Current and Voltage Theory

7/29/2019 Current and Voltage Theory

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Chapter 2Current and Voltage

ECET 1010 Fundamentals


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2.1 Atoms and Their Structure Need to understand atoms and their

structure to understand concepts of

current and voltage


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Atoms and Their Structure


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Simplest Atom Hydrogen Proton

Positive charge

Radius ~ 2 x 10-15 m (dime)

Electron

Negative charge

Radius ~ 2 x 10-15 m

Orbit ~ 5 x 10-11 m (1/4 mile)


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Helium Two protons and two electrons

Two neutrons

No charge Slightly heavier than protons

NOT contained in hydrogen

Contained in ALL other elements

In all neutral atoms the number of electrons isequal to the number of protons.


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Mass Electron 9.11 x 10-28 g

Proton 1.672 x 10-24 g

Neutron 1.672 x 10-24 g

Protons and neutrons have about 2,000times the mass of electrons

Radius is on the order of 2 x 10-15 m


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Shells and Subshells of the

Atomic Structure


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Atomic ShellsShell Identifier Number of

Electrons

1st k 2

2nd l 8

3rd m 18

4th n 32

nth 2n2


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Atomic SubshellsSubshell Number of

Electrons

s 2

p 6

d 10

f 14


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Coulombs Law Charles Augustin de Coulomb (1736-

1806)

Unlike charges attract

Like charges repel

Force of attraction (repulsion) betweentwo bodies given as:

F = k Q1 Q2 / r2


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Coulombs Law F is the force of attraction (repulsion) in

Newtons

k is a constant, 9.0 X 109 Nm2/C2

Q1, Q2 charges in Coulombs, C

r distance between two charges inmeters


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Removing Electrons Easier to remove electron from outer

subshell than inner subshell

Electrons easier to remove fromsubshells that are incomplete AND havefew electrons


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Copper Most commonly used metal in

electrical/electronic industry

29th

electron loosely bound Distance to nucleus

Only electron in shell

Incomplete shell

Easy to become free electron In 1 in3 of copper at room temperature there

are 1.4 x 1024 free electrons


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Other Metals With Same

Property Silver 47

Gold 79

Aluminum 13

Tungsten 74

Okay, but what keeps a nucleus together?


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The Strong Nuclear Force and

Binding Energy Google: What keeps the nucleus of an

atom together?

http://theory.uwinnipeg.ca/mod_tech/node178.html
http://theory.uwinnipeg.ca/mod_tech/node178.htmlhttp://theory.uwinnipeg.ca/mod_tech/node178.html


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2.2 Current


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Cross Section of Copper Wire Random motion of free electrons at

room temperature with no external

forces applied Positive ions created when an atom

loses its free electron

Free electrons move about Positive ions oscillate about a fixed

position


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Charge Carrier The free electron is the charge carrier in a

copper wire or any other solid conductor ofelectricity

Free electrons are constantly gaining andlosing energy through: Changes in position

Collisions with other electrons and positive ions Attractive forces of positive ions

Force of repulsion from other electrons


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Flow of Charge With no external forces applied, the net flow

of charge in a conductor in any one directionis zero

Connecting a battery and light bulb creates asimple electrical circuit

Chemical energy in battery puts positive

charge at one terminal and negative chargeat other

Free electrons travel from negative terminal(supply) to positive terminal

Analogous to water hose


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Ampere If 6.242 x 1018 electrons drift at a

uniform velocity through an imaginary

cross section in 1 second, the flow ofcharge, or current, is said to be 1

Ampere

Andr Marie Ampre (1775-1836)


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Charge per Electron 1 Coulomb is the charge associated

with 6.242 x 1018 electrons

Charge per electron is determined as:

1 / 6.242 x 1018 = 1.602 x 10-19 C


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Calculating CurrentI = Q / t

I = current in Amperes (A)

Q = charge in Coulombs (C)

t = time in seconds (s)

This equation may be solved for Q and t


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Example 2.1The charge flowing through an imaginary

surface is 0.16 C every 64 ms.

Determine the current in Amperes.

I = Q / t

= 0.16 C / 64 x 10-3s= 2.50 A


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Example 2.2Determine the time required for 4 x 1016

electrons to pass through an imaginarysurface if the current is 5 mA.

