1

ELEC130 Electrical Engineering 1

Week 2Module 1 Introductory Circuit Techniques

23-Feb-99 Lecture 2 2

Software

Electronic Workbench: Simulation Software Faculty PC’s Rm. ES210 - Go to Diomedes Login: cstudentnumber Password: access keys on students card + daymonth (ddmm)

of birth

TopClass: Class Discussion & Notices

http://www.newcastle.edu.au:86/topclass/ Username: first name.last name Password: date of birth ddmmyy

Email: first name.last name@studentmail

23-Feb-99 Lecture 2 3

Administration Items

Laboratory & Tutorials start THIS WEEK A couple of corrections have been given to the Tutors

and Laboratory demonstrators

Quiz 1 - Week 3 - Lecture NEXT MONDAY Will cover to the end of Module 1 which will be

completed next lecture before the quiz.

Survey

Subject Home Page: - through Dept. Pages http://www.ee.newcastle.edu.au/ http://www.ee.newcastle.edu.au/undergradcourse.html

23-Feb-99 Lecture 2 4

Last week

Charge Symbol: Q q(t) Units: Coulombs or C

Current Symbol: I i(t) Units: Amperes or A

Voltage Symbol: V v(t) Units: Volts or V

Power Symbol: P p(t) Units: Watts or W

Resistance Symbol: R Units: Ohms or

(I = Q / t Amps & V = P.t / Q volts)

P = V . I WattsV = R . I Ohms

23-Feb-99 Lecture 2 5

Conventions

Current - positive charge flow - through element

Voltage - measured across an element

Power

3 A - 3 A=

+

_

I

Circuit or element

+

-

+

v(t)_

I

Absorbing power

Delivering power

I

v(t)

23-Feb-99 Lecture 2 6

Resistance

Material - resistivity R = .l / A Poor conductor is large e.g. plastics, wood Good conductors is small e.g. copper, gold, aluminium

Resistance - the most common materials used are: carbon composition nickel chromium wire wound (for high power applications)

Can be physically small (10mm long) or large (>1m), can be fixed or variable

23-Feb-99 Lecture 2 7

Resistance

Common - are small fixed with colour coded values:

Black 0 Green 5 Brown 1%Brown 1 Blue 6 Red 2%Red 2 violet 7 Gold 5%Orange 3 Grey 8 Silver 10%Yellow 4 White 9 Nil 20%

23-Feb-99 Lecture 2 8

Resistance

Charge tends to flow from a higher voltage (potential) to a lower voltage

Determine direction of the current. If not labelled - GUESS the direction.

Potential of resistor where the current enters is positive and leaves is negative.

(If guess is wrong - just get negative voltage for an answer)

4 V 10

I

+

_

23-Feb-99 Lecture 2 9

Conductance

Sometimes easier to use inverse of resistance called conductance

Symbol: G Units: Siemens S (mhos)

G = R-1

e.g. 2 = 0.5 S

NB: Useful when resistors are connected in parallel

23-Feb-99 Lecture 2 10

Some Analogies

Charge Volume (of gas)

Voltage Pressure

Current Flow Rate

Resistance Constriction

23-Feb-99 Lecture 2 11

Series and Parallel Elements

Series elements have the same current

Share voltage

Parallel elements have the same voltage

Share current

ia(t)

ic(t)

ib(t)i(t)

+ v(t) -

i(t)

+ va(t) - + vb(t) - + vc(t) -

+ v(t) -

23-Feb-99 Lecture 2 12

Kirchoff’s Voltage Law

The sum of the voltages around a closed path is zero:

(closed path) V = 0

Convention is to move around a closed loop in a clockwise direction

Analogy - Walk around campus

How do you specify the polarity of voltages in the circuit?

23-Feb-99 Lecture 2 13

Kirchoffs Voltage Law - example

+

-

IR1

R2

V1

+

_

V2

+

_

Vs

021 sVVV

Example: If Vs = 12 V and R1= R2 , then V1 = V2

= 6 V

23-Feb-99 Lecture 2 14

Series Resistance

Vs = V1 + V2 + …….+ Vn where e.g. V1 = R1 I by

Ohm’s Law

Vs = R1 I + R2 I + …….+ Rn I

Vs = (R1 + R2 + …….+ Rn)I

Thus Req = R1 + R2 + …….+ Rn

I

+ -Vs

+ Vn -

Rn

+ V2 -

R2

+ V1 -

R1

23-Feb-99 Lecture 2 15

Lecture Exercise

I

VX

+

-

23-Feb-99 Lecture 2 16

Kirchoff’s Current Law

Total charge (current) accumulating at a node is zero:

(entering) I - (leaving) I = 0

Convention is current entering a node is positive and leaving a node is negative

Analogy - road intersection

How do you specify the direction of current if it is not given?

23-Feb-99 Lecture 2 17

Kirchoff’s Current Law - example

I1 + I3 - I2 = 0

nodeI1 I2

I3

23-Feb-99 Lecture 2 18

Parallel resistance

Is = I1 + I2 + …..+ In

[ I = V. 1/R = V G ]

Is = VG1 + VG2 +... + VGn

Is = V (G1 + G2 +... + Gn)

Is = V Geq

Geq = G1 + G2 +... + Gn

1/Req = 1/R1+ 1/R2+...+ 1/Rn

Is R2R1

+

V

_

Rn

I1 I2 In

23-Feb-99 Lecture 2 19

Two Parallel Resistors

1/Req = 1/R1 + 1/R2

= (R1 + R2)/ R1.R2

Req = R1.R2 / (R1 + R2)

Vs R2R1

I1 I2

+

-

23-Feb-99 Lecture 2 20

Current Division

NB: more current flows through path of lesser resistance

R2R1

I1 I2

+

-Vs

+

_

ss

ss

ss

IRR

RI

GG

GI

GGG

IGVI

GG

IV

21

2

21

11

121

11

21

23-Feb-99 Lecture 2 21

Voltage Division

Vs

+

-

IR1

R2

V1

+

_

V2

+

_

s

s

s

VRR

RV

VRR

RIRV

RR

VI

2!

22

2!

111

2!

23-Feb-99 Lecture 2 22

Series Sources

Ideal independent voltage sources in series add algebraically

NB cases of parallel voltage sources are not resolvable. WHY?

+ - + - + - + -I V1 V2 V3

Vn

- VR +

RI

23-Feb-99 Lecture 2 23

Parallel Sources

Ideal independent current sources in parallel add algebraically

NB cases of series current sources are not resolvable. WHY?

In

I3I2I1

R

+

V

_

IT

23-Feb-99 Lecture 2 24

Example

R2 and R3 are effectively open circuited and therefore can be omitted

R7 and R8 are short circuited, and can be omitted

23-Feb-99 Lecture 2 25

Example continues

23-Feb-99 Lecture 2 26

Wye Delta Transformations

Need to find equivalent resistance to determine current. HOW?(They are not in series, not in parallel)

Use Y to transformation

23-Feb-99 Lecture 2 27

Equating Resistance's

Resistance between X - Y

In Ra // (Rb + Rc)

In Y R1 + R3

RbRa

Rc

R1 R2

R3

XX

Y

Y

Z

Z

31)(

)(RR

RRR

RRRR

cba

cbaXY

23-Feb-99 Lecture 2 28

Solving simultaneously ….

To obtain R1, R2, R3 in terms of Ra, Rb, Rc

and vice versa

23-Feb-99 Lecture 2 29

Example cont.

X

Y Z

Y

X Z

23-Feb-99 Lecture 2 30

Linearity

A linear circuit is one that contains only linear elements.

Resistors, Voltage & Current sources, Inductors and Capacitors are linear elements.

An example of a nonlinear element is a lamp or a diode. A diode allows current to flow freely in one direction, but blocks the flow of current in the other.

Power is not linear due to V2 or I2 !

23-Feb-99 Lecture 2 31

Superposition

What to do when there is more than one source in a circuit?

SUPERPOSITION - If a linear circuit is excited by more than one independent source, then the total response is simply the sum of the responses of the individual sources.

How do you temporarily remove sources? Voltage source by a short circuit Current sources by an open circuit

23-Feb-99 Lecture 2 32

Superposition example

+

-Vs

R1

R2R3 Is

IR2