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Unit 5: Electrical network analysis.

Introduction: junction, branch, loop, network(multi-loop circuit).

Kirchhoffs Rules: junction and loop rules.

Superposition principle.

Equivalent resistor of a passive network.

Thvenins theorem.

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Introduction: definitions

Electrical network: Set of dipoles (active andpassive elements) interconnected between them.

If all the dipoles show linear rates between V and I,the circuit is a linear network.

R

C R

R

L

L

C

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Junction:point of the net where arejoined threeor more wires being different the electric potential.

Network with three junctions:

R

C R

R

L

L

C

There are the same junction

Introduction: definitions

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Branch: is the path joining two junctions. Electricalnetwork with five branchs:

This is not a branch

R

C R

R

L

L

C

Introduction: definitions

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Loop: closed circuit made with branchs, withoutanyone inside. Electrical network with three loops:

R

C R

R

L

L

C

Introduction: definitions

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Junction Rule: The sum of the currents into thejunction must be equal to the sum of the currents

out of the junction. Algebraic addition = 0. Its an expression of the charge conservation principle.

1I

2I

3I kI

nI

0= kI

Tipler, chapter 25, section 25.5

Kirchhoffs Rules: Junction rule

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Loop rule: Algebraic sum of the changes inpotential around a loop must be equal zero.

Its an expression of energy preservation principle. A point can not havetwo different potentials at the same time.

1 2

kn

V1

V2

Vk

Vn 0= kV

Kirchhoffs Rules: loop rule

Tipler, chapter 25, section 25.5

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To solve a circuit, must be writen:

(Junctions -1) equations of junction rule

Loops equations of loop rule

RC R

R

L

L

C

Kirchoffs rule application

Example: 2 equations of junction rule + 3 equations of loop rule = 5 equations

5 unknown (intensity of currents)

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On a circuit with several generators, the solution ofthe circuit (calculus of currents and potentials) is

the algebraic sum corresponding to each generator(ideal) acting alone.

Superposition principle.

a BR

CR DR

A B

1I

2I

AR b

c

a BR

CR

DR

A

AI1 A

I2

AR b

c

= +

a BR

CR

R

B

BI1

I2

AR

b

c

BABA IIIIII

222111 +=+=

This calculus can be made not only for currents, but for potentials too.

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Is a resistor ( ) such that when applying the samed.d.p., current flowing is the same:

eqR

Passive

network

1I1

2 3

4 ...

... n

A

B

1I

eqR

A

B

Equivalent resistor of a passive network.

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A linear active circuit with output terminals A and B isequivalent to a generator of e.m.f. equal to thedifference of potential between A and B, and an

internal resistance equal to the equivalent resistanceof the passive network between A and B (withoutideal generators).

Linear

Active

circuit

A

B

A

B

eqT RR =

ABT V=

Thevenins theorem

Its useful to analyze circuits by splitting it in little pieces.