BASIC ELECTRICAL IDEAS AND UNITS.pdf

BASIC ELECTRICAL IDEAS

AND UNITS

Electron Theory of Electricity



All matter is composed of atoms which are

made up of fundamental subatomic particle

called protons, neutrons, and electrons.



Each atom represents a sort of microscopic

solar system in which the nucleus contains

protons and around which the electrons

Orbital Electrons



All negatively charged electrons revolve

about the positive nucleus in definite orbits



Basically, there is a force of attraction

between the positive nucleus and each

negative electron



This force is counterbalanced by one that is

determined by the orbital motion of the

electron

Energy of the revolving electron

 The energy required to displace the electron from the nucleus so that it may revolve at some fixed radius from the atomic center

 The energy represented by its motion around the nucleus, and

 As the atoms become increasingly complex, the positive charge of the nucleus is strengthened by acquiring additional protons

 Electrons rises proportionately to provide a structure that is electrically neutral

 Neutrons are also added to the nucleus but have no effect upon the atomic charge

 Protons and neutrons are bunched together in a central core

 Electrons are presumed to revolve in orbits or shells around the nucleus

Electron Shell and Orbits

 Electron orbit the nucleus of an atom at certain distance from the nucleus

 Electrons near the nucleus have less energy than those in more distant orbits

 Energy levels

- orbit from the nucleus corresponds to a certain energy level

- orbits are grouped into shells (energy band) - each shell has a fixed maximum number of

- the shells are designated K, L, M, N and so on - with K being the closest to the nucleus

Valence Electrons and Conductivity in

Solids

 the outermost shell s known as the valence shell and electrons in this shell are called valence electrons

 Solid materials may be classified as conductors, insulators, and semiconductors

 Classification depends upon the number of valence electrons

-Conductor : material that easily conducts electric current. Valence electron<4

- Insulators: material that does not conduct electrical current under normal conditions.

valence electron>4 ex. Phosphorus

- Semiconductor: material that is between

conductors and insulators in its ability to conduct electrical current

valence electron = 4

Electric Charge and Electric Current

 Electric charge unit – coulombs

 For each negatively charged electron it is  Or one coulomb of electric charge is

 When one coulomb of electric charge passes a given point every second the electric current is said to be one ampere

 One coulomb per second is one ampere

19 1.59 10 coulombx  18 6.24 10x e

Q

I

t



Where: I = current, Ampere Q = charge, coulombs

t = time, sec, during which electrons move  If the current is constant, charge is transferred at a

constant rate Q= It

 For non-uniform current, the transferred charge will vary with current changes, q=it

 Where: q = geometrically an area i = plotted along y-axis

Variations of current with time

i (amp

ere

)

 The shaded area represents the number of coulombs transferred in sec

q

Example:

 The current in a conductor changes uniformly from zero to 2 amp in 3sec, remains steady at 2 amp for 6 sec, and then drops uniformly to 1.5 amp in 8 sec. Calculate the total amount of charge transferred in the elapsed time of 17 sec.

 Between t= 1ms and t = 14ms, 8µC of charge pass though a wire. What is the current?

Electromotive Force (EMF)

 Unit is volt ( V)

 When an emf is applied to the ends of a conductor it is proper to refer to the existence of a potential

difference between such ends

 Several methods are employed to develop an emf : - combining certain kinds of metals and

chemicals into a device (battery)

- building a machine which generates voltage when conductors are rotated near magnets.

Electrical Resistance and Resistivity

 One of the fundamental relationships of circuit theory is that between voltage, current and

resistance

 This relationship and the properties of resistance were investigated by the German physicist Georg Simon Ohm

 Ohm found that current depended on both voltage and resistance.

 From his investigation he was able to define the resistance of a wire and show that the current was

inversely proportional to this resistance Resistance of Conductors

 resistance of a material depends upon several

factors:

- type of material

- length of the conductor - cross-sectional area



the resistance of a conductor is dependent

upon the type of material



the resistance of a metallic conductor is

directly proportional to the length of the

conductor



the resistance of a metallic conductor is

inversely proportional to the

cross-sectional area of the conductor

 Factors governing the resistance of a conductor

at a given temperature may be expressed mathematically:  Where: ρ = resistivity l = length A = cross-sectional area

l

R

A







 Notes:

 ρ is the constant of proportionality called

resistivity

o Resistivity has a unit of Ω-m if the length is in

meter and area is in meter square, and a unit of

CM-ohms/ ft if the length is in feet and the area

is in CM

 Since most conductor are circular,

cross-sectional area 2 ₂ 2 2 4 d d A 







 units of cross-sectional area of a conductor: - square meter

- sq ft.

- Circular Mil (CM) - Square-Mil (sq.mil)

Circular-Mil (CM)

 A wire that has a diameter of 1 mil has an area of 1 circular mil (CM)  d = 1 mil 2 2 4 (1 ) 4 . 4 1 . 4 d A A mil A sq mil CM sq mil         

If d = 0.001 inch 2 6 2 6 2 (0.001 ) 4 10 4 1 10 4 A inch A x in CM x in        

Square-Mil

 Unit of cross-section of small conductor whose side is equal to one mil

s= 1 mil 2 2

(1

)

4

1 .

A

s

A

mil

sq mil

CM











 If s = 0.001 inch

 For conversion purposes

2 6 2 (0.001 ) 1 10 A inch A x  in   4 no. of sq mils sq. mils no.of CM 4 CM x x    

For a wire with a diameter of N mils (N =

any positive number)

2 2 2 2 2 sq. mils 4 4 4

substituting 1 sq mil, we have 4 . ( )( ) 4 4 d N A CM N N A sq mils CM N CM            

 Since d = N, the area in circular mils is simply equal to the diameter in mils square, that is,

2

(

)

CM mils

Volume to Resistance

Since the volume of the body is V=LA

 

from

;

if

l

R

A

V

L

A

V

A

R

A











V

R

A



 

If A=

V

L

L

R

V

L





L

R

V



 

Resistivity of Common Elements and Alloy @ 200_C

Elements/ Alloy Resistivity (Ω-CM/ft)

Copper, annealed 10.37 Aluminum 17 Tungsten 33 Zinc 36 Nickel 47 Manganin 265 Nichrome 600

Examples

 Most homes use solid copper wire having a diameter of 1.63 mm to provide electrical distribution to

outlets and light sockets. Determine the resistance of a 75 meters solid copper wire having the above

diameter.

 Calculate the resistance of the following conductor at 200_{C (a) material: copper with length 1000ft and}

area of 3, 200CM (b) material: aluminum with length 4 miles and diameter of 162 mils

 A kilometer of wire having a diameter of 11.77mm and a resistance of 0.031Ω is drawn so that its

diameter is 5mm. What does its resistance become?  A copper wire whose diameter is 0.162 in has a

resistance of 0.4Ω. If the wire drawn through a series of dies until its diameter is reduced to 0.032 in.

What is the resistance of the lengthened conductor? Assume that the resistivity remain unchanged.

Seatwork

 A copper wire of unknown length has a diameter of 0.25 in. and a resistance of 0.28 ohm. By several

successive passes through drawing dies the diameter of the wire is reduced to 0.05 in. Assuming that the resistivity of the copper remains unchanged in the drawing process, calculate the resistance of the

reduced wire.

 Calculate the resistance of 1km long cable, composed of 19 strands of similar copper conductors, each

strand being 1.32 mm in diameter. Allow 5% increase in length for the lay or twist of each strand in

1.723 x 10-8_Ω-m.

 A piece of silver wire has a resistance of 1 ohm. What will be the resistance of manganin wire of one-third of the length and one third the diameter, if the

specific resistance of manganin is 30 times that of silver.

Temperature-Resistance Effect

escape their orbits, causing additional collision within the conductor.

 Any increase in the number of collision translates into a relative increase or decrease in resistance.  For most conducting materials, the increase in the

number of collisions translate into a relatively linear increase in resistance, as shown in Figure 3-6.

 The rate at which the resistance of a material

changes with the variation on temperature is called

 Any material for which resistance increases as temperature increases is to have a positive temp. coefficient (+α)

 For semiconductor materials, as the temperature increases the number of charge electron increases, resulting in more current.

 Therefore, an increase in temp. results in a decrease in resistance.

 Semiconductors have negative temp. coefficient (-α)

 Referring to fig 3-6, applying similar triangle we obtain

 This expression may be rewritten to solve for the resistance, R₂ at any temp t₂ as follows

2 1 2 1

R

R

t



T



t



T

t

T

R

R

t

T







 Derived formula of R₂ in terms of α





2 1 1 2 1

1 1

1

(

)

where:

temperature coefficient of t













Examples:

 The tungsten filament in an incandescent lamp has a resistance of 9.8Ω at a room temp of 200 _{C and a}

resistance of 132Ω at normal operating temp. Using the temp coefficient formula for resistance calculate the temperature of the heated filament.

 A platinum coil has a resistance of 3.146Ω at 400 C and 3.767Ω at 1000 _{C. Find the resistance at 0}0 _{C and}

the temp coefficient at 400 _C.

 Two coils connected in series have a resistance of 600Ω and 300Ω with temp coefficient of 0.1% and 0.4% respectively at 200 _{C. Find the resistance of the}

combination at a temp of 500 _{C. What is the effective}

Seatwork

 An aluminum wire has a resistance of 20Ω at room temp. (200 _{C). Calculate the resistance of the same}

wire at temp of -40o _{C, 100}o _{C and 200}o _C.

 Tungsten wire used as filament in incandescent light bulbs. Current in the wire causes the wire to reach extremely high temp. Determine the temp. of the filament of a 100W light bulb if the resistance at room temp. is measured to be 11.7Ω and when the light is on, the resistance is determined to be 144Ω  Calculate the temp coefficient of resistance of

aluminum at 20 _{C. Using the value obtained,}

at 620 _{C if its resistance at 2}0 _{C is 7.5 Ω.}

 The resistance of electric device is 46 Ω at 250 C. If the temp coefficient of resistance of the material is 0.00454 at 200 _{C, determine the temp. of the device}

Rules in Sizing a Conductor

1. Every change of three gage number changes the

circular-mil area and resistance in the ratio of 2 to 1 or 1 to 2, depending upon the direction of the

change.

2. Every change of 10 gage numbers changes the

circular-mil area and resistance in the ratio of 10 to 1 or 1 to 10, depending upon the direction of the

change

3. Every change of one gage number changes the

circular-mil area and resistance in the ratio of 1 ¼ to 1 or 1 to 1 1/4 , depending upon the direction of the change

4. A No. 10 wire may be assumed, for practical

purposes, to have a diameter of 100 mils, an area of 10, 000 cir mils, and a resistance of 1 ohm per

1,000ft.

5. A No.5 wire has a weight of 100lb per 1,000ft;

moreover, for every change of three gage numbers

the weight is halved or doubled , depending upon the direction of the change

6. A No.15 wire has 100ft per lb (very nearly);

moreover, for every change of three gage numbers the number of feet per pounds is doubled or halved,

depending upon the direction of the change.

7. Every change of 10 gage numbers changes the pounds per 1,000ft and the feet per pound in the ratio of 10 to 1, depending upon the direction of the change

Example

 Without consulting the wire table, determine the following data for a No.17 copper wire: (a) circular mils; (b) resistance per 1,000ft; (c) pounds per