EGR 2201 Unit 2 Basic Laws - PowerPoint Presentation

Slide1

EGR 2201 Unit 2Basic Laws

Read Alexander &

Sadiku

, Chapter 2.

Homework #2 and Lab #2 due next week.

Quiz next week.Slide2

Ohm’s Law

Ohm’s law

says that the voltage

v across a resistor is equal to the current i through the resistor times the resistor’s resistance R. In symbols:v = i  RThe voltage’s polarity and current’s direction must obey the passive sign convention, as shown in the diagram at right. Otherwise, you need a negative sign in this equation: v = i  R.Slide3

Ohm’s Law Rearranged

The equation

v

= i  R is useful if we know i and R, and we’re trying to find v.Often we’ll need to rearrange the equation to one of the following forms:i = v  R orR = v

 iSlide4

Ohm’s Law Game

Given values for two of the three quantities in Ohm’s law, you must be able to find the third quantity.

To practice, play

my Ohm’s Law game.Slide5

Short Circuit

An element with

R

=0 (or with an extremely small resistance) is called a short circuit. Since a short circuit’s resistance is zero, Ohm’s law tells us that the voltage across a short circuit must also be zero:v = i  R = i  0 = 0 But we can’t use Ohm’s law to compute a short circuit’s current:i

= v 

R

= 0



0 = ???Slide6

Open Circuit

An element with

R

= (or with an extremely large resistance) is called an open circuit. Since an open circuit’s resistance is infinite, Ohm’s law tells us that the current through an open circuit must be zero:i = v  R = v   = 0But we can’t use Ohm’s law to compute an open circuit’s voltage:

v = i 

R =

0





= ???Slide7

Power Dissipated by a Resistor

When current flows through

a resistor,

electric energy is converted to heat, at a rate given by the power law: p = v  iOnce the energy has been given off as heat, we can’t easily reverse this process and convert the heat back to electric energy. We therefore say that resistors dissipate energy. In contrast, we’ll see later that capacitors and inductors store energy, which can easily be recovered.Slide8

Other Power Formulas for Resistors

By combining the power law (

p

= v  i) with Ohm’s law (v = i  R or i = v  R), we can easily derive two other useful formulas for the power dissipated by a resistor:p = i 2

 R

p

=

v

2



R

Of course, each of these equations can in turn be rearranged, resulting in a number of useful equations that are summarized in the “power wheel”….Slide9

The “Power Wheel”

This is a useful aid for people who aren’t comfortable with basic algebra, but you shouldn’t need it.

The important point is that if you know any two of these four quantities (

P, V, I, and R), you can compute the other two, as long as you remember p=vi and v=iR.Slide10

Power Calculation Games

Given values for two of the following four quantities—voltage, current, resistance, power

—

you must be able to find the other two quantities.To practice, play these games: Ohm’s LawPower LawPower-Current-ResistancePower-Voltage-ResistanceSlide11

Conductance

It’s sometimes usefu

l to work with

the reciprocal of resistance, which we call conductance.The symbol for conductance is G:G = 1  RIts unit of measure is the siemens (S).Example: If a resistor’s resistance is 20 , its conductance is 50 mS.Slide12

Review: Some Quantities and Their Units

Quantity

Symbol

SI Unit

Symbol

for the Unit

Current

I

or

i

ampere

A

Voltage

V

or

v

volt

V

Resistance

R

ohm



Charge

Q

or

q

coulomb

C

Time

t

second

s

Energy

W

or

w

joule

J

Power

P

or

p

watt

W

Conductance

G

siemens

SSlide13

Ohm’s Law and the Power Formulas Using Conductance

As the book discusses, Ohm’s law and our power formulas can be

rewritten using conductance

G instead of resistance R.Example: Instead of writingv = i  R we can write v = i  GBut I advise you to ignore this, and always use R instead of G.Slide14

Circuit Topology: Branches

When describing a circuit’s layout (or “topology”), it’s often useful to identify the circuit’s branches, nodes, and loops.

A

branch represents a single circuit element such as a voltage source or a resistor.Example: This circuit (from Figure 2.10) has five branches.Slide15

Dots or No Dots?

In schematic diagrams, our textbook sometimes draws dots at the points where two or more branches meet, as in this diagram.

But most of the time the book omits these dots, as in this diagram.

There’s no difference in meaning.Slide16

Circuit Topology: Nodes

A

node

is the point of connection between two or more branches.Example: This circuit has three nodes, labeled a, b, and c.Slide17

Circuit Topology: Loops

A

loop

is any closed path in a circuit.Example: This circuit has six loops.Don’t worry about the book’s distinction between loops and independent loops.Slide18

Elements in Series

Two

elements

are connected in series if they are connected to each other at exactly one node and there are no other elements connected to that node. Example: In this circuit, the voltage source and the 5- resistor are connected in series.Slide19

If two elements

are

connected in

series, they must carry the same current. Example: In this circuit, the current through the voltage source must equal the current through the 5- resistor.But usually their voltages are different.Example: In the circuit above, we wouldn’t expect the voltage across the 5- resistor to be 10 V.Current Through Series-Connected ElementsSlide20

Elements in Parallel

Two

or more elements

are connected in parallel if they are connected to the same two nodes. Example: In this circuit, the 2- resistor, the 3- resistor, and the current source are connected in parallel.Slide21

If two elements

are

connected in

parallel, they must have the same voltage across them. Example: In this circuit, the voltage across the 2- resistor, the 3- resistor, and the current source must be the same.But usually their currents are different.Example: In the circuit above, we wouldn’t expect the current through the 3- resistor to be 2 A.Voltage Across Parallel-Connected ElementsSlide22

Sometimes elements are connected to each other

but are

neither connected in series nor connected in parallel.

Example: In this circuit, the 5- resistor and the 2- resistor are connected, but they’re not connected in series or in parallel. In such a case, we wouldn’t expect the two elements to have the same current or the same voltage.This type of connection doesn’t have a special name.Some Connections are Neither Series Nor ParallelSlide23

Series Circuits

Two simple circuit layouts are series circuits and parallel circuits.

In a

series circuit, each connection between elements is a series connection. Therefore, current is the same for every element. (But usually voltage is different for every element.)A series circuit is a “one-loop” circuit.

Another series circuit

A series circuit:

Same circuit on

the breadboard:Slide24

Analyzing a Series Circuit

Find the

total resistance

by adding the series-connected resistors:RT = R1 + R2 + R3 + ...Use Ohm’s law to find the current produced by the voltage source:is

= vs



R

T

Recognize that this same current passes through each resistor:

i

s

=

i

1

=

i

2

=

i

3

=

...

Use

Ohm’s law to find the voltage across each

resistor:

v

1

=

i

1



R

1

and

v

2

=

i

2



R

2

and

...

+

v

1



+

v

2





v

3

+

i

s

i1

i2

i3 Slide25

Parallel Circuits

In

a

parallel circuit, every element is in parallel with every other element.Therefore, voltage is the same for every element. (But usually current is different for every element.)Another parallel circuitA parallel circuit:Same circuit on the breadboard:Slide26

Analyzing

a Parallel Circuit

Recognize that

the voltage across each resistor is equal to the source voltage:vs = v1 = v2 = v3 = ...Use Ohm’s law

to find the current through each resistor:i

1

=

v

1



R

1

and

i

2

=

v

2



R

2

and

...

+

v

1



+

v

2



+

v

3



i

1

i

2

i

3

Slide27

We’ve seen that series circuits and parallel circuits are easy to analyze, using little more than Ohm’s law.

But most circuits don’t fall into either of these categories, and are harder to analyze.

Some authors call these

series-parallel circuits. Others call them complex circuits.More Complicated CircuitsExamples that are neither series circuits nor parallel circuitsSlide28

Kirchhoff’s Current Law (KCL)

Kirchhoff’s current law

: The algebraic sum of currents entering a node is zero.

Example: In this figure,i1  i2 + i3 + i4  i5 = 0 Alternative Form of KCL: The sum of the currents entering

a node is equal to the sum

of the currents

leaving the

node.

Example: In the figure,

i

1

+

i

3

+

i

4

=

i

2

+

i

5

Slide29

KCL

Applied to a Closed Boundary

You can also apply KCL to an entire portion of a circuit surrounded by an imaginary boundary. The sum of the currents entering the boundary is equal to the sum of the currents leaving the boundary.

Example: In this figure,

i

1

+

i

5

=

i

2

+

i

7

+

i

8Slide30

Kirchhoff’s

Voltage Law (KVL)

Kirchhoff’s voltage law

: Around any loop in a circuit, the algebraic sum of the voltages is zero.Example: In this figure,v1 + v2 + v3  v4 + v5 = 0

Alternative Form of KVL: Around any loop, the

sum of the voltage drops is equal to the sum of the voltage rises.

Example: In the figure,

v

2

+

v

3

+

v

5

=

v

1

+

v

4

Slide31

Equivalent Resistance

In analyzing circuits we will often combine several resistors together to find their

equivalent resistance

.Basic idea: What single resistor would present the same resistance to a source as the combination of resistors that the source is actually connected to?Slide32

Resistors in Series

The

equivalent resistance of any number of resistors connected in series is the sum of the individual resistances:

Req = R1 + R2 + ... + RNWe’ve already used this earlier in Step 1 of our analysis of series circuits.Slide33

Parallel Resistors

The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum

:

Note

that the equivalent resistance is always less than each of the original resistances

.

 Slide34

More Than Two

Resistors in Parallel

For more than two resistors in parallel, you

cannot simply extend the product-over-sum rule like this:

Instead, either use the product-over-sum rule repeatedly (with two values at a time), or…

…use the so-called

reciprocal formula

:

 Slide35

Parallel Resistors: Two Shortcut Rules for Special Cases

Special Case #1: For

N

parallel resistors, each having resistance R, Special Case #2: When one resistance is much less than another one connected in parallel with it, the equivalent resistance is very nearly equal to the smaller

one:If R1 <<

R

2

,

then

R

eq



R

1

 Slide36

Series-Parallel Combinations of Resistors

In many cases, you can find the equivalent resistance of combined resistors by repeatedly applying the previous rules for resistors in series and resistors in parallel.

Hint: Start farthest from the source or (in a case like the one above from

Figure 2.34) farthest from the open terminals, and work your way back toward the source or open terminals.Slide37

Building Complex Circuits on the BreadboardSlide38

Voltage Division

For resistors in series, the total voltage across them is divided among the resistors in direct proportion to their resistances.

Example: In the

circuit shown(Figure 2.29), if R1 is twice as big as R2, then v1 will be twice as big as v2.See next slide for a formula that captures this…Slide39

The Voltage-Divider Rule

The

voltage-divider rule

:For N resistors in series, if the total voltage across the resistors is v, then the voltage across the nth resistor is given by:

Example: In the circuit shown,

and

 Slide40

The Voltage-Divider

Rule in More Complex Circuits

The voltage-divider rule

is easiest to apply in series circuits, but it also holds for series resistors in more complex circuits.

Example: In the

circuit shown,

suppose we

know the value of

the voltage

v

. Then

we can say that

and

 Slide41

Current Division

For resistors in parallel, the total current through them is shared by the resistors in

inverse proportion

to their resistances.Example: In the circuit shown(Figure 2.31), if R1 is twice as big as R2, then i1 will be one-half as big as i2.See next slide for a formula that captures this…Slide42

The

Current-Divider

Rule

The current-divider rule:For two resistors in parallel, if the total current through the resistors is i, then the current through each resistor is given by:

and

 Slide43

The

Current-Divider Rule in More Complex Circuits

The

current-divider rule is easiest to apply in parallel circuits, but it also holds for parallel resistors in more complex circuits.

Example: In the

circuit shown,

suppose we

know the value of

the current

i

. Then

we can say that

and

 Slide44

Review of Short Circuits

Recall that an

element with

R=0 (or with an extremely small resistance) is called a short circuit. Recall also that, since the resistance of a short circuit is zero, the voltage across it must always be zero.Sometimes short circuits are introduced intentionally into a circuit, but often they result from a circuit failure.Slide45

New Observations about Short Circuits

The

equivalent

resistance of a short circuit in parallel with anything else is zero.An element or portion of a circuit is short-circuited, or “shorted out,” when there is a short circuit in parallel with it.No current flows in a short-circuited element; instead all current is diverted through the short circuit itself.Example: In this circuit, no current will flow through

R2 or R3.Slide46

Potentiometers & Rheostats

A

potentiometer

is an adjustable voltage divider that is widely used in a variety of circuit applications. It is a three-terminal device.A rheostat is an adjustable resistance. It has only two terminals.Slide47

Useful Microsoft Word Features For Your Lab Reports

Italics

Subscript

Bold

SuperscriptSlide48

Useful Microsoft Word Features For Your

Lab Reports (cont’d.)

Creating a TableSlide49

Useful Microsoft Word Features For Your

Lab Reports (cont’d.)

Inserting Symbols

Then select the Symbol

Font to find

Greek letters

and other symbols.