Parallel Circuit
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VFP2 Parallel Circuit TTC Dr. Frank Neumann Rayan Ateeq 308 202333308 Table of content 1.Didactic Reflection ............................................................................... 2 1.1.Curriculum Analysis .......................................................................... 2 1.2.Content Analysis ............................................................................... 4 1.2.1The TVTC Curriculum RCT ............................................................. 4 1.2.2The Internet Web- Research ........................................................... 6 1.2.3Comparison between TVTC and web- research ............................ 9 1.2.4The content : ................................................................................... 9 1.3.Didactic Analysis ............................................................................. 13 2.Lesson Plan ....................................................................................... 14 3.References ........................................................................................ 16 Rayyan Ateeq 308 Page 1 1. Didactic Reflection 1.1. Curriculum Analysis The name of this module is electrical circuit 1, which is in trimester 2. The unit has four contact hours a week three hours Theoretical and one hour for tutorial. The subject of the lesson is Methods of connecting resistors. It gives the students basic knowledge of electrostatic, batteries, and fundamentals of DC current. The unit code is (ELT 106 ) . The contact hours for this Module is 52. the students are having passed through this course. the students will study Electrical Circuits- 2 . Electrical Power & Specialization: Machinery & Equipment Department: Electrical Technology Module Name: Methods of connecting resistors Course code: ELT 106 Prerequisites: None Trimester 2 Credit Hours 3 The Module contains an explanation of electrostatics laws, batteries, DC circuit analysis, electromagnetism and magnetic circuits. The unit contents include: capacitors, Ohm's law, Kirchhoff's laws, series & parallel circuits, power, and DC bridges. Contact Hours (h/w) L P 3 0 T 1 Source : Curriculum of Electrical Technology in RCT 1.1.1. The trainee should study before the lesson : Unit-1 Electrostatics: A. Electric charge: Electric charge Coulomb's law Force between two charges Electric field Electric potential Potential difference Rayyan Ateeq 308 Page 2 B. Capacitors: Capacitance of an isolated ball Capacitance of an earthed ball capacitor Capacitance of a parallel plate capacitor Series and parallel connections of capacitors Energy stored in capacitors Unit-2 DC circuits: Electrical Quantities: Quantity of charge Current and current intensity DC voltage and current Resistance and resistors Ohm's law Unit-3 Methods of connecting resistors: Series connection of resistors. Unit- 4 Kirchhoff's laws: Kirchhoff's voltage laws. 1.1.2. The trainees studying. Unit-3 Methods of connecting resistors: Parallel connection of resistors. Unit- 4 Kirchhoff's laws: Kirchhoff's current laws. 1.1.3. The trainees studying after the lesson : Unit-3 Methods of connecting resistors: Calculation of resistances connected in series-parallel connections. Unit-5 Simple circuit calculations: Series connection. Voltage divider rule. Parallel connection. Current divider rule. Series parallel connection. Star or delta connection. Star or delta transformations. Rayyan Ateeq 308 Page 3 1.2. Content Analysis 1.2.1 The TVTC Curriculum RCT: If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law. Fig 1 of parallel circuit Source: Principles of Electric circuits, Thomas L. Floyd, 1999, page 189 To calculate total resistance. RT = To find the resistances 1 1 1 1 1 R1 + R 2 + R 3 + … … … … … … . R N total resistance of all components, add the reciprocals of the of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance: To calculate total current. IT = I1 + I2 + I3 … … … … … … IN Each voltage are equal. E=V1 = V2 = V3 = VN Rayyan Ateeq 308 Page 4 To calculate the power V2 2 PN = V × IN or PN = IN × R N or PN = R N The power is hasn't change we for each circuit in parallel and series circuit. To calculate total power PT = P1 + P2 + P3 … … … … … … PN Example 1 : Find out the following if R1 = 9 Ω , R 2 = 18 Ω and E = 27v 1. R T 2. IT Fig 2 of Parallel circuit 3. I1 , I2 4. P1 , P2 5. Pin 1. R T = 1 1 1 + R1 R2 or we use in this situation this furmala 𝑅𝑇= Source :Handout of Eng, Kahaled , in RCT R1 ×R2 R1 +R2 To calculate the total Resistors R T , we use this formula only in parallel circuit RT = 1 1 1 9 + 18 V IT = RT = 6Ω You have taken already ohm's law to find out the current we use it. 2. IT = 27V 6A = 4.5 A V 3. A. I1 = R I1 = 1 27v = 3A 9 V B. I2 = R I2 = 2 27 v = 1.5A 18 Rayyan Ateeq 308 Page 5 4. A. P1 = V × I1 The power is hasn't change we for each circuit in parallel and series circuit. P1 = 27v × 3A = 81 w B. P2 = V × I2 P2 = 27 v × 1.5 A = 40.5 w 5. A . Pin = P1 + P2 Pin = 81w + 40.5 w = 121.5w other method to solve Pin B. Pin = E × IT 1.2.2 The Internet Web- Research: 1.2.2.1 Properties of a Parallel Circuit Fig.3 of Parallel circuit of The same voltage is effective across each individual resistor in a parallel circuit as in Fig. 3. All upper ends of the resistors are connected to plus and all lower ends, to the negative pole of the input voltage. Source: Direct Current Technology, Elabot Trainings systems page 34 Therefore, it applies: U = U1 = U2 = U3 = UN If there is a voltage difference between the ends of a resistor or consumer, a current flows through the component. In a parallel circuit, the current in each branch is given by: I1 = U R! , I2 = U R2 , I3 = U R3 ,In = U Rn The branch currents in a parallel circuit are added to give the total current flow, IT : The current, It flowing from the plus pole of the input voltage is divided through the individual resistors. Thus the term, 'voltage divider'. If a resistor is connected in parallel to an existing resistor, the current finds an extra path for a charge carrier balance between the poles of the voltage source. It = I1 + I2 + I3 … … … IN A total resistance Rtot, has an effect on the voltage that is smaller than the smallest individual resistor. This is given by the formula: The relatively complicated formula for a parallel circuit can be simplified for 2 special cases. With only 2 resistors in parallel, the formula becomes: Rayyan Ateeq 308 Page 6 Easier still, is the calculation of the total resistance if all parallel connected resistors have the same value: RT = 1 1 1 1 1 + + + ………………. R1 R2 R3 RN 𝑅𝑔𝑒𝑠 = RT = R N 𝑅1 × 𝑅2 𝑅1 + 𝑅2 n = Number of equal-value resistors Fig 4 of Kirchhoff's law 1.2.2.2 Kirchhoff’s Current Law: The sum of the currents into a node ( total current ) is equal to the sum the currents. A node is any point or junction in a circuit where two or more components are connected .In a parallel circuit , a node or junction is a point where the parallel come together . For example in the circuit of Fig 4of Kirchhoff's Source: Principles of Electric circuits, Thomas L. Floyd, 1999, page 185 current law point A is one node and point B is another . Let's start at the positive terminal of the source and follow the current .the total current It from the source is into is node A. At point, the current splits the (I1 , I2 and I3 ) is out of node A. Kirchhoff's current law says that total current into node A is equal to the total current out of node A; that is, It = I1 + I2 + I3 Now, following the current in Fig 1 of Kirchhoff's current law though the branches ,you see that they come back together at node B. Fig.5 of kirchhoff's law Currents I1 , I2 and I3 are node B, and It is out of node B. Kirchhoff's current law formula at node B is therefore the same as at node A. It = I1 + I2 + I3 Fig 5 of Kirchhoff's current law illustrates the general case of Kirchhoff's current be written as IIN(1) + IIN(2) + IIN(3) + ⋯ + IIN(n) = IOUT(1) + IOUT(2) + IOUT(3) + ⋯ + IOUT(m) = 0 Rayyan Ateeq 308 Page 7 This equation shows that all current into and out of the junction sums to zero and can be stated as: The algebraic sum of all the current entering and leaving a node is equal to zero An equivalent way of writing Kirchhoff's current law can be expressed using the mathematical summation shorthand as was done for Kirchhoff's voltage law : ∑𝑛𝑖=1 𝐼𝐼 =0 Fig 6 of example use Kirchhoff's Source: Principles of Electric circuits, Thomas L. Floyd, 1999, page 187 Example 2 : Use Kirchhoff's current law to find the current measured by ammeters A3 and A5 in figure of example 2 Solution , The Total current into node X is mA. Two currents are out of node X: 1.5mA through resistor 𝑅1 and the current thoughA3 Kirchhoff's current law applied node X gives 5mA - 1.5mA -IA3 = 0 The total current into node Y is IA3 = 3.5mA two currents are out of node Y: 1 mA though resistor 𝑅2 and the current though A5 and 𝑅3 . Kirchhoff's current law applied at node Y gives 3.5mA - 1mA - IA5 = 0 solving forIA5 yields -IA5 = 3.5mA - 1mA = 2.5mA How much current will an ammeter measure when it placed in the circuit be low 𝑅3 in figure 6? Below the negative battery terminal ? Rayyan Ateeq 308 Page 8 1.2.3 Comparison between TVTC and lesson of the internet web- research The lesson for the RCT Lesson of The Internet WebResearch: by , Direct Current Technology Elabot Trainings systems and Principles of Electric circuits, Thomas L. Floyd, 1999 Less information about parallel connection. the teacher can explain it in one class . The RCT has a few details and important laws for use to calculate the voltage drop, power and current. Only theory hasn't practice . More information about parallel connection . it is not enough to teach the student these information in one time . the parallel circuit has more details .the lesson from website clear information. Has a few example and it is more easy . It has practice and theory Has more example and it is more complicated . 1.2.4 The content : Step 1 : In series connection the amperes doesn't change in each loads. as you see in this circuit we have 2A only for each loads in this circuit . you have taken this already . But now we will take parallel connection . have a look to this circuit we have three situations of amperes who can tell me what these situations, the total amperes is 2A but in some point divided in two one 1A for each branches . fig 7 of the parallel circuit Source: Own Development Rayyan Ateeq 308 fig 8 parallel circuit Source: Own Development Page 9 fig 9 of Parallel circuit Step 2 : These are shapes of parallel connection , each shape has different connection but the result hasn't change . Source: Principles of Electric circuits, Thomas L. Floyd, 1999, page 182 Step 3 : If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applicable to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff’s current law. fig 10 of the content To calculate total resistance. RT = 1 1 1 1 + + + R1 R2 R3 ………………. source : Principles of Electric circuits, Thomas L. Floyd, 1999, page 189 1 RN To find the total resistance of all components, add the reciprocals of the resistances of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance: To calculate total current. IT = I1 + I2 + I3 … … … … … … IN The current, It flowing from the plus pole of the input voltage is divided through the individual resistors. Thus the term, 'voltage divider'. If a resistor is connected in parallel to an existing resistor, the current finds an extra path for a charge carrier balance between the poles of the voltage source. Rayyan Ateeq 308 Page 10 Each voltage are equal. E=V1 = V2 = V3 = VN To calculate the power PN = V × IN or V2 2 PN = IN × R N or PN = R N The power is hasn't change we use it for each circuit in parallel and series circuit. To calculate total power PT = P1 + P2 + P3 … … … … … … PN Step 4 : Example 1 : Find out the following if 𝑅1 = 9 𝛺 , 𝑅2 = 18 𝛺 and 𝐸 = 27v Fig 11. of example 1. R T Source: Handout of Eng, Kahaled , in RCT 2. IT 3. I1 , I2 4. P1 , P2 5. Pin solution 1. R T = RT = 1 or we use in this situation this formula R T= 1 1 + R1 R2 1 1 1 9 + 18 R1 ×R2 R1 +R2 =6 Ω V 2. IT = R T You have taken already ohm's law to find out the current we use it. IT = 27V = 4.5 A 6A V 3. A. I1 = R I1 = 1 27v = 3A 9 Rayyan Ateeq 308 Page 11 V B. I2 = R I2 = 2 27 v = 1.5A 18 4. A. P1 = V × I1 to calculate the power 1 most be multiplied the voltage with the current of the resistor one P1 = 27v × 3A = 81 w B. P2 = V × I2 P2 = 27 v × 1.5 A = 40.5 w 5. A . Pin = P1 + P2 Indicated in step 3 (page10) the power sum of power will lead to the total . Pin = 81w + 40.5 w = 121.5w other way to solve Pin if you don't like to sum the power you can slove it by m multiplication the voltage with total current . B. Pin = E × IT Pin = 27 v × 4.5 A = 121.5w step 5 : Kirchhoff’s Current Law The sum of the currents into a node ( total current ) is equal to the sum the currents . fig 12 of Kirchhoff's law fig 13 of Kirchhoff's law Source:http://www.xzx4ever.com/vb/s Source:http://www.physics.uoguelp howthread.php?t=9946 h.ca/tutorials/ohm/Q.ohm.KCL.html It = I1 + I2 Rayyan Ateeq 308 Page 12 step 6 : Example: Find out the total current by using Kirchhoff's law if the first current equal 1A , and second current equal 2A solution fig 14 of example Source: Principles of Electric circuits, Thomas L. Floyd, 1999, page 186 It = I1 + I2 It = 5mA + 12mA = 17mA 1.3. Didactic Analysis There have to be expected up to 20 trainees in class and each trainee has at the General Certificate