Principles & Applications of Electrical Engineeringhome.konkuk.ac.kr/~parkjk/courses/2018spring/electrical...Ammeter –series connection, zero resistance Voltmeter –parallel connection,

Dept. of Aerospace Information Engineering

Konkuk University

Principles & Applications of

Electrical Engineering

Ch. 2 Fundamentals of Electric Circuits

Spring, 2018

Rizzoni, 6th Ed.

http://www.konkuk.ac.kr/

Dept. of Aerospace Information Engineering2

Contents Learning objectives

Understand principal elements of electric circuits

voltage and current source• Ideal vs dependent

nodes, loops, meshes, and branches

Apply Kirchhoff’s law to the basic circuit networks

KCL, KVL

Derive basic circuit equations and compute power dissipation

Apply voltage and current divider laws

to calculate unknown variables in simple series/parallel circuits


Ideal voltage source

Electric device generating a prescribed voltage at its

terminals, irrespective of the magnitude of the current

flowing through it

Source can be either AC or DC


By convention, the direction of current flow is out

of the positive sign of voltage source

In the analysis, symbolic representation will be used


Ideal current source

Device that can generate a prescribed current

independent of the circuit to which it is connected

Generates an arbitrary voltage across its terminal loads


Dependent sources (diamond-shaped) 2 types

Voltage controlled

Current controlled


Definitions of electric circuit elements

Branch

Any portion of a circuit with two terminals containing one or

more circuit elements

Node

Junction of two or more branches

‘Supernode’ is defined as a region that encloses more than one

node


Definitions of electric circuit elements

Loop

Any closed connection of branches

Mesh

Loop that doesn’t contain any other loop

1-4

2-6

3-4

4-1


Network analysis

Electrical network – collection of elements through

which current flows

Determine each of the unknown

branch currents and node voltages

Construct a set of equations

relating these variables

Solve the equations

by means of suitable techniques


Charge, current and Kirchhoff current law

Charge: fundamental electric quantity

The smallest amount of charge is carried by one

electron

Unit of charge: C (coloumb)

(electric) current: the time rate of the change of charge

Denoted by i

Unit of current: A (amperes)

][10602.1 19 Cqe

[ / ]dq

i C sdt


Kirchhoff Law

Kirchhoff’s current law

Concept: charge cannot be created but must be

conserved at one node

Total amount of incoming current is equivalent with total

amount of outgoing current, at one node

At one node,

01

N

i

ni


Kirchhoff Law

Voltage and Kirchhoff’s voltage law

Volt or potential difference

Energy required to move unit charge from one point

to the other point

Kirchhoff’s voltage law: KVL

Concept: No energy is lost or created in an electric

circuit

Net voltage around a closed circuit becomes zero

Around a mesh or loop,

][

][1][1

Ccoulomb

JjouleVvolt

1

0N

n

i

v


Electric power and sign convention

power is defined as the work done per unit time

In electric circuit, product of voltage across the element

and current flowing through it

Simple passive sign convention,

Power dissipated by a load is

denoted by positive value

ivtime

charge

charge

work

time

workPower


Focus on methodology: how to compute power

dissipated by loads?

Choose an arbitrary direction of current flow

Label polarities of all active elements

Assign polarities to all passive elements

for passive elements current always flows into the

positive terminals

Compute power dissipated by each elements

If positive current flows into the positive terminal,

power dissipation is positive and if negative terminal,

then power dissipation is negative


Sign convention

If you use a consistent sign convention, the result is

always the same!!


Circuit elements and their i-v characteristics

Relationship or the ratio between current and voltage

decides the ‘electric resistance’ of the circuit wire/cable

This derives the Ohm’s law

Nonlinear i-v characteristics of tungsten bulb

)(vfi


Ohm’s law

The voltage across the resistor is directly proportional to

the current flow through it

Unit of resistance:

The resistance is computed by resistivity (rho) or

conductivity (sigma) determined by the material

characteristics

Conductance: inverse of resistance

RIV

[ ]ohm

A

lR )( 1

1 [ ]G R siemens S

I G V


i-v characteristics and derivation of R

Linear or nonlinear


Open Circuit

Circuit element with resistance approaching infinity

Short Circuit

Circuit element with resistance approaching zero


Series resistors

Two or more circuit elements are said to be in series if

the current from one element exclusively flows into the

next element

From KCL, all series elements have the same circuit

current

Equivalent series resistance denoted by

1

Nseries

EQ n

n

R R


Parallel resisters

Two or more circuit elements are said to be in parallel if

the element share the same terminals (i.e., node)

From KVL, all parallel elements have the same

voltage

Equivalent series resistance denoted by

||||||][][ 321

1

1

111

3

1

2

1

1 RRRRRRRRN

n

n

parallel

EQ


Voltage divider

Voltage across each resistor in a series circuit is directly

proportional to the ratio of its resistance to the total

resistance

Current divider

Current in a parallel circuit divides in inverse

proportional to the resistances of the individual parallel

resistance

S

Nn

nn v

RRRR

Rv

21

S

Nn

nn i

RRRR

Ri

/1/1/1/1

/1

21


Example 2.13

321 || RRR

vi s

2 3

1 2 3

||

||s

R Rv v

R R R


Example 2.14

Wheatstone bridge,

Vab=?


Practical voltage and current source

Physical limitation in providing current or voltage across

objective loads

Assumes inherent internal resistor

Practical model


Measuring device

Ohmmeter

Ammeter – series connection, zero resistance

Voltmeter – parallel connection, infinite resistance


Ammeter (analog)

Multimeter (digital)

Multimeter (analog)


Summary

Summary

Identify the principal elements of electric circuits

Nodes, loops, meshes, branches

Voltage and current source

Apply Ohm’s law and Kirchhoff’s law to simple circuits

and derive basic circuits equations

Apply passive sign convention and compute power

dissipated by elements

Solve voltage and current in the series, parallel, and

series-parallel circuits

Understand rules for connecting measuring instruments

to electric circuits for the measurement of voltage,

current, and etc…

Dept. of Aerospace Information Engineering

Konkuk University

Example illustration

http://www.konkuk.ac.kr/


Prob. 2.25

Power dissipation?

Power generation?


Prob. 2.37

Find currents

Find power dissipated and generated


Prob. 2.60

Equivalent resistance

Current i?

Principles & Applications of Electrical Engineeringhome.konkuk.ac.kr/~parkjk/courses/2018spring/electrical...Ammeter –series connection, zero resistance Voltmeter –parallel connection,

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