Theme 2

DC Network Analysis and Network Theorems

Independent Sources

• Ideal Voltage Source- Voltage at Terminals independent of Load

+-

+-

Ideal Voltage Source

• Non-Ideal Voltage Source – – An Ideal voltage source is only theoretical and

does not exist in reality – A practical voltage source can be modelled with a

small resistance in series with an Ideal voltage source

+-

Rs

RL

+

-

VoE

Equation)Divider (Voltage

)( sL

Lo RR

REV

o

Ls

VEThen

,RRWhen

• Ideal Current Source – Current supplied is independent of Load

Ideal Current Source

• Non-Ideal Current Source- Can be modeled with a large resistor in Parallel

Rs RL

IL

I

Equation)Divider (Current

)( Ls

sL RR

RII

L

Ls

IIThen

,RRWhen

Network Theorems

• Kirchoff’s Current Law- The algebraic sum of currents leaving a NODE is zero, at any given instant

i1

i3

i2

i4

04321 iiii

• Convention Used: Currents Entering a Node are POSITIVE, and Currents Leaving a Node are NEGATIVE.

• Kirchoff’s Voltage Law- The algebraic sum of voltage drops around a closed path is zero.

+-

R1 R2

R3

R4

+ - + -

+ -+ -

V1 V2

V3

V4

E

04321 VVVVE

I• Convention

Used: Voltage drop Given a NEGATIVE Sign

• Class Example:– Find Value of I1, I2, I3 , I4 and Direction of I2, and value of R2

R1=5Ω

V3=18V

I3

R2=?

R3=3Ω

R4=4Ω

+ -

V2=24V

+ - V4=20V+ - V1=15V

I1=?

2I4I2=?

• Class Example: Find the Voltage drops across each Resistor.

+-

R

+ -V1

E+ -V2

+ -V

32R

3R

I

• LOOP CURRENT NETWORK ANALYSIS– Formulate circuit equations using a set of current

variables.– The Variables(Unknown Currents) Satisfy KCL.– Thus circuit can be described using independent

KVL equations.• METHOD• Take the shortest KVL loop (Current loops in

Clockwise direction) and write KVL equation.• Where more than one loop Flows in an Element,

the algebraic sum of the currents is used-thus voltage across that element can be found.

+-

R1

R3

R2

EA

I1

+-

+-

EC

EBI2

• Class Example: Write down the KVL Equations using unknown Variables I1 and I2.

0)(

0)(

31222

32111

CB

CA

ERIIRIE

ERIIRIE

23213

23131

21

)(

)(

:I andIfor Solve and Rearrange

IRRIREE

IRIRREE

BC

CA

• Class Example: Find I1 and I2

+-

R1=15Ω

R3=

12Ω

R2=20Ω

EA

=12V

I1

+-

+-

EC=

10V

I2EB=16V

• NODAL VOLTAGE NETWORK ANALYSIS– Formulation of circuit equations where the

variables (Unknown Voltage Nodes) satisfy KVL.– KCL Equations are used to find selected voltage

node values, thus currents through a given element can be found.

• METHOD– Identify independent Nodes, and select one node

as the reference. – Write the KCL Equations and solve

+-

R1

R3

R2

EA

+-

I1

I3

I2

EB

Node M with a Voltage VM

Node O

33

22

11

321

;;

(1) 0

R

VI

R

VEI

R

VEI

III

MMBMA

Solve andSubject theV Make

(1);in Substitute

M

321 R

V

R

VE

R

VE MMBMA

• Class Example: Find I1, I2, I3 and VM

+-

10Ω=R1

6Ω=R3

5Ω=R2

12V EA

+-

I1

I3

I2

8VEB

O

M

VM