# ATAT 105 Basic Electricity > # [[T105 Week 5| ◀️ ]] &nbsp;[[T105 Home| Home ]] &nbsp;[[T105 Week 9| ▶️ ]] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[QR T105 Week 6| 🌐 ]] ># [[T105 Week 6|Week 6]] >- [[T105 Week 6#Series-Parallel Circuits|Series-Parallel Circuits]] ># [[T105 Week 6#Lab|Lab]] >- [[T105 Week 6#1 Calculations in a Series Parallel Circuit|Calculations in a Series Parallel Circuit 1 & 2]] >[!jbplus|c-blue]- Lesson Intro >### What >In this lesson you will learn about series-parallel circuits, and how this opens up many more possibilities for useful electric circuits. > >### Why > >The combination of the fundamentals we have learned about series and parallel circuits leads to a large leap in the potential complication and sophistication of circuits. The relationships between voltage, current and resistance and the mathematical calculations that allow us to derive values in a circuit will become more complicated, and troubleshooting and full comprehension become even more important. > >It is important that you fully understand this material on DC. 70% is too low a bar, and anything less than a full understanding will hurt your progress in the second half of the course, and the program. > >### Approach and Objectives > >By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course. > >#### Course Learning Objectives >CLO 7. Validate using Kirchoff's Laws the values of voltage and current in a DC circuit. CLO 8. Calculate the equivalent resistance for Series, Parallel and Series-Parallel circuits. CLO 9. Calculate the power dissipated across an electrical load given other basic values. CLO 10. Assemble a functional electrical circuit using components according to a given circuit diagram. CLO 11. Show using a Digital Multimeter (DMM) the measurement of voltage, current and resistance in a circuit. CLO 12. Identify factors that determine the strength and polarity of a magnetic field created by a current carrying coil of wire. > > >### Testing > >You will be tested on this material on the midterm test and the final test. Details [[T105 Intro#Testing and Grades|here]]. >[!jbplus|c-blue]- Prof >### Objectives > >In this lesson we will learn about series-parallel circuits, and how this opens up many more possibilities for useful electric circuits. This week brings together everything we have learned so far. It is perfect preparation for the midterm and MP105-1. > > ### Theory >For the theory course, calculators out! Students should be doing all calculations in class as you go. You can warn them that this is direct preparation for the MP next week. >### Lab >For the lab, calculate and measure, with an emphasis on speed both in calculating and measuring. While there is no explicit time limit on these objectives, if a student requires more than 100 minutes to do these two circuits, there are learning shortcomings that should be addressed immediately. For efficiency, referring the students to the SSG is a good first step. If they are still confused, try to find the concept that is derailing them. ## Series-Parallel Circuits ### Identifying Series-Parallel Circuits Most practical circuits have both series and parallel components. As we know, components that are connected in series will share a common path. Note that this circuit is a series circuit. We use the term parallel strictly in an electrical sense, not a geometric one. ![[Pasted image 20210808134348.png|350]] We also know that components that are connected in parallel will be connected across the same nodes ![[Pasted image 20210808134411.png|350]] When combined we have a circuit that is more complicated. However, you have all of the individual pieces of knowledge to make quick sense of this. ![[Pasted image 20211102030122.png|350]] Of course the combinations can become quite varied. ![[Pasted image 20211102030341.png|350]] Adding components adds to the level of complexity, but does not make the circuit more difficult to analyse. ![[Pasted image 20211102030433.png|350]] We will use these varieties of circuits in our exercises because they present all of the component pieces of a series-parallel circuit. Later we will show more complex circuits, but for now we will get very used to the fundamentals as they combine in these circuits. ### Combining Circuits You can frequently simplify circuit analysis by combining series and parallel components. An important analysis method is to form an equivalent circuit. An equivalent circuit is one with characteristics that are electrically the same as another circuit, but is generally simpler. For example: ![[Pasted image 20210808134551.png|350]] If we are only interested in total resistance, we can simplify this circuit by reducing