Module 1 – Part 1 What are Voltage and Current?

1. Module 1 – Part 1What are Voltage and Current? Filename: DPKC_Mod01_Part01.ppt

2. Overview of this Part In this part of the module, we will cover the following topics: • Definitions of current and voltage • Hydraulic analogies to current and voltage • Path dependent and path independent • Reference polarities and actual polarities Note: Some of these topics will be review for some students, particularly those who have had some exposure to circuits before. However, it would be wise to skim through this material quickly, to make sure that we are using terms in a way that is familiar to you.

3. Textbook Coverage This material is covered in your textbook in the following sections: • Circuits by Carlson: Section 1.1 • Electric Circuits 6th Ed. by Nilsson and Riedel: Section 1.4 • Basic Engineering Circuit Analysis 6th Ed. by Irwin and Wu: Section 1.2 • Fundamentals of Electric Circuits by Alexander and Sadiku: Sections 1.3 & 1.4 • Introduction to Electric Circuits 2nd Ed. by Dorf: Sections 1-2 & 1-4

4. Current • Current is the net flow of charges, per time, past a plane in some kind of electrical device. • For circuits, we are generally only concerned with the flow of positive charges. The fact that electrons have negative charges does not matter. A negative charge moving to the right is conceptually the same as a positive charge moving to the left. • Mathematically, this is expressed as Charge, typically in Coulombs [C] Current, Typically in Amperes [A] Time, typically in seconds [s]

5. Ampere Definition • An Ampere is defined as being a Coulomb per second. • Remember that current is defined in terms of the flow of positive charges. One coulomb of positive charges per second flowing from left to right is equivalent to one coulomb of negative charges per second flowing from right to left.

6. Moving to 2 Dimensions • In schematic diagrams, wires, which have a non-zero cross section, get represented as a line, which has no cross section. • Therefore, we think of current as charges moving past a point. Remember, that this is just a simplification related to the way we represent circuit diagrams. • We will typically look at circuits using 2 dimensional diagrams called schematics. Actual Wire Schematic Wire

7. Hydraulic Analogy for Current • It is often very useful, particularly at the beginning, to think in terms of hydraulic analogies. • The analogy here is that current is analogous to the flow rate of water. Charges going past a plane per time – is analogous to – volume of water going past a plane in a pipe per time.

8. Water flow » Current • So, if we put a plane across a water pipe, and counted the number of cubic inches of water that moved past that plane in a second we would get the flow rate. • In a similar way, current is the number of positive charges moving past a plane in a current carrying device (like a wire) in a second. • The number of charges per second that we use is called a Coulomb, which is about 6.24 x 1018 electron charges. Animated graphic provided by David Warne, student in UH ECE Dept.

9. Voltage • Voltage is a little more difficult concept for many beginning students in circuit analysis. However, it will also have an analogy that we can use to help us understand. • Voltage is the change in potential energy as we move between two points. It is referred to as a potential difference. When we move a charge in an electric field, energy is transferred. • Mathematically, this is expressed as Energy, typically in Joules [J] Voltage, typically in Volts [V] Charge, typically in Coulombs [C]

10. Volt Definition • A Volt is defined as being a Joule per Coulomb. • Remember that voltage is defined in terms of the energy gained or lost by the movement of positive charges. One Joule of energy is lost from the electric system when a Coulomb of positive charges moves from one potential to another potential which is one Volt lower.

11. Hydraulic Analogy for Voltage • The hydraulic analogy here is that voltage is analogous to the height. In a gravitational field (as we are), the higher that water is, the more potential energy it has. The voltage between two points – is analogous to – the change in height between two points, in a pipe.

12. Height » Voltage • The change in potential energy, for water in a pipe, occurs when the water moves from one height to another height. We say it is moving in the gravitational field. • In a similar way, voltage is the change in potential energy for a charge between two points. We say it is moving in an electric field. • There is a fundamental difference, in that we do not have negative mass and positive mass, but we do have negative charges and positive charges. However, in circuit analysis, we usually only think about positive charges, so this is not as big a change as it might seem. Go back to Overview slide.

13. Current Through and Voltage Across • Current is a path dependent variable. This means that the value of the current going between two points depends on which path you use to go between those two points. • Voltage is a path independent variable. The value of the voltage between two points does not depend on how you go between those two points.

14. Hydraulic Analogy of Two Paths Again, we will use a hydraulic analogy to try to make these points clearer. See the diagram.

15. Current Through Current is a path dependent variable. The hydraulic analogy is that if we have two pipes running between two points, the flow rate through one pipe can be different from the flow rate through the other. The flow rate depends on the path.

16. Go back to Overview slide. Voltage Across Voltage is a path independent variable. The hydraulic analogy is that if we have two pipes running between two points, the change in height is the same between the two points, no matter which pipe you follow to go between those points.

17. Polarities It is extremely important that we know the polarity, or the sign, of the voltages and currents we use. Which way is the current flowing? Where is the potential higher? To keep track of these things, two concepts are used: • Reference polarities • Actual polarities.

18. Reference Polarities The reference polarity is a direction chosen for the purposes of keeping track. It is like picking North as your reference direction, and keeping track of your direction of travel by saying that you are moving in a direction of 135 degrees. This only tells you where you are going with respect to north, your reference direction.

19. Actual Polarity The actual polarity is the direction something is actually going. We have only two possible directions for current and voltage. • If the actual polarity is the same direction as the reference polarity, we use a positive sign for the value of that quantity. • If the actual polarity is the opposite direction from the reference polarity, we use a negative sign for the value of that quantity.

20. Reference Polarities Reference polarities do not indicate actual polarities. They cannot be assigned incorrectly. You can’t make a mistake assigning a reference polarity to a variable. Rather, the only mistake you can make would be by incorrectly solving for the sign of the value of a variable once it has been defined. Always assign reference polarities for the voltages and currents that you name. Without this step, these variables remain undefined. All variables must be defined if they are used in an expression.

21. Polarities for Currents • For current, the reference polarity is given by an arrow. • The actual polarity is indicated by a value that is associated with that arrow. • In the diagram below, the currents i1 and i2 are not defined until the arrows are shown.

22. Polarities for Voltages • For voltage, the reference polarity is given by a + symbol and a – symbol, at or near the two points involved. • The actual polarity is indicated by a value that is placed between the + and - symbols. • In the diagram below, the voltages v1 and v2 are not defined until the + and – symbols are shown.

23. Why bother with Reference Polarities? • Students who are new to circuits often question whether this is intended just to make something easy seem complicated. It is not so; using reference polarities helps. • The key is that often the actual polarity of a voltage or current is not known until later. We want to be able to write expressions that will be valid no matter what the actual polarities turn out to be. • To do this, we use reference polarities, and the actual polarities come out later. Go back to Overview slide.