Unit 5: Electrical network analysis. Introduction: junction, branch, - - PowerPoint PPT Presentation

Unit 5: Electrical network analysis.

• Introduction: junction, branch, loop, network

(multi-loop circuit).

• Kirchhoff’s Rules: junction and loop rules.
• Thèvenin’s theorem.

Introduction: definitions

• Electrical network: Set of interconnected dipoles

(active and passive elements).

• If all the dipoles show linear ratios between V and

I, the circuit is a linear network.

R C R R L L C

V

V

• Junction: point in the net where three or more

wires are joined. Two junctions with the same potential are taken as the same junction. Network with three junctions:

R C R R L L C

V

V

These are the same junction

Introduction: definitions

• Branch: is the path having some device between

two junctions. Electrical network with five branches:

This is not a branch

R C R R L L C

V

V

Introduction: definitions

• Loop: closed circuit with branches and no other

loops inside. Electrical network with three loops:

R C R R L L C

V

V

Introduction: definitions

• Junction Rule: The sum of the currents into the

junction must be equal to the sum of the currents

• ut of the junction. Algebraic addition = 0.
• This an expression of the charge conservation principle.

1

I

2

I

3

I

k

I

n

I

=



k

I

Tipler, chapter 25, section 25.5

Kirchhoff’s Rules: Junction rule

• Loop

rule: Algebraic sum

• f

the changes in potential around a loop must be equal to zero.

• This an expression of the energy conservation principle. A point can not

have two different potentials at once.

1 2 k n V1 V2 Vk Vn

=



k

V

Kirchhoff’s Rules: Loop rule

Tipler, chapter 25, section 25.5

• To solve a circuit, we must write:
• (Junctions -1) equations of junction rule
• (Number of loops) equations of loop rule

R C R R L L C

V

V Application of Kirchoff’s rule

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

5 unknown (intensities of current)

• To solve a circuit, we must write:
• (Junctions -1) equations of junction rule
• (Number of loops) equations of loop rule

Application of Kirchoff’s rule

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

5 unknown (intensities of current)

1 2 4

1: Junction I I I − =

2 5 3

2: Junction I I I + =

I2 I3

R C R R L L C

V

V

I1 I4 I5 1 2 3

1 5 4 3

3: Junction I I I I + = +

Junc 3 = Junc 1 + Junc 2 linearly depending

• A linear active circuit with output terminals A and B is

equivalent to a generator with e.m.f. equal to the difference in potential between A and B and an internal resistance equal to the equivalent resistance

• f the passive network (without ideal generators)

between A and B. Linear Active circuit

A B ≡ A B

eq T

R R =

AB T

V = ε Thevenin’s theorem

It is easier to analyze circuits by splitting them into little pieces.