resistor or in the whole circuit, to the individual or total current, and resistor(s) in the circuit.  In a series circuit (only one path for current): – the total voltage is the sum of individual voltages across each resistor in the circuit. – The total current through the circuit is the same as the current through individual resistors in the circuit. – The total resistance of the circuit is the sum of individual resistors in the circuit  In a parallel circuit ( more than one path for current): – the voltage across each element in the circuit is the same. – The total current is the sum of all individual currents through each resistor in the circuit. – The reciprocal of the effective resistance is the sum of the reciprocal of each resistor  A variable magnetic field will induce an electric current and a variable current will induce a magnetic field. Electric power is generated by rotating a coil in a magnetic field  Step up transformers are used to increase the source voltage and decrease the current to minimize the ratio of power loss during transmission. Step down transformers are used to lower the high voltage and increase the low current to make them usable by consumers in homes and business places.

Essential Questions:

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How does the voltage, current and resistor relate in a closed circuit? Quantify this relation mathematically Why is resistivity of different materials differ? And how is resistivity related to resistance? Explain the difference between series and parallel circuits in relation to  Path, total voltage in relations to voltage drop across each resistor in the circuit, and total current in relations to currents through individual resistors in the circuit? Draw both series and parallel circuits, and write the above relations mathematically  Which circuit is used for home wiring, and why? Explain the principle of electric power generation? Describe how this principle is used in hydro-electric power generation, or any other form of power generation

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Explain how electric power is transmitted from power generation plant to a consumer at home? Draw a diagram of step up and step down transformers, and explain their operation and significance in power transmission? Why did AC technology preferred over DC technology in electric power generation, and transmission? Draw a diagram of an AC generator and explain how it generates electricity?

Anticipated Learning Outcome  Students will understand – the relationship between voltage, current, and resistor in a closed circuit (Ohm’s Law). – Why homes are wired in parallel. – Relate mathematically the total voltage to the voltages across each resistor, total current to the current through each resistor, and total resistance to each resistor in both series and parallel circuits. – Draw the schematic diagram of both circuits – Explain how electric power is generated. – Why step up and step down transformers are used in transmission of electric power

Evidence of Learning  Use –

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A. Formative assessment – Guiding questions during learning – Discussions related to the process, procedures, gathering of data and its analysis to get to the desired results (mathematical formulation) – Explanation how p.d., resistance, and current relate to each other B. Summative assessment – Perform as per rubrics on hands on and written assessments

– http://www.physics.uoguelph.ca/~phyjlh/ Prob/Soweto/ElectricityI%20(multiple%2 0choice%20questions).mht – http://www.code-electrical.com/ohms-lawquiz/ 6

Key Terms            

Electric charge Resistivity Conductance Electric power Circuit Parallel circuit Kirchhoff’s Law Ampere Joules Terminals Step up transformer Transmission Line

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Potential difference Resistor Current Electric energy Series circuit Series-parallel circuit Volts Ohms Watts AC generator Step down transformer Electric power loss ratio

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Assessment and Rubrics Rubrics for Labs

http://www.ncsec.org/intranet/webwiz/team3_2/Lab%20Rep ort%20Rubric.doc

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Introduction (Background)  A circuit is a loop through which electric current flows. Open circuit has no current flow, but may have a potential difference between the two terminals.  Resistivity (p) of a material depends on the materials, and shape (length and cross sectional area) – – R = p L/A – The resistance of a given sample will increase with the length, but decrease with greater cross-sectional area. Resistance is measured in ohms. Length over area has units of 1/distance. To end up with ohms, resistivity must be in the units of "ohms × distance" (SI ohm-meter, US ohm-inch). – In a hydraulic analogy, increasing the cross-sectional area of a pipe reduces its resistance to flow, and increasing the length increases resistance to flow (and pressure drop for a given flow).

Resistivity and Resistance  The electrical resistance of a wire is greater for a longer wire and less for a wire of larger cross sectional area. The resistance depend on the material of which it is made and can be expressed as:  R=ρL/A (1)  where  R = resistance (ohm)  ρ = resistivity coefficient (ohm m)  L = length of wire (m)  A = cross sectional area of wire (m2)  The factor in the resistance which takes into account the nature of the material is the resistivity. Since it is temperature dependent, it can be used to calculate the resistance of a wire of given geometry at different temperatures.  The inverse of resistivity is called conductivity and can be expressed as:  σ=1/ρ (2)  where  σ = conductivity (1 / Ω m)

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Ohm’s Law (V = IR) Ohm's Law defines the relationships between (P) power, (E) voltage, (I) current, and (R) resistance. One ohm is the resistance value through which one volt will maintain a current of one ampere. ( I ) Current is what flows on a wire or conductor like water flowing down a river. Current flows from negative to positive on the surface of a conductor. Current is measured in (A) amperes or amps. ( E ) Voltage is the difference in electrical potential between two points in a circuit. It's the push or pressure behind current flow through a circuit, and is measured in (V) volts. ( R ) Resistance determines how much current will flow through a component. Resistors are used to control voltage and current levels. A very high resistance allows a small amount of current to flow. A very low resistance allows a large amount of current to flow. Resistance is measured in ohms. ( P ) Power is the amount of current times the voltage level at a given point measured in wattage or watts.

