EENG 2610: Circuit AnalysisClass 1: Basic Concepts, Ohm’s Law

Oluwayomi AdamoDepartment of Electrical EngineeringCollege of Engineering, University of North Texas

Electro-technology is driving force in all engineering disciplineCircuit analysis is fundamental to electro-technology

Power Grid

Motherboard of Computer

Integrated Circuits (IC chips)

Basic Strategy in Circuit Analysis

Typical Electric Circuit

a b2 TERM INALS C O M PO NENT

characterized by thecurrent through it andthe vo ltage diff erencebetween term inals

NO DE

NO DE

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

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:

Basic Quantities 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

dq

dwv

tt

)(ti)(tiAC DC

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 gainenergy 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.

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Circuit Element

)()( titvp 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 regardlessof the current through it.

Independent Current Source Maintain a specified current

between its terminals regardlessof 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 ControlledSources

CurrentcontrolledSources

Example 1.7: Use power balance to compute I0

The Principle of Conservation of Energy Power supplied in a circuit network is exactly equal to the power

absorbed. Electrical circuits satisfy this principle

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)

0 ),()( RtiRtv

Linear approximation

Actual v-I relationship

)(tv

)(tiLinear range

Ohm’s Law Power absorbed by a resistor

Conductance G (unit: siemens S) 1 S = 1 A / V

Two specific values of resistance

R

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Short Circuit Open Circuit

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