Q = 4 x 1016 electrons / 6.242 x 1018 electrons/C= 6.41 x 10-3 C

t = Q / I= 6.41 x 10-3 C / 5 x 10-3 A=1.282 s


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Conventional Flow versus

Electron Flow


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Safety Considerations Even small levels of current can cause serious side

effects to the human body

Any current over 10 mA should be considered

dangerous Currents of 50 mA can cause severe shock

Currents over 100 mA can be fatal

Resistance of dry skin is high enough to limit current

through body to safe levels

Water (or other liquids) and electricity do not mix!


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2.3 Voltage Potential energy

Notation

Terminology


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Potential Energy Energy is defined by the capacity to do work

w = mgh

w potential energy (J)

m mass

g gravitational acceleration, 9.8 m/s2

h height (m)


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Potential Difference


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Potential Difference A potential difference of 1 volt (V) exists

between two points if 1 Joule (J) of energy is

exchanged in moving 1 Coulomb (C) ofcharge between two points

A potential difference or voltage is alwaysmeasured between two points in a system

Changing either point may change thepotential difference between the two pointsunder investigation


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Potential DifferenceV = w / Q

V potential difference in volts

w work in Joules

Q charge in Coulombs


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Example 2.3Find the potential difference between two

points in an electrical system if 60 J of

energy are expended by a charge of 20C between two points.

V = w / Q= 60 J / 20 C= 3 V


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Example 2.4Determine the energy expended moving a

charge of 50 C through a potential

difference of 6 V.

w = V * Q

= 6 V * 50 * 10-6 C= 300 * 10-6J = 300 J


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Notation Efor voltage sources (volts)

Vfor voltage drops (volts)


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Terminology Potential

The voltage at a point with respect to anotherpoint in the electrical system.

Typically the reference point is ground, which is atzero potential.

Potential difference The algebraic difference in potential (or voltage)

between two points of a network. Voltage

When isolated, like potential, the voltage at apoint with respect to some reference such as

ground (0 V).


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Terminology Voltage difference

The algebraic difference in voltage (or potential)between two points of the system.

A voltage drop or rise is as the terminology wouldsuggest.

Electromotive force (emf) The force that establishes the flow of charge (or

current) in a system due to the application of adifference in potential.

This term in not applied that often in todaysliterature, but is associated primarily with sources

of energy.


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2.4 Fixed (dc) Supplies dc Voltage Sources

dc Current Sources


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dc Voltage Sources Symbol for a dc voltage source

dc stands for direct current

Unidirectional flow of charge

Categories of sources

Batteries (chemical action)

Generators (electro mechanical)

Power supplies (rectification)


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Batteries


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BatteriesAlkaline and lithium-iodine primary cells

Lead-acid secondary cell

Nickel-cadmium secondary cell

Nickel-hydrogen and nickel-metalhydride secondary cells

Solar cell


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Ampere-Hour Rating

Life (hrs) = Ampere-Hour Rating (A-hrs)

Amperes Drawn (A)


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Ampere-Hour Rating Factors that affect the life (hours):

Temperature

Rate of discharge

The capacity of a dc battery decreases withan increase in current demand.

The capacity of a dc battery decreases at

relatively (compared to room temperature)low and high temperatures.

The terminal voltage of a dc batterydecreases with the length of the discharge

time at a particular drain current.


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ExampleDetermine the capacity in

Ampere-hours and life inminutes for an Energizer D

cell if the discharge currentis 450 mA.

Life = 10.75 A-hr / 450 mA= 23.889 hr= 1,433.333 min


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ExampleAt what temperature

will the A-hr

rating of this cellbe 90%?

90% (18.2 A-hr) =16.38 A-hr

40F (4.444C)110F (43.333C)


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GeneratorsApplied torque of some external source

of mechanical power

Terminal voltage usually 120 V or 240 V


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Power Supplies Rectification or filtering

Typically three output levels

Above ground, e.g., 10 V

At ground, 0 V

Below ground, e.g., -15 V


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dc Current Sources Note: dc voltage sources (ideally) provide a

constant level of voltage over time.

dc current sources provide a constant level ofcurrent over time.

The current source will supply, ideally, a fixedcurrent to an electrical/electronic system

even though there may be variations in theterminal voltage as determined by thesystem.

Current and Voltage Theory

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