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03-Circuit Elements

Text: Chapter 1.6–

 1.9, 2.3

ECEGR 210

Electrical Circuits I

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Overview

• Circuit Topology

• Series and Parallel Connections

• Sources

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Circuit Topology

• Circuits are usually described graphically

• Need to be proficient in understanding basiccircuit symbols

• Road map:

Circuit topology (branches, nodes, loops)

Active elements

Passive elements (later lectures)

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Branch

• Branch: a single element in a network

Examples: single voltage source, resistor

Orientation does not matter

Terminals are part of the branch

• Example below has five branches

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branch

branch

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Node

• Node: point of common connection between twoor more branches

• Example below has three nodes

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Loops

• Loop: any closed path in a network

• Start at a node, pass through at least one othernode and return to the original node

Direction matters

• Independent loop: a loop that contains at leastone branch not contained in another loop

Independent loops have independent equations

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Topology Relations

• For all networks

B = L + N -1

• Where

B = number of branches

L = number of loops

N = number of nodes

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Series Connections

• Two branches (elements) are in series if theyexclusively share a single node

• Same current flows through each element

• Network below:

A and B are in series

No other elements are in series

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B

A C D E

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Parallel Connections

• Two branches (elements) are in series if theyshare both nodes

• Network below:

C, D, E are in parallel

• It is possible for two elements to not be in seriesor in parallel (e.g. B and C)

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B

A C D E

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Example

• Which elements are in series?

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B

A

D

C F

E

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Example

• Which elements are in series?

A, B

D, E, F

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B

A

D

C F

E

C prevents B and D from being in series

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Example

• Which elements are in parallel?

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B

A

D

C F

E

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Example

• Which elements are in parallel?

None

But C is in parallel if D, E and F can be combinedinto a single element G (more on this later)

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B

A

D

C F

EB

A C

G

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Circuit Elements

• Two types of elements:

Active: supplies energy

• Batteries, generators, etc

Passive: cannot supply energy (may or may notconsume energy)

• Resistors, inductors, capacitors

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Voltage and Current Sources

• V-I characteristics

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current

  v  o   l  t  a  g

  e 

voltage

  c  u  r  r  e  n  t

Ideal current sourceIdeal voltage source

Examples of non-ideal sources

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Voltage/Current Sources

• Current and voltage sources are active elements

• Two types:

Independent (I or V are independent from othercircuit elements)

Dependent: (I or V depend on other circuit

elements)

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Independent/Dependent Sources

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+

-

Voltage Current

   + 

-

Independent

Dependent

DC DC

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Dependent Sources

• Dependent Voltage Sources:

Often controlled by voltage or current in the circuit

Generators voltage controlled by rotational speed

• Dependent Current Sources:

Often controlled by voltage or current in the circuit

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V 10i

 A

+

-

   + 

-B

C

i

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Example

• Find the power consumed or supplied by each

element

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+

-0.2I20V 8V

12V+ -

+

-6A

I=5A

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Example

• Find the power consumed or supplied by each

element 20 x -5 = -100W (supply)

12 x 5 = 60 W

6 x 8 = 48W

-0.2x5 x 8 = -8 W(supply)

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+

-0.2I20V 8V

12V+ -

+

-6A

I=5A

60W

48W

-100W -8W

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Sources

• Voltage sources can be easily conceptualized as a

battery

• What about current sources?

One example is in the internal model of aphotovoltaic cell

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