Chapter1 DC Circuit

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1

Dr Taj Mohammad BalochDr Taj Mohammad Baloch

Senior Lecturer

EE Department

Office: 22-03-29

Ph: 05-368-7828

Email: [email protected]

EAB1024 Network Analysis



C hapter 1



Students need to know :

basic elements in electric circuits,

relation between current and voltage in each element,

physical laws regulate the relation between currents

and the relation between voltages in a complicated circuit,

how to write the equation system of a circuit,

properties of linear circuits.



V oltage sourceV oltage source ee

g!S

R

-- generates current i = j generates current i = j

-- internal resistanceinternal resistance

0!S

R

C urrent sourceC urrent source J J

Independent

sources

Controlled

sources

-- generates voltage v = egenerates voltage v = e

-- internal resistanceinternal resistance10sint

12 V

3V 52 I 6

C ircuit Elements



R esistor R esistor R R d issipates energy d issipates energy

P > 0 P > 0

Ind uctor Ind uctor LLstores energy stores energy

P = 0 P = 0

C apacitor C apacitor C C stores energy stores energy

P = 0 P = 0

Riv !

dt di Lv !

´! dt iC v

1



M utual ind uctance M

dt

id M v

M

1

2!

All the elements e, j, R , L, C , M are i d eal. Practical d evices

will be presented by these i d eal elements, e.g. a coil may be presented by a L in series with a R .



.,777999 i Rvi Rv

.8.4

4.2

,10

922

11

V

I ev

V ev

.dt

diM

dt

diLv 85

55!

E.g.Write the voltage across elements in the following circuit.



idt cdt

d L Rv

idt cdt

di L Riv

vvvvC L R

¹ º

¸©ª

¨

´

´1

1

Z dt cdt

d L R Let !¹

º ¸©

ª¨ ´1

iv >

: impedance operator

: general Ohm¶s law

G eneral Ohm¶s law Physical Laws in Electric C

ircuits



K irchhoff¶s

C urrent law (

K C L)

1.

0

§§

§

nodenode

node

jior

i

.

,0

2

2

jiior

jii

!

!

E.g.

Sum of incoming

currents at a junction

(node) is equ

al to sum

of outgoing currents



K irchhoff¶s V oltage law ( K V L)

.

2,

.0

§

§§

§

!

!>

!

abline

ab

meshmesh

mesh

vvor

eior

v

43521 E E vvv !

E.g.

The algebraic

sum of all

volatges arou

nda closed loop is

zero



; n-1 K 1 equations

; m K 2 equations)3(±°

±

¯

®

!>

!

§§

§§

meshmesh

nodenode

ei

ji

G enerally, it can be d emonstrated that in a circuit includ ing b

branches, n nod es, m meshes there are

n -1 ind epend ent K 1 equations written for n -1 nod esand

m = b-(n -1) ind epend ent K 2 equations written for m meshes.

In total, we have b equations written for b branch currents i1 ,i2

,..ib .

C ombine equations (1) and (2) we have the following equation syste

C ircuit Equation System



T he system (3) is calle

d the general mathematical mo

d el of electric circuits. It is used for calculating all sort of electrical

electronic circuits (linear or non-linear circuit),all kind of states

(stead y or transient state).

So the system (3) of b equations is written for b unknown

branch currents i. It can be solved to find b branch currents i,

then from i find b branch voltages v = Z i, at last find the power in

branches p = vi. T hat means that the whole state of the circuit

can be calculated .

)3(±°

±̄

®

!>

!

§§

§§

meshmesh

nodenode

ei

ji



0)(:

)4(:

0:

223332

22111

321

!

!

!

i Ridt

d L Rm Mesh

E i Ri Rm Mesh

iiia Node

T he electric d evice system (Fig.1) can be replaced by the circuit d iagram

(Fig.2).

In Fig.2 we can write the following equations for i1 , i2 , i3 :

From(4) the currents i1 , i2 , i3 and the whole state of the circuit can be

calculated .

E.g.



T he state of a circuit is measured by i, v, p.T here are two main states :

States of electric circuits



T ransient stateis a state that approaches the stead y state and begins at the moment when in the circuit there is a switchingaction or a change of parameter .

Stead y stateis a state, where responses take d etermined values withunchanged parameters.



V 3= 10 sin2t

I 7 = 0.6 sin2t A

V 3= 20 sin2t V

I 7 = 1.2 sin2t A

E.g.

Linearity : In a linear circuit, the response y always

varies

proportionally with the excitation x. y = k x, k = const.

Properties of linear circuits



E.g.

Superposition :A

response caused

by several excitationsacting at the same time equals the sum of responses

caused

by each excitation acting separately.

62616iii !



C ircuit synthesis :- G iven excitation and response.

- R equired to find the circuit ( elements and / or

configuration ).

;!p

!

!

3010

1041

2

2

21

1

2

R R

R R

R J I

E.g.

C alculate R2 ?



V oltage source

C urrent source

R esistor

Ind uctor

C apacitor

M ut. ind uctor

G en.Ohm¶s law

C ircuit equations

dt d M v

M

1

2 !

idt cdt

d L Rv ¹

º

¸©ª

¨ ´1

±°

±¯®

!>

!

§§§§

meshmesh

nod enod e

meshesm for ei

nod esn for ji 1

J i !

ev !

Riv R .!

d t

d i Lv L !

d t iC

vc .1

´!

Chapter1 DC Circuit

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