of Secondary Education in the natural sciences. Most of trainees are from Riyadh and the range of age is from 19-23. An experience in the electrical power can't be expected , to perform the lesson in an appropriate way the following equipment will be necessary , Projector, Whiteboard, Computer, Power Point and Loudspeaker. The lesson is started on 4 May 2014, 8:50 am in room 12F, building 20 an RCT will take place. Using video because: Visualize information from other methods campus. Presenting the students example from the subject. Using feedback control because: The trainees shall reflect video, in order to increase the memorizing video. Trainee's shall think and build an own opinion. Rayyan Ateeq 308 Page 13 Using In step 1 , step 3 , step 4 and step 6 classroom conversation because the trainees shall be able to : Discuses about the differences between series and parallel connections . Communicate with the others. Increase the attention . Make the students more active. Using lecture in step 2 and step 5 because the trainees shall receive: Clear information about parallel circuit and Kirchhoff's law . An introduction about parallel connection . A cover to guidance to appropriate learning. Using Group work in Task (1) of group 1 and group and homework because: Make trainees more active. Connect theory example with practice example Horizontal reduction . Motivate the trainees to work. Presenting difference between parallel and series circuit . 2. Lesson Plan II. Objectives General Objectives: The Trainees: will increase their social competencies by participating Specific Learning Objectives: The Trainees will be able to: explain Parallel circuit (Reorganization). explain the voltage and current and resistor (Reorganization). calculate the voltage, the current and resistor by using the formula of Parallel circuit (Reorganization). Learn how to measuring the current in the circuit. Rayyan Ateeq 308 Page 14 III. Overview of the Intended Process Opening / Entrance / Motivation Time Methodology Media Minutes Expected Trainer-action Expected Trainee-action The trainer welcomes the trainees - - - - Projector Video 5 - Presentation video visualization Control Question The trainees should answer what the different between parallel and series circuit . Feedback Control Explanation what the different between series and parallel connection - Classroom conversation Lecture Slid 1 - Slide 2 Body (Information / Elaboration) 2 2 Time Media Expected Trainer-action Expected Trainee-action Methodology Explanation what does mean parallel connection and showing shapes of parallel connection - Lecture Explanation of the formulas of parallel connection voltage, current , power , and resistors - Minutes Slide 3 4 Classroom conversation Classroom conversation Slide 4 7 Handout 1 Whiteboard Calculation of the currents , resistors and powers and gives them example. - Classroom conversation Slide 5 9 Handout 2 The trainer divides the trainees to two groups The trainer gives the first group Task (1) in theory The trainees of group 1solve the ask in theory the questions. 9 Task (1) The trainees of group 2 take the values of experiment Group Work Slide 6 The trainer gives second group task (1) practical Rayyan Ateeq 308 Page 15 The trainees are comparing about the task1on the whiteboard and the trainer asks them why you use these method One of each groups write and explain the solution the question and the values on the whiteboard Whiteboard 4 Slide 7 3 Explanation of definition of Kirchhoff’s Current Law - Lecture Calculation of Kirchhoff’s Current Law - Classroom conversation Slide 8 3 The trainer gives them Homework - - Homework Nothing Close (Reflection, Exercises, Homework, Feedback) Time Media Expected Trainer-action Expected Trainee-action Methodology The trainer ask them questions about the parallel connection - Classroom conversation Minutes Slid 9 2 3. References Principles of Electric circuits, Thomas L. Floyd, 1999, page 182,184,185,188,189 Electrical circuit The Theory And Technology , JOHN BIRD , Fourth Edition 2010 ,Pages , 39, 40,41,42,43 http://books.google.com.sa/books?id=v1elek6nS_sC&q=parallel#v=snippet&q=parall el&f=false Electrical circuit 1 Arabic book from TVTC , 2008,Pages 103, 104,105,106,107,108 and 109. fig 11 of the content http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.KCL.html fig 12of the content http://www.xzx4ever.com/vb/showthread.php?t=9946 Direct Current Technology Elabot Trainings systems Page , 34 and 35 Rayyan Ateeq 308 Page 16
