E12 And E24 Values

E12 and E24 values If you have any experience of building circuits, you will have noticed that resistors commonly have values such as 2.2 , 3.3 , or 4.7 and are not available in equally spaced values 2 ,3 ,4 ,5 and so on. Manufacturers don't produce values like these - why not? The answer is partly to do with the fact that resistors are manufactured to a percentage accuracy. Look at the table below which shows the values of the E12 and E24 series: E12 series 10% tolerance

E24 series 5% tolerance

10

10 11

12

12 13

15

15 16

18

18 20

22

22 24

27

27 30

33

33 36

39

39 43

47

47 51

56

56 62

68

68 75

82

82 91

Resistors are made in multiples of these values, for example, 1.2 1.2 , 12 , 120 and so on.

, 12

, 120

,

Consider 100 and 120 , adjacent values in the E12 range. 10% of 100 is 10 , while 10% of 120 is 12 . A resistor marked as 100 could have any value from 90 to 110 , while a resistor marked as 120 might have an actual resistance from 108 to 132 . The ranges of possible values overlap, but only slightly. Further up the E12 range, a resistor marked as 680 might have and actual resistance of up to 680+68=748 , while a resistor marked as 820 might have a resistance as low as 820-82=738 . Again, the ranges of possible values just overlap. The E12 and E24 ranges are designed to cover the entire resistance range with the minimum overlap between values. This means that, when you replace one resistor with another marked as a higher value, its actual resistance is almost certain to be larger. From a practical point of view, all that matters is for you to know that carbon film resistors are available in multiples of the E12 and E24 values. Very often, having calculated the resistance value you want for a particular application, you will need to choose the nearest value from the E12 or E24 range.

Colour code How can the value of a resistor be worked out from the colours of the bands? Each colour represents a number according to the following scheme: Number

Colour

0

black

1

brown

2

red

3

orange

4

yellow

5

green

6

blue

7

violet

8

grey

9

white

The first band on a resistor is interpreted as the FIRST DIGIT of the resistor value. For the resistor shown below, the first band is yellow, so the first digit is 4:

The second band gives the SECOND DIGIT. This is a violet band, making the second digit 7. The third band is called the MULTIPLIER and is not interpreted in quite the same way. The multiplier tells you how many noughts you should write after the digits you already have. A red band tells you to add 2 noughts. The value of this resistor is therefore 4 7 0 0 ohms, that is, 4 700 , or 4.7 . Work through this example again to confirm that you understand how to apply the colour code given by the first three bands. The remaining band is called the TOLERANCE band. This indicates the percentage accuracy of the resistor value. Most carbon film resistors have a gold-coloured tolerance band, indicating that the actual resistance value is with + or - 5% of the nominal value. Other tolerance colours are: Tolerance

Colour

±1%

brown

±2%

red

±5%

gold

±10%

silver

When you want to read off a resistor value, look for the tolerance band, usually gold, and hold the resistor with the tolerance band at its right hand end. Reading resistor values quickly and accurately isn't difficult, but it does take practice!

Electrical Resistance The Physics Hypertextbook™ © 1998-2008 by Glenn Elert -- A Work in Progress All Rights Reserved -- Fair Use Encouraged prev | up | next

Discussion introduction Yech! What a mess this is. Conduction: S. Gray, 1729 -- Resistance: Georg Simon Ohm, 1827. Regular version … I∝V V I= ⇒ R

V = IR ⇒

R=

V I

Symbology … quantity: rsistance R unit: ohm [Ω] Georg Simon Ohm (1787-1854) Germany •

Fancy version (the magnetohydrodynamic theory version?) … J∝E J = σE = − σ ∇V &

1 ρ= ⇒ σ

E J = or ρ

E = ρJ

Symbol hell … quantity: conductivity σ (not to be confused with surface charge density) unit: siemens [S] Werner Siemens (1816-1892) Germany • quantity: resistivity ρ (not to be confused with volume charge density) unit: ohm meter [Ωm = S−1] •

Ohm's law isn't a very serious law. It's the jaywalking of physics. Sensible materials and devices obey it, but there are plenty of rogues out there that don't. Resistor Color Code first & second bands

third band

fourth band

(first & second digits) black 0 brown 1 red 2 orange 3 yellow 4 green 5 blue 6 violet 7 gray 8 white 9

(multiplier) black 1 brown 10 red 100 orange 1,000 yellow 10,000 green 100,000 blue 1,000,000 silver 0.01 gold 0.1

(tolerance) none ±20% silver ±10% gold ±5%

Bad Booze Rots Our Young Guts But Vodka Goes Well. Better Build Roof Over Your Garage Before Van Gets Wet.

solids Resistance and resistivity. Factors affecting resistance in a conducting wire. R=

ρℓ A

Conductors vs. insulators Best electrical conductors: silver, copper, gold, aluminum, calcium, beryllium, tungsten Resistivity and conductivity are reciprocals. Conductivity in metals is a statistical/thermodynamic quantity. Resistivity is determined by the scattering of electrons. The more scattering, the higher the resistance. σ=

ne2ℓ mevrms

Where … σ n e me vrms ℓ

= electrical conductivity = density of free electrons = charge of an electron = mass of an electron = root-mean-square speed of electrons = mean free path length

Graphite

Where does this idea belong? Nichrome was invented in 1906, which made electric toasters possible. Conducting polymers. Resistivity of Selected Materials (~300 K) (Note the difference in units between metals and nonmetals.) metals ρ (nΩ·m) nonmetals ρ (Ω·m) aluminum 26.5 aluminum oxide (14 °C) 1 × 1014 brass 64 aluminum oxide (300 °C) 3 × 1011 chromium 126 aluminum oxide (800 °C) 4 × 106 copper 17.1 carbon, amorphous 0.35 gold 22.1 carbon, diamond 2.7 iron 96.1 carbon, graphite 650 × 10−9 lead 208 germanium 0.46 lithium 92.8 pyrex 7740 40,000 mercury (0 °C) 941 quartz 75 × 1016 manganese 1440 silicon 640 nichrome 1500 silicon dioxide (20 °C) 1 × 1013 nickel 69.3 silicon dioxide (600 °C) 70,000 palladium 105.4 silicon dioxide (1300 °C) 0.004 platinum 105 water, liquid (0 °C) 861,900 plutonium 1414 water, liquid (25 °C) 181,800 silver 15.9 water, liquid (100 °C) 12,740 solder 150 steel, plain 180 steel, stainless 720 tantalum 131 tin (0 °C) 115 titanium (0 °C) 390 tungsten 52.8 uranium (0 °C) 280 zinc 59 temperature The general rule is resistivity increases with increasing temperature in conductors and decreases with increasing temperature in insulators. Unfortunately there is no simple mathematical function to describe these relationships. The temperature dependence of resistivity (or its reciprocal, conductivity) can only be truly understood with quantum mechanics. In the same way that matter is an assembly of microscopic particles called atoms and a beam of light is a stream of microscopic particles called photons, thermal vibrations in a solid are a swarm of microscopic particles called phonons. The electrons are trying to drift toward the positive terminal of the battery, but the phonons keep crashing into them. The random direction of these collisions disturbs the attempted organized motion of the electrons against the electric field. The deflection or scattering of electrons with phonons is one source of resistance. As temperature rises, the number of phonons increases and with it the

likelihood that the electrons and phonons will collide. Thus when temperature goes up, resistance goes up. For some materials, resistivity is a linear function of temperature. ρ = ρ0(1 + α(T − T0))

The resistivity of a conductor increases with temperature. In the case of copper, the relationship between resistivity and temperature is approximately linear over a wide range of temperatures. For other materials, a power relationship works better. ρ = ρ0(T ∕ T0)μ

The resistivity of a conductor increases with temperature. In the case of tungsten, the relationship between resistivity and temperature is best described by a power relationship. see also: superconductivity magnetoresistance photoconductivity

liquids electrolytes

gases dielectric breakdown plasmas

microphones A carbon microphone is a backward nothing Microphones and How They Work sounds produce which cause type changes in … changes in … carbon granule density resistance condenser plate separation capacitance dynamic coil location flux

which result in changes in … voltage voltage voltage

piezoelectric

compression

polarization

voltage

Summary •

bullet

Problems practice 1. A standard 60 W 120 V light bulb has a tungsten filament that is 53.3 cm long and 46 μm in diameter. a. What is the light bulb's operating resistance? b. Determine the cross sectional area of the filament. c. Determine the resistivity of tungsten. d. How does the resistivity calculated above compare to the value quoted in standard reference tables? Why are these two values so different? e. How can a 53.3 cm filament fit into a light bulb that is only a few centimeters wide? Solutions …

2.

2. 3.

f. Answer it. g. Answer it. h. Answer it. i. Answer it. j. Answer it. Write something. o Answer it. Write something. o Answer it. Write something completely different. o Answer it.

conceptual 1.

Given a wire with a resistance R, what will be the new resistance if … a. the wire is cut in half and only one half is used to conduct electricity, b. the wire is folded in half and both halves are used to conduct electricity? 2. A tungsten rod and an aluminum rod have the same length and resistance. a. What is the ratio of the cross sectional area of the tungsten rod to the aluminum rod? b. What is the ratio of the diameter of the tungsten rod to the aluminum rod?

numerical 1. A