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Series and Parallel Circuits

 Series Circuit

 In series circuits, all components are connected end-to-end to form only one path for electrons to flow through the circuit:  Voltage drops add to equal total voltage. ( V = V1 +V2 + V3+ …)  All components share the same (equal) current. ( I = I1 = I2 = I3 = ….)  Resistances add to equal total resistance. ( R = R1 + R2 + R3 + …) Parallel Circuits

 In parallel circuits, all components are connected between the same two sets of electrically common points, creating multiple paths for electrons to flow from one end of the battery to the other. 1. All components share the same (equal) voltage. ( V = V1 = V2 = V3 = …) 2. Branch currents add to equal total current. ( I = I1 + I2 + I3 + …) 3. Resistances diminish to equal total resistance. 1/R = 1/R1 + 1/R2 + 1/R3 +…)

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Series-Parallel Combination

If circuit components are series-connected in some parts and parallel in others, we won't be able to apply a single set of rules to every part of that circuit. Instead, we will have to identify which parts of that circuit are series and which parts are parallel, then selectively apply series and parallel rules as necessary to determine what is happening.

Kirchhoff's Law The Loop Rule (Voltage Law)  The sum of the potential difference (p.d) positive or negative that transverse any closed loop must be zero.  (Note – the p.d. across resistance is the direction of current is negative (drops by -IR) – the p.d. in the opposite direction of the current is positive (increases by IR). – moving across a source from negative to positive terminal across a battery is positive (increases) – going from positive to negative terminal across a battery is negative (decreases) The Junction Rule (Current Law)  The total current that enters a junction must be equal to the current that leaves the junction

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 Electric Generators –

Electric generators operate on the principles of electromagnetic induction (Faraday’s Law of Electromagnetic Induction.)  An AC generator converts mechanical energy to electromagnetic energy.  AC generators consist of a wire loop rotated in a magnetic field by some external means (ex. In hydroelectric huge flow of water hits the turbine to rotate in a magnetic field and create electricity)

 AC Generator

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Transmission Line

Transformers

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Significance of Transformers  Electric power is transmitted from the power generating station to the customers with the help of step up (at the generating station), and step down transformers (at the customers)  Step up transformers increases the voltage to 200 or 400 kV, and reduces the current significantly to mA, thereby reducing loss over the transmission line due to heat ( E = I2R) and saving the line from damage  Step down transformers decrease the voltage to from few thousands volts to a few hundred volts so that customers can use it safely.

Implementation of the Lesson Plan  Can we salvage all those Christmas light that were discarded because only one or a few bulbs were damaged?  How much are you costing your parents in your usage of electric energy?  Why can’t we directly connect to high voltage power lines instead of the ones connected to step down transformers?  Demonstrate how to use digital multi-meters to measure voltage, current, and resistance along with electric safety in labs; and then introduce the following lab activities to answer the above.  http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html - Measure/record the readings of voltage (V) and current (I) by keeping the resistance (R) constant. (record your measurements in table 1)

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- Measure/record the readings of current (I) and Resistance (R) by keeping the voltage (V) constant. (record your measurements in table 2) - Graph your data and formulate the relationship between voltage and current, voltage and resistance, and current and resistance in words. Let the students complete the following labs, ask them to make Observation: Simulated and hands on labs given or linked Data Collection: (use the tables provided and record) Graph use graph paper Analysis and Conclusion: Analyze the simulated data, measured data, and their respective graphs and make conclusion Table 1 Constant Resistance in Ohms Voltage (p.d.) in volts

Current (I) in Amps

Table 2 Constant Voltage (p.d) in Volts Resistance in Ohms

Current (I) in Amps

- From your data in table 1, and table 2, what can you conclude about the relationship between current and voltage when resistance was constant; and between current and resistance when voltage was constant? - Formulate the above relationship mathematically - Is your mathematical formulation the same as rhe formulation of Ohm’s law stated in the book? If not why?  http://homepage.mac.com/cbakken/physlab/labs/ohms.html 15

 - (Complete this Ohm’s Law lab and answer all the questions)  http://jersey.uoregon.edu/vlab/Voltage/  and complete the exercise to mathematically formulate Ohm’s law from the simulated data  http://www.teachengineering.org/collection/wsu_/activities/wsu_circuits_and _ohm_activity1/ohms_law_worksheet.pdf  Complete the assignments  http://mrmaloney.com/mr_maloney/SHSdocs/electricity/current/L13_circuits _lab.pdf Complete this lab and answer all the questions related to series and parallel circuits  http://homepage.mac.com/cbakken/physlab/labs/ohms.html   (Complete this Ohm’s Law lab and answer all the questions)  http://jersey.uoregon.edu/vlab/Voltage/   and complete the exercise to mathematically formulate Ohm’s law from the simulated data  http://www.teachengineering.org/collection/wsu_/activities/wsu_circuits_and _ohm_activity1/ohms_law_worksheet.pdf  – Complete the assignments  http://mrmaloney.com/mr_maloney/SHSdocs/electricity/current/L13_circuits _lab.pdf – Complete this lab and answer all the questions related to series and parallel circuits    

Discuss the experimental data, its graphs, and check students’ analysis of the data. Check their conclusion, and mathematical formulation of the results Check their lab reports, and answers to the quizzes Summarize Ohm’s Law, and the basic relations between voltage, current, and resistance in both series and parallel circuits.  Assign homework and practice questions and problems.

Summary : Emphasize the importance of experimental data in formulating or verifying the existing laws like Ohm’s law, Kirchhoff’s law, etc. Summarize Ohm’s law, the relationships between p.d., currents, and resistances in both series and parallel circuits

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mathematically and conceptually. Summarize the principles of generators, and transformers. Explain the importance of transformers in electric power transmission. References  http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html  http://homepage.mac.com/cbakken/physlab/labs/ohms.html  http://jersey.uoregon.edu/vlab/Voltage/  http://mrmaloney.com/mr_maloney/SHSdocs/electricity/current/L13_circuits _lab.pdf  http://www.worsleyschool.net/science/files/transformers/page.html

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