Applied Circuit Analysis Chapter 1 – Basic Concepts Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Circuit Theory Circuit theory is the basis upon which many branches of electrical engineering rests. For electrical engineering technology education, circuit theory is the single most important course taken. Virtually anything that is either plugged into a wall outlet or runs off a battery can be analyzed with circuit theory. 2

What is a circuit? An electric circuit is an interconnection of electrical elements. It may consist of only two elements or many more: 3

Units When taking measurements, we must use units to quantify values We use the International Systems of Units (SI for short) Prefixes on SI units allow for easy relationships between large and small values 4

SI Units Any measurement that is made must be compared to a standard reference. This reference is called a ‘unit’ such as kilograms or feet. Units are found everywhere and are collected together in sets. The set that is recognized and used across the world is the International System (SI). 5

SI Units II 6

Converting Units Despite the universally adopted SI units, other sets of units exist. One often needs to change a measured value from one set of units to another. This is done by multiplying or dividing by a “conversion factor.” An example of this is that there are 60 seconds in a minute. 7

Converting Units II Let’s take an example of a time measured to be 30 seconds. In this case, we have a conversion factor of 60 seconds per minute. We need the seconds units to cancel, therefore we divide by the factor: 8

Conversion Factors 9

Scientific Notation Often engineers and scientists work with very large or very small numbers. Writing them out fully is impractical. Instead, two notation methods exist for making the numbers more manageable to write. In Scientific Notation the number is expressed in powers of ten with a single digit to the left of the decimal point. For example 6.02x

Engineering Notation Engineering notation differs slightly from scientific notation. In this case, only powers of 10 that are multiples of three are used i.e. 10 3, 10 6, 10 9,… A prefix is then attached to the unit to note the power of ten used. This is almost exclusively used with SI units. 11

SI Prefixes Here is a list of the SI prefixes that are typically found. 12

Electric Charge We know from elementary physics that matter is made of atoms. Atoms consist of a nucleus and electrons orbiting it. Although in solid matter the nuclei don’t move much, in certain materials the electrons can move freely between atoms. 13

Electric Charge As such, the electric charge is what allows any electronics to function. It is natural for anyone working in electronics to use the charge of the electron as a reference. But, due to historical reasons, the electron is considered to have a negative charge. 14

Charge Charge is a basic SI unit, measured in Coulombs (C). Counts the number of electrons (or positive charges) present. Charge of single electron is 1.602* C One Coulomb is quite large, 6.24*10 18 electrons. 15

Charge II In the lab, one typically sees (pC, nC, or μC). Charge is always multiple of electron charge. Charge cannot be created or destroyed, only transferred. 16

Current The movement of charge is called a current. Historically the moving charges were thought to be positive. Thus we always note the direction of the equivalent positive charges, even if the moving charges are negative. 17

Current II Current, i, is measured as charge moved per unit time through an element. Unit is Ampere (A), is one Coulomb/second. 18

DC vs. AC A current that remains constant with time is called Direct Current (DC). Such current is represented by the capital I, time varying current uses the lowercase, i. A common source of DC is a battery. A current that varies sinusoidally with time is called Alternating Current (AC). Mains power is an example of AC. 19

Direction of current The sign of the current indicates the direction in which the charge is moving with reference to the direction of interest we define. We need not use the direction that the charge moves in as our reference, and often have no choice in the matter. 20

Direction of Current II A positive current through a component is the same as a negative current flowing in the opposite direction. 21

Classes of Materials In terms of the ease in which a charge can move through a material, we use three categories for matter. Conductors: Such as copper, silver, or gold easily allow electrons to pass through. Semiconductors: Such as silicon and germanium still allow electrons to pass, but not as readily. 22

Classes of Materials II You will be familiar with semiconductors such as silicon for their use in “chips.” Their operation is beyond the scope of this course. Insulators: Such as rubber, wood, or plastic do not allow electrons to pass through. They obviously are important for isolating charges. 23

Voltage Electrons move when there is a difference in charge between two locations. This difference is expressed at the potential difference, or voltage (V). It is always expressed with reference to two locations. 24

Voltage II It is equal to the energy, W, needed to move a unit charge between the locations. Positive charge moving from a higher potential to a lower yields energy. Moving from negative to positive requires energy. 25

Power and Energy Voltage alone does not equal power. It requires the movement of charge, i.e. a current. Power is the product of voltage and current It is equal to the rate of energy provided or consumed per unit time. It is measured in Watts (W). 26

Passive Sign Convention By convention, we say that an element being supplied power has positive power. A power source, such as a battery has negative power. Passive sign convention is satisfied if the direction of current is selected such that current enters through the terminal that is more positively biased. 27

Conservation of Energy In a circuit, energy cannot be created or destroyed. Thus power also must be conserved. The sum of all power supplied must be absorbed by the other elements. Energy can be described as watts x time. Power companies usually measure energy in watt-hours 28