This document provides an overview and lessons for a basic electrical math training course for solar technicians. The 5 lesson topics are: [1] Voltage, Amps and Resistance including Ohm's Law, [2] Series Electric Circuits, [3] Parallel Electric Circuits, [4] Electric Power Sources, and [5] Sun Angle and Solar Panel Orientation. Each lesson includes examples and practice problems to help students understand electrical formulas and circuit calculations needed for solar installation work.

1. Basic Electrical Math Presented by Jim Wylie

2. This pre-class is to help you to prepare for the Solar Technician Course. The goal is to be able to understand the technical lessons of the main course, not become frustrated or fall behind the other students. Jim Wylie, your instructor, has posted regular office hours to help you to successfully complete the Solar Technician Course. If you need times not posted, contact Jim by email or Blackboard and make other arrangements.

4. PV Installers must be able to do simple geometric and trigonometric problems

5. The instructor assumes that students are capable of simple addition, subtraction, multiplication and divisions.

7. Ohms Law is possibly the most important concept to learn in electrical technology. It is used by every electrician and equally used by solar installers. The formula E=IR explains the relationship of current, resistance to the voltage of all electric circuits. In this lesson we will use the Ohms formula to explain the relationship of volts, amps and ohms. Learn this lesson well before you continue to Lesson Two. If you feel that you are not learning the lesson, contact the instructor during his office hours for some help. Ohms Law V=IR

8. Lesson 1: Apply Ohms Law The formula V=IR is manipulated to calculate the I (current) when we know the V (voltage) and R (resistance) You must learn that V=IR and that V=Voltage, I=Amps and R=Resistance Repeat: Learn this formula – Electrical potential equals the current times the resistance or V=IR. The electrical potential is measured in volts. Current is measured in amps and resistance is measured in ohms.

9. Calculate the Current If V=IR, to get I= ? First divide on both sides of the equal sign by R. V/R=IR/R the answer is V/R=I or reverse the formula I=V/R Explanation: The current in amps is equal to electrical potential in volts divided by resistance in ohms or the current in amps is inversely proportional to the resistance in ohms and directly proportional to the electrical pressure (potential) in volts.

10. Lesson 1: Continue Using the same process for calculating (I), calculate (R) Remember that Ohms Law is V=IR (memorized by now) We calculate the formula for resistance (R) when you know what the voltage potential and current in amps are ? Go to the next slide and see if you have the correct answer reasoning. If the answer is wrong go back to the first slide in this lesson before continuing.

11. Answer: Find R, If V=IR V=IR by dividing both sides of the equal sign by I. V/I=IR/I The results is V/I=R or R=V/I QUIZ: Describe the process and results in math terms? Stand on your head for the answer You can say that the resistance in ohms is equal to electrical potential in volts divided by current in amps or you can say that resistance in ohms is inversely proportional to the current in amps and directly proportional to the electrical pressure (potential) in volts.

12. Calculate the Resistance If V=IR, to get R= ? First divide on both sides of the equal sign by I. V/I=IR/I the answer is V/I=R or reverse the formula R=V/I Explanation: The Resistance in ohms is equal to electrical potential in volts divided by current in amps or the resistance in ohms is inversely proportional to the current in amps and directly proportional to the electrical pressure (potential) in volts.

15. V=IR

16. I=V/R

17. R=V/I

18. Explain each of the Ohm’s Law variation with mathematical terms –

20. Answer to Problems V=IR R=V/I I=V/R

21. Lesson 2: Series Electric Circuits A series circuit is connected in a line with the back side of electrical object attached to the front side of the next electrical object.

22. Lesson 2: How It Works SERIES CIRCUITS A Series Circuit has only one path to ground, so electrons must go through each component to get back to ground. All loads are placed in series. 1. An open in the circuit will disable the entire circuit. 2. The voltage divides (shared) between the loads. 3. The current flow is the same throughout the circuit. 4. The resistance of each load can be different

23. Lesson 2: Voltage Drop VOLTAGE DROP CALCULATIONWhen current flows in a circuit, the presence of a resistance in that circuit will cause the voltage to fall or drop as it passes through the resistance. The resultant difference in the voltage on each side of the resistance is called a voltage drop. When current (I) flows in the following circuit, voltage drops V1 and V2 across resistances R1 and R2 can be determined as follows from Ohm's law. (The value of current I is the same for both R1 and R2 since they are connected in series.)

24. Series Voltage Drop Calculation

25. example:

26. Series Circuit Summary Remember these points and understand how the voltage drop calculations are done There is only one path to the ground Current remains the same throughout the circuit The presence of a resistance in the circuit will cause the voltage to drop

27. Lesson 3: Parallel Circuits A parallel circuit is like a ladder with the steps being the resistance between the sides representing the positive and negative wires. Voltage and current flows independently through each resistant step.

28. Lesson 3: How It Works PARALLEL CIRCUITA parallel circuit has more than one path for current flow. The same voltage is applied across each branch. If the load resistance in each branch is the same, the current in each branch will be the same. If the load resistance in each branch is different, the current in each branch will be different. If one branch is broken, current will continue flowing to the other branches.

29. Lesson 3: calculations Resistance in a parallel circuit is calculated with the formula: Current is calculated by the formula:

30. Parallel Circuit Summary Remember these points and understand how the resistance and current calculations are done A parallel circuit will have more than one path to the ground The same voltage will appear across each branch Different current will result from different resistance of the branches If a branch is opened current will continue through the other branches

31. Lesson 3: Power Sources We will use our knowledge of Ohms Law, Series and Parallel electric circuits to understand how power sources like batteries and solar panels work.

32. Power Source in Series Voltage will increase by adding each individual battery or solar panel to find the total voltage of battery pack or array Current will remain the same

33. Power Source in Parallel Current will increase by adding each individual battery or solar panel to find the total current of battery pack or array Voltage will remain the same

34. Summary of Training List important points from each lesson. Provide resources for more information about the subject. List resources on this slide. Provide handouts with additional resource material.

35. Reread lesson three to commit the points to memory Solar panels are wired through a controller, inverter and electrical panel.

36. Lesson 4: Sun angle and Solar Panel Orientation

37. Assessment and Evaluation Prepare a quiz or challenge to assess how much information participants learned. Survey participants to see if they found the training beneficial.