the separate resistances into one. There are no electrical measurements that can distinguish the boxes. Another example: ![[Pasted image 20210808134629.png|350]] Again, there are no electrical measurements that can distinguish the boxes. Are you verifying that the calculations for total resistance are correct in the previous two circuits? Combining these two techniques allows us to simplify circuits, often in several steps: ![[Pasted image 20210808134705.png|350]] And combining further gives us: ![[Pasted image 20210808134738.png|350]] What we end up with is an equivalent circuit that contains one resistance, that is, the total resistance, or as you will often see: R<sub>T</sub> ### Kirchoff's Laws Kirchhoff's voltage law and Kirchhoff's current law can be applied to any circuit, including combination circuits. You must however be very precise in terms of where you are in the circuit. In regards to the rules about adding resistances or Kirchoff's Laws for current or voltage, in a parallel section, parallel rules apply, and in series sections, series rules apply. ![[Pasted image 20210808134848.png|350]] What are the current readings for node A? Can you see that this graphic is correct without a calculator? ![[Pasted image 20210808134931.png|350]] ## Circuit Analysis of a Series Parallel Circuit In analyzing a series parallel circuit, you must apply all that you have learned up to now. If you are becoming comfortable with the previous calculations and measurements, you will soon see that these problems are not necessarily more difficult, but have more steps. ![[Pasted image 20210808135038.png|350]] ![[Pasted image 20210808135052.png|350]] Rather than reexplain all the component parts of the required calculations, review and be prepared to use all of these calculation skills: - [[T105 Week 4#Kirchoff's Law of Voltage|Kirchoff's Law of Voltage]] - [[T105 Week 4#Kirchoff's Law of Current|Kirchoff's Law of Current]] - [[T105 Week 4#Calculating Values in a Circuit|Calculating Values in a Circuit]] - [[T105 Week 5#Ohm's Law and Power Law Formulas|Ohm's Law and Power Law Formulas]] - [[T105 Week 5#Parallel Circuit Rule for Voltage|Parallel Circuit Rule for Voltage]] - [[T105 Week 5#Parallel Circuit Rule for Resistance|Parallel Circuit Rule for Resistance]] - [[T105 Week 5#Calculating Values in a Parallel Circuit|Calculating Values in a Parallel Circuit]] - [[T105 Week 5#Kirchhoff's Current Law|Kirchhoff's Current Law for Parallel Circuits ]] Remember to watch for opportunities to apply these rules as an error checking technique, by using one method to calculate, and another method to verify. For example, you could use Ohm's Law to solve for voltage, and then use Kirchoff's Law to verify. Observe some things from the example above. - the current in R1 is equal to the sum of the branch currents in R2 and R3. ![[Pasted image 20210808135156.png|350]] - the sum of the voltage drops across R1 and R2 equal the supply voltage. - the sum of the voltage drops across R1 and R3 equal the supply voltage. Examine the calculations in this example and those that you will do in eCentennial. Make sure that you look at each one and recognize that you understand how that value is achieved and calculated in the circuit. Anything less will lead to confusion as we proceed. ## In the Lab This week you will continue to improve your circuit calculation and measurement skills, by analyzing a series-parallel circuit. This will prepare you for [[MP105 1|MP 105-1]], which we will do in Week 8. Understand, this is a good news/bad news proposition. Good news is that you have 2 weeks to make sure you are ready for this MP. Bad news is that if you are not reviewing this material over the break, you stand a high chance of not succeeding on the MP. Now that you know, your decision should be clear! # Lab [[T105L WS06.pdf|Lab Worksheet]] |[[T105L EQ W06|Equipment List]] | [[T105L SAFETY|Safety Briefing]] ## 1. Calculations in a Series Parallel Circuit On your lab worksheet, complete the calculations for the following circuit. ![Circuit 1|350](<Pasted image 20211102030122.png>) Where: R<sub>1</sub> = 270Ω R<sub>2</sub> = 2.2KΩ R<sub>3</sub> = 1KΩ %%R<sub>4</sub> = 10KΩ %% V<sub>S</sub> = 9V Only after all of your calculations are complete, proceed to measure all values in the circuit. Review the correct procedures for use of the measuring instruments if necessary: [[T105 Week 2#1 Voltmeter|Voltmeter]] [[T105L W03#Ohmmeter|Ohmmeter]] [[T105L W04#Ammeter|Ammeter]] This concludes the material covered on the midterm next week. Be sure to use: - this SSG - the practice quizzes - lab procedures - lab worksheets - your notes - questions to the prof to prepare you for a successful midterm.