chap1 electrical technology

8/13/2019 chap1 Electrical technology

1/34

Chapter 1: Basic Concepts

Basic Circuit Elements and Laws

ELE1110B Basic Circuit Theory


2/34

ELE 1110B Lecture 01 - 2

Topics To Cover

Concepts

Charge, Current, Voltage, Power, Energy

Basic circuit elements and device laws

Resistor, Capacitor, Inductor

Circuit concepts and definitions

Nodes, branches, and loops Basic circuit laws

Kirchhoffs laws

Basic circuit analysis Reference

Alexander and Sadiku, Chapters 1, 2 and 6.


3/34


Introduction an electric circuit

A circuit = the path of flow for charge carriers

To communicate from one point to another

To transfer energy from one point to another

Charge carriers are

electrons in a conductor

ions in an battery

Battery

(source)

Light bulb(device)

Switch


4/34


An electric circuit

A circuit consists of source (energy) and/or drain

(device) elements

A circuit has constant flow of charges when it isclosed

The polarity of an electric circuit segment defines the

flow direction

Battery

(source)

Light bulb

(device)

Switch


5/34


Charge and Current

Charge: coulombs (C)

1 C = 6.24 x 1018 electrons

Single electron has 1.6 x 10-19 C Conservation of Charges:

charges can neither be created nor destroyed, onlytransferred

The algebraic sum of the electric charges in a closed systemdoes not change with time

Electric current

dc: direct current, remains constant with time

ac: alternating current, varies (sinusoidally) with time

dt

dqi= =

t

todiq )(


6/34


Voltage / potential difference It is the energy required to move one unit charge through an element

Polarity of a circuit segment indicates the flow direction of charges

a

b

+

-

Vab (= -Vba)

+ve charges(e.g. ions in

battery)

-vecharges

(electrons)

+I

-I

Passive sign convention

Powerp = vi

+ve: consumption

-ve: generation

dq

dEVab =


7/34


Power supply and absorption

v

i i

i

+

-v+

-v+

-

v

i

+

- v

+

-

i

Independent voltage source

(const. or time-varying voltage)

Independent voltage source

(constant voltage)

Independent current source

Dependent voltage source Dependent current source


8/34


Ideal Sources Ideal Independent Sources

Voltage source

An active element (which provides energy) provides a specific voltage

with its zero internal resistance. It is completely independent of other circuit variables, e.g. current through

it.

Current source

An active element provides a specific current with its infinite resistance.

It is completely independent of other circuit variables, e.g.voltage acrossthe source.

Ideal Dependent (Controlled) Sources An active element in which the source quantity is controlled by another

voltage or current. Voltage-controlled voltage source (VCVS), Current-controlled voltage

source (CCVS), Voltage-controlled current source (VCCS), Current-controlled current source (CCCS)


9/34


Energy and Power

Energy

Average power

More convenient to measure than instantaneous power, e.g. bywattmeter

)()()( titvdt

dq

dq

dE

dt

dEtp ===

== t

t

t

tdivdptE

00

)()()()(

+

=

Tt

taverage

o

o dttpTp )(

1

time-varying, so called instantaneous power

instantaneous

voltage

instantaneous

current

v(t)

i(t)

p(t)


10/34


Example 1.1 Example: Calculate the power supplied or absorbed by each element:

By passive sign convention,

p1 = 20(-5) = -100W (supplied power)

p2 = 12(5) = 60W (absorbed power)

p3 = 8(6) = 48W (absorbed power)

p4 = 8(-0.2I) = 8(-0.2 x 5) = -8W (supplied power)

p1 + p2 + p3 + p4 = 0 (Energy Conservation Law: p = 0)

20 V p1

p2

8 Vp3 p4

I = 5A

6A

0.2I+

-

12 V+ -


11/34


Ohms Law

Short circuit: R=0

Open circuit: R=

Circuit Element resistor

+

-

v

i

R

vRivip

22 ===

GiGvvip

2

2===

resistance

conductance

GR

1=

iRv=


12/34


Resistors in series

=

=++=N

n

nNeq RRRRR1

21 ...

=

=

=

=

=

=

N

nn

N

n

n

N

n

n

Ri

iR

vv

1

1

1

vRR

Rv

21

11

+= v

RR

Rv

21

22

+=Note:

Known as

voltage divider


13/34


Resistors in parallel

Neq RRRR1...111

21

+++=

=

=

=

=

=

=

N

n n

N

n n

N

n

n

Rv

R

v

ii

1

1

1

1

i

RR

Ri

21

21

+

=

iRR

Ri

21

12

+= Known as

current divider

Note:


14/34


Example 1.2

Calculate the equivalent resistance Rab in the circuit

a

b

Rab

10 1

632

c d

b b

a

b

Rab 32

c d

b b

10a

b

11.2


15/34


Example 1.3 Calculate the equivalent resistance Rab in the circuit

a

b

Rab

10 1 1

54

6

3

12

c d

b b

a

b

Rab

10 1

632

c d

b b


16/34


-to-Y transformationa

b c

a

b c

Rc Rb

Ra

R1

R2 R3

cba

ba

cba

ac

cba

cb

RRR

RRR

RRR

RRR

RRR

RRR

++=

++=

++=

3

2

1

3

133221

2

133221

1

133221

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

c

b

a

++=

++=

++=


17/34


Circuit Element capacitor

Open circuit to dc signal

An ideal capacitor can store (in its electric field) and deliver energy without

dissipation, but real capacitor has a leakage resistance in parallel combined with theideal capacitive part.

When a voltage source v is applied to a capacitor, the amount of charge stored

q = Cv

For parallel-plate capacitor,

For electrolyte capacitors, High capacitance

Can endure high voltage

Polarity is prearranged and not allowed to be interchanged

d

AC

=


18/34


Capacitor device laws

i C

v+ -

dt

dvvCivp ==

dtdvC

dtdqi ==

1. v const. i = 0 open circuit

2. v cannot change instantaneously because i = is needed

C

QvCtE

tEdiv

tEdptE

o

t

t

o

t

t

o

o

22

1)(

)()()(

)()()(

22 ==

+=

+=

)(1

)( ot

ttvid

Ctv

o +=

if E(to) = 0


19/34


Capacitors in series

Neq CCCC

1...

111

21

+++=

)(1

)(1

)(1

)()(

11

1

1

oeq

t

teq

N

n on

t

t

N

n n

N

n

t

t on

n

N

n

n

tvidC

tvidC

tvidC

tvtv

o

o

o

+=

+

=

+=

=

==

=

=


20/34


Capacitors in parallel

=

=++=N

n

nNeq CCCCC1

21 ...

dt

dvC

dt

dvC

dtdvC

tii

eq

N

n

n

N

n

n

N

n

n

=

=

=

=

=

=

=

1

1

1

)(


21/34


Circuit Element inductor

Short circuit to dc signal If current is allowed to pass through an inductor, it is found that

The proportional constantL is called inductance and

An ideal inductor can store (in its magnetic field) and deliver energywithout dissipation, but a real inductor has a winding resistance in seriescombined with the ideal inductive part.

air-core iron-core

l

ANL

2

=

dtdiLv=


22/34


Inductor device laws

i

dt

diLivp

==

dt

di

Lv=

1. i const.(dc current) v = 0 short circuit

2. i cannot change by a finite amount in zero time because v = is needed

)()(

1

)( o

t

t tidvLti o +=

If i(-) = 0

2

21)(

)()(

)()(

iLtE

Lidi

div

dptE

t

t

t

=

=

=

=


23/34


Inductors in series

=

=++=N

n

nNeq LLLLL1

21 ...


24/34


Inductors in parallel

Neq LLLL1...111

21

+++=


25/34


Example 1.4

i(t)

vR(t)

vC(t)

vL(t)

i(t)

i(t)

i(t)

+

-

+

-

+

-

RtitvR = )()(

)()(

1

)( ot

tC tvdiCtv o +=

dt

tdiLtvL

)()( =


26/34


Example 1.5

i(t)

vR(t)

vC(t)

vL(t)

i(t)

i(t)

i(t)

+

-

+

-

+

-

RtitvR = )()(

)()(

1

)( o

t

tC tvdiCtv o +=

dt

tdiLtvL

)()( =

impulse


27/34


Symbol and units

joule (J)EEnergy

watt (W)pPower

volt (V)V, vVoltage

ampere (A)I, iCurrent

coulomb (C)QCharge

henry (H)LInductance

farad (F)CCapacitance

siemens (S)

or mho ( )

GConductance

ohm ()RResistance

UnitSymbol

prefixes:

1012 tera (T)109 giga (G)

106 mega (M)

103 kilo (k)

10-2

centi (c)10-3 milli (m)

10-6 micro ()

10-9 nano (n)

10

-12

pico (p)10-15 femto (f)


28/34


Circuit concept and definition

Node a point where two or more circuit elements join (e.g a, b, c, d, e, f, g)

Essential node a node where three or more circuit elements join (e.g. b, c, e, g)

Branch connects between two nodes (i.e. consists of one circuit element)

Essential Branch connects between two essential nodes

v1

v2

R1

R2 R3

R4

R5

R6

R7 I

a

c

f

d

b

e

g


29/34


Circuit concept and definition - Loop

Path

a trace of adjoining elements withno element included more than once

Loop

a closed path with no node passed

more than once(there are 8+ loops) Mesh

a loop that does not enclose any other loop

4 meshes

v1

v2

R1

R2 R3

R4

R5

R6

R7 I

a

c

f

d

b

e

g

V1 - R1 - R5 - R6 - R4 - V2V1 - R1 - I - R 4 - V2V1 - R1 - R7 - R4 - V2I - R5 - R6V1 - R1 - R5 - R3 - R2

V2 - R2 - R3 - R6 - R4R5 - R7 - R6R7 - I


30/34


Kirchhoffs Current Law (KCL)

i1i2

i3

i4

iN

0=N

ni

Note: Assume one direction to be +ve, and in theabove case the direction of entering the node


31/34


Kirchhoffs Voltage Law (KVL)

0=N

nv

Note: Assume one direction in the loop to be +ve, and

in the above case the anti-clockwise direction

vn

+

-

v1+

-

v2 +-v3 +-

v4+

-

v5+

-


32/34


Example 1.6

500V

+ V-5i

io

+

Vo

-

205i

ab

c

Loop A

By KVL around loop A,

By KCL at node b,

Put (2) into (1):

)1...(1004

0)20()5(500

=+

=++

o

o

ii

ii

)2...(6

05

=

=+

ii

iii

o

o

VV

VV

Ai

Ai

ii

o

o

480)20(24

20)5(4

24

4

100)6(4

==

==

=

=

=+

Total power generated

Total power dissipated

W

PP iV

11600

)4)(5(480)4(500

5500

=

+=

+=

W

PP

11600

)24(480)4(20

205

=

+=+=


33/34


50

Example 1.7(a)

500V

2.2

20 30

46 9

io

a

b c

d 500V

2.2

46 9

a

b c

d

R2 R3

R1

=++

=

=++=

=++

=

15503020

)50(30

10503020

)50(20

6503020

)30(20

3

2

1

R

R

R

Find io


34/34


Example 1.7(b)

500V

2.2

46 9

a

b c

d

A

VV

i

VR

V

V

R

V

VV

o 350

126)336(9

9

276)336(

46

46

336)500(24//562.8

24//56

32

3

3

2

2

1

=

=

=+

=

=

+

=

=+

=

6

10 15

500V

2.2 + 6 = 8.2

10 + 46

= 5615 + 9

= 24

+

-V2 V3

+

-

V1

+

-

chap1 electrical technology

Documents