ECE 2070 Lecture 1

1 ECE 2070 Basic Electrical Engineering

ECE 307 Lecture 1

DC Circuit Components, Connections, and KCL

Department of Electrical and Computer

Engineering

Clemson University


Electric Charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. The SI unit of charge is Coulomb.

Electric charges are quantized It comes in integer multiples of individual small units called the

elementary charge (e), approximately equal to 1.6021019 coulombs (except for particles called quarks, which have charges that are integer multiples of e/3).

There are two types of charges: positive and negative. The proton has a charge of +e, and the electron has a charge of e.


Electrical Work

Electrical work is the work done on a charged particle by an electric field. The SI unit for electric work is Joule.

Q is the charge of the particle, E is the electric field

F = q0E

a

b

+++++++++++++

- - - - - - - - - - - - -

Q

Q

F = q0E

ha

hb

a

b F = mg

F = mg

( )ab a bW mg h h

b

ab

a

W Q E dr


Electric Potential

The electric potential at a point in an electric field is defined as the work done in moving a unit positive

charge from infinity to that point.

The SI unit for electrical potential is Volt.

The electric potential difference

b

abab a b

a

WV V V

Q E dr

a

aa

WV

Q

E dr


Electric Current

Electric Current is defined as the time flow rate of electric charges

The SI unit for electric current is Ampere [coulombs per second)

The Electrical Engineering convention

The positive direction of current flow is that of positive charges.

Direct Current (DC): the flow of electric charges (current) is unidirectional.

Alternating Current (AC): the flow of electric charges (current) periodically reverses its direction.

dQI

dt


Electric Power

Electric power, like mechanical power, is the rate of doing work, measured in watts [joules per second].

Electrical Engineering convention

The power dissipated by a load is a positive quantity

Power is generated/stored (negative) or dissipated (positive) when charges are moved between different

electric potentials.

Work Work Charge = =

Time Charge TimeElectric Power Voltage Current

P VI


Electric Circuit Performs a function: oProcess Information

oTransfer Power

Characterized by: oVoltages

oCurrents

oPower

oEnergy

Circuit Components

Resistor Voltage Source Current Source Switch

Connections

Terminal Node Branch Loop Mesh

Similar

Electric Circuit

Reductions

Source Transformation Parallel Series Thevenin Equivalent Norton Equivalent

Analysis Tools

Kirchoffs Current Law

Node Voltage Method Kirchoffs Voltage Law

Mesh Current Method Superposition

Overview of DC Electric Circuits

DC Lecture 1 -

DC Circuit Components,

Connections, and KCL


Overview of Lecture

Introduce Six Elements Used in a DC Circuit

Constant Voltage Source

Constant Current Source

Resistor

Open Circuit, Short Circuit, Switch

Connect the Elements to Build a Circuit

Define Connection Terminology: Terminal, Node, Branch, Loop, Mesh

Define Series and Parallel Connections

Kirchhoffs Current Law (KCL)

Describes the currents at a connection



Examples of Constant Voltage Sources:

Car Battery supplies

constant 12V to power the

lights and accessories

AA Battery used in a

flashlight to supply a

constant 1.5V.

Solar Cell used to convert

light into electricity to power

this toy robot creates 0.5V

constant voltage.

Rechargeable Battery

supplies 3.7V to power

the cell phone


Mathematical Model:

Voltage is Constant Current oCurrent is determined by

connections to other

components

oCan supply any current

Symbol:

Svor

Time Volt

age

Constant -> no change over time

Behavior:

Produces a constant voltage that

is not affected by connections to

other components

+ -

+

- Sv



What does it do when connected to other components?


Sv+ -

Electric

Circuit

Case 2:

The electric circuit does work to

charge the battery

-

Sv+ -

Battery

Charging

Circuit

-

Current results from this connection Current results from this connection

Case 1:

Does work to move electrons and

supply energy to the rest of the

electric circuit

Note: We will have to solve the entire circuit in order

to know the amount of current.

i i



Examples of Constant Current Sources:

Welder supplies constant

current to create the heat

needed to fuse metal pieces.

Cell Phone charger

supplies constant current at

the beginning of a full-

charge cycle.



si

Time Curr

ent Constant -> no change over time

Behavior:

Produces a constant current that

is not affected by connections to

other components

Mathematical Model:

Current is Constant Voltage oVoltage is determined by

connections to other

components

oCan supply any voltage

Symbol:



si


Does work to move electrons and supply energy to the rest of the electric

circuit

Electric

Circuit

-

A voltage can be

measured across

the current

source as a result

of this

connection

+

-

v

Note: We will have to solve the entire circuit in

order to know the amount of voltage.


Resistor

Examples of Resistors:

The Heating Element of a

toaster (the part that gets hot)

resists the flow of electrons and

gets hot.

The Filament in a light bulb

(the part that produces light)

resists the flow of electrons and

gets very hot to produce light.

An extension cord is used

to connect appliances and

has very low resistance.

The resistance of the extension cord is not zero and can be

significant depending on the application.


Resistor

R

Voltage

Cu

rren

t

1slope =

is constant.R

Behavior:

Constant relationship between

voltage and current.

Mathematical Model:

Constant R summarizes material properties, temperature, and size.

Ohms Law relates the voltage and current using R:

v = iR

Symbol:


Resistor

R


Resists the flow of electrons. A resistor removes energy from the circuit

and dissipates it as heat.

Electric

Circuit

A voltage can be

measured across

the resistor as a

result of this

connection

+

-

v

Current results from this connection

-

Note: We will have to solve the entire circuit in order to

know either the voltage or the current. We do know that

voltage and current are related by Ohms Law as v = iR

i


Application of Ohms Law

Rv

R is a circuit model of a physical material that

has length, width, height, and property of

conductivity that constitute the resistance.

Examples (given same size):

Copper wire (low resistance)

Nichrome wire (medium resistance)

Gold wire (low resistance)

Insulation on wire (high resistance)

For the current referenced into a voltage drop as shown

v=iR

+

-

i


Application of Ohms Law

Must adjust the sign (+/-) in Ohms law for other referenced directions,

This is the standard

convention

v= - iR

v= iR

Rv

+

-

Rv

+

-

i i


Example 1: Applying Ohms Law given fixed voltage

and current references

v= - iR

= -(-2A)(10W)

= 20V

v= iR

= 2A(10W)

= 20V

v= iR

= (-2A)(10W)

= -20V

These are all the same circuit. 2A goes into the resistor from the top and there is a

20 V drop from top to bottom.

10W

2A

v

+

-

10W

2A

v

+

-

10W

2A

v

+

-


Open and Short Circuits

Resistance is Electric

Circuit

NO current can be

measured across

the opening

+

-

v

No Current

-

Short Circuit:

No resistance to current flow, ~ zero R

Open Circuit:

No current can flow, ~ infinite R

Electric

Circuit

NO voltage can be

measured across

the short

+

-

v

Current

-

Resistance is zero

i i


Switch

Examples of Switches:

Switch on the wall turns

the lights on or off. Each button on the phone

or key on the keyboard is a

Switch.

Switch on the coffee

maker turns the appliance

on or off.


Switch

Behavior:

Can stop or allow the flow of current.

Mathematical Model:

No current flows when the switch is open.

Current flows freely when switch is closed.

Symbol:


Switch


Connects or disconnects part of the circuit

RElectric

Circuit

NO current can be

measured across

the opening

+

-

v

No Current

-

Closed:

Acts like a short circuit

Open:

Acts like an open circuit

RElectric

Circuit

NO voltage can be

measured across

the switch

+

-

v=0V

Current

-

i i


Connect Components to Create an Electric Circuit

Example: Connect a battery and a resistor to build a portable light.

Device: Flashlight

1.5V 1W 1.5V

Circuit Model

1.5A

1.5A


Electric Circuit (Electric Network)

Connection of Components

Terms to describe the connection of components

Terminal

Node

Branch

Loop

Mesh

Learning a new

vocabulary !


Electric Circuit Connections

Terminal point where a component or part of the circuit connects to other components or other parts of

the circuit

Node connection point

Electrically anywhere

in here is the

connection point

Pick a point and call it the node

R3

R1

R2

R3

R1

R4


Terminals v1 + - R

v1 + -

R1

R2

R3 Each element alone

has two terminals

A connection of

components has terminals

v1 + -

R1

R2

R3

R4

These internal

connections are

not the terminals

of the connected

components.

Example 2: Identify Terminals


Example 3: Identify Nodes

Electrically,

anywhere along

the wires in this

area is the

connection point

Pick a point and

call it the node

Note that this connection

is an electrical circuit and

could be a model for a

system such as the

electrical system in a car

R1 + - R2 R3 v1

Label the nodes in the circuit.



Branch portion of a circuit with only two external

terminals

terminals

Each element is a branch.

The connection between

and is also a branch 1t 3t

Each element is a branch. The

connection is NOT a branch

because it has 3 external terminals

t1 , t3, and t4 and three

components connect at t2 .

R1

v1 + -

3t

2t

1t

R1

R2

v1 + -

4t

1t

2t

3t


3W

Example 4: Identify Branches

Find branches in the circuit.

28A

2W

4W6W

1W 2W

+ -

40V

Each of the components are individually a branch, 8 components means 8 branches.

First identify the nodes.

There is a branch containing the 40V source and the 3W and 1W resistors the connection has two terminals.

The branch at the right has two terminals that connect this sub-circuit to the rest of the circuit.


Parallel Connection

Elements of a circuit which share the same two nodes

+ - R1 R3 R2 i1

Electrically,

anywhere along

the wires in this

area is the

connection point

Pick a point and

call it the node

v1

All components of the circuit connect to the same two

nodes and are therefore in parallel.

We often use the symbol || to indicate that elements are in parallel, here v1 || i1 || R1 || R2 || R3


28A

2W3W

4W6W

1W 2W

+ -

Example 5: Indentify Parallel Elements

40V

4 W and 28A source are

in parallel. The branch containing

the 40V source and the

3W and 1W resistors is

in parallel with 6W

resistor

Which elements in the circuit are connected in parallel?

First indentify the nodes.

No other individual

components are in parallel


R1

R2 R3

v1 + - R5 R4


Loop a closed connection of branches

Mesh a loop that does not contain other loops

How many nodes?

How many meshes?

How many loops?

5

2

The two meshes plus the

third exterior loop

2+1=3

Form a closed connection of branches by starting at a node and

traversing the circuit until we get back to the starting node.

Cannot use the same node twice.


+ -

R1

+ -

R2

R3 R4 v2 i1 v1

1N 3N2N

4N

Example 6: Identify nodes, loops, meshes

How many nodes?

How many meshes?

How many loops?

What is not a loop?

5

4

5 + +

A path that crosses the same node twice

R5


Kirchhoffs Current Law (KCL)

Equal amounts of charge enter and exit a node.

Algebraic sum of currents into and out of a node is zero:

Convention 1: Current labeled as pointing into a node is given a negative sign in the summation and current labeled as pointing out of the node is positive.

Convention 2: Current labeled as pointing into a node is given a positive sign in the summation and current labeled as pointing out of the node is negative.

1

0N

n

i


Example 7: Applying KCL

1i2i

3i

4i

Find i3 in terms of the other currents.

4

1 2 3 4

1(i out of node +)

0 0n

i i i i i

3 1 2 4i i i i

Node

Using Convention 1:

4

1 2 3 4

1(i out of node -)

0 0n

i i i i i

3 1 2 4i i i i

Using Convention 2: Both conventions yield the

same result. We will

generally use Convention 1

Solve for i3:

Solve for i3:


Example 7 (cont): Applying KCL

1i2i

3i

4i

Given:

1 5Ai

2 3Ai

4 2Ai

Find : 3i4

1 2 3 4

1(i out of node +)

0 0n

i i i i i

3 1 2 4 ( 5 ) 3 ( 2 )

0A

i i i i A A A

Note: i2 = -3A means

that the current actually

flows in the direction

opposite to the arrow

Node


Example 8: Applying KCL

1i

2i

3i

4i

Same problem with some of the current directions

changed. Find i3 in terms of the other currents.

4

1 2 3 4

1(i out of node +)

0 0n

i i i i i

3 1 2 4i i i i

Node

Using Convention 1:

4

1 2 3 4

1(i out of node -)

0 0n

i i i i i

3 1 2 4i i i i

Using Convention 2: Both conventions yield the

same result. We will

generally use Convention 1

Solve for i3:

Solve for i3:


R1 + - R2 R3

R4

v1

Example 9: Applying KCL in a Circuit

1N

2N

KCL at Node 1 :

at Node 2:

5

1 2 3 4

1(i out of node +)

0 0Sn

i i i i i i

5

1 2 3 4

1(i out of node +)

0 0Sn

i i i i i i

i1 i2 i3

i4

is

Apply KCL at each node.

Identify the nodes in the circuit and label.


Example 9 (cont): Applying KCL in a Circuit

1 2 35A 1ASi , i i i

Node 1:

2:

4 45A 1A 1A 1A 0 2Ai i

4 45A 1A 1A 1A 0 2Ai i

If we knew some actual values:


Example 10: Solving a Circuit Using KCL

What is the current through the 5W resistor?

4

1(i out of node 1)

0 -5 -15 8 0an

i A A A i

5 15 -8 12ai A A A A

12 5 60Va av i R A W Once we know the current in a resistor, we can use Ohms law to find the voltage:

KCL at the

top node

yields:

ia 15A 8A 5A 5W

Identify the nodes in the circuit and apply KCL to create equations to solve for ia.

We need to solve for ia.

+

-

va

Here we only

needed to write 1

equation and solve

for the 1 unknown.

1

2


Series Connections

Elements of a circuit connected so that the current out

of one component goes into the next.

3W

28A

2W

4W6W

1W 2W

+ -

40V

We say that the 40V source, the 3W resistor, and the 1W

resistor are connected in series.


Example 11: Show that series components have the

same current.

a b ci i i

3W

28A

2W

4W6W

1W 2W

+ -

40V

ia

ib

ic

N1 N2 N3

N4 N5 N6

Write KCL equations at nodes N1 and N4:

4

1

1(i out of node +)

: 0 0a bn

N i i i

4

2

1(i out of node +)

: 0 0b cn

N i i i

4


Electric Circuit Performs a function: oProcess Information

oTransfer Power

Characterized by: oVoltages

oCurrents

oPower

oEnergy

Circuit Components

Resistor Voltage Source Current Source Switch

Connections

Terminal Node Branch Loop Mesh

Similar

Electric Circuit

Reductions

Source Transformation Parallel same voltage Series same current Thevenin Norton

Analysis Tools

Kirchoffs Current Law Node Voltage Method

Kirchoffs Voltage Law

Mesh Current Method Superposition

Summary

DC Lecture 1 -

DC Circuit Components,

Connections, and KCL

ECE 2070 Lecture 1

Documents

Transcript of ECE 2070 Lecture 1