EENG 2610: Circuit Analysis Class 1: Basic Concepts, Ohm’s Law Oluwayomi Adamo Department of Electrical Engineering College of Engineering, University of North Texas

Electro-technology is driving force in all engineering discipline Circuit analysis is fundamental to electro-technology Power Grid This course is your first course in Electrical Engineering. It’s very important to master the materials that you will learn in this course to become a good Electrical Engineer. This course is the foundation to almost all other EE courses that you will take in the future. Even though you may not have noticed, electrical technology is one of the most fundamentally important technologies in this world and we have been relying on electrical technology for our daily life. Motherboard of Computer Integrated Circuits (IC chips)

Basic Strategy in Circuit Analysis Typical Electric Circuit

The concept of node is extremely important. ELECTRIC CIRCUIT IS AN INTERCONNECTION OF ELECTRICAL COMPONENTS The concept of node is extremely important. We must learn to identify a node in any shape or form

BASIC CONCEPTS LEARNING GOALS System of Units: The SI standard system; prefixes Basic Quantities: Charge, current, voltage, power and energy Circuit Elements: Active and Passive

International System of Units – SI Standard System

Standard SI Prefixes Give some example: For example 2x10^3 m = 2 km, 2x10^9 m = 2 Gm, …… SI prefixes used to form decimal multiples and submultiples of SI units. These standard prefixes are employed throughout our study of electric circuits.

Basic Quantities Electric Charge (unit: coulomb) Q, q, q(t) The most elementary quantity in electric circuit analysis Charged particle in matter: electron (-), proton (+), neutron (no charge) Electric Circuit A pipeline where electric charge can be transferred from one point to another An interconnection of electrical components, each of which we will describe with a mathematical model Electric Current (unit: ampere) i, i(t) The time rate of change of charge: 1 A = 1 C/s (A: ampere, C: coulomb, s: second) Conventional current flow represents the movement of positive charges, even though in metallic conductors current flow is resulted from the motion of electrons, negative charge. I = 2 A means 2 C of charge pass from left to right each second Must specify both magnitude and direction: Show on white board: equivalent circuit for negative current.

Basic Quantities Two types of current we will study in this course DC AC Two types of current we will study in this course Alternating current (AC) Direct Current (DC) Voltage (or potential) between two points in a circuit (unit: volt) Defined as the difference in energy level of a unit charge located at each of the two points: The energy required to move a unit positive charge is the defined voltage 1 V = 1 J/C = 1 N·m/C (V: volt, J: joule, C: coulomb, N: newton, m: meter) The + and – signs define a reference direction for V A unit charge moved between A and B will have energy change Must specify both magnitude and direction

Basic Quantities Energy and Energy Transfer W, w(t) When the element is absorbing energy, a positive current enters the positive terminal and leaves via the negative terminal. When the element is supplying energy, a positive current enters the negative terminal and leaves via the positive terminal. A negative current in one direction is equivalent to a positive current in the opposite direction, and vice versa. The same is the voltage. Charges gain energy as passing Charges spend Energy as passing Vbulb Vbattery

Basic Quantities Power (unit: watt) P, p(t) Defined as the time rate of change of energy: The change in energy in a period of time: 1 W = 1J/s = 1 V·A (W: watt, J: joules, V: volt, A: ampere) Passive Sign Convention – Sign Convention for Power Variables for the current and voltage should be arranged as shown in the figure: Current enters an element via positive voltage reference point If the sign of power is positive, power is being absorbed by the element; if the sign is negative, power is being supplied by the element. + - Circuit Element Power:

Example 1.2: Determine whether the elements are supplying or receiving power and how much

Circuit Elements In general, all elements will be terminal devices that are completely characterized by the current through the element and the voltage across it. Active or passive elements Active element is capable of generating energy. Passive element cannot generate energy. Passive Elements Resistor, Capacitor, Inductor We will define these in coming classes Independent Voltage Source Maintain a specified voltage between its terminals regardless of the current through it. Independent Current Source Maintain a specified current between its terminals regardless of the voltage across its terminals. Independent sources normally supply energy, but they can also absorb energy

Circuit Elements Dependent (or Controlled) Sources Unlike independent sources, dependent (or controlled) sources generate a voltage or current that is determined by a voltage or current at a specified location in the circuit. Four different types of dependent sources: Voltage Controlled Sources Current controlled Sources

The Principle of Conservation of Energy Power supplied in a circuit network is exactly equal to the power absorbed. Electrical circuits satisfy this principle Example 1.7: Use power balance to compute I0

Ohm’s Law Ohm’s Law Defines a passive element Resistor R (unit: ohm) It only absorbs power; converts electrical energy to thermal energy Ohm’s Law: The voltage across a resistor is directly proportional to the current flowing through it: 1 Ω = 1 V/A (Ω: ohm, V: volt, A: ampere) Linear approximation Linear range Actual v-I relationship

Ohm’s Law Two specific values of resistance Power absorbed by a resistor Conductance G (unit: siemens S) 1 S = 1 A / V Two specific values of resistance - = + v = i Short Circuit Open Circuit

Example 2.1: Determine voltage, current, and power absorbed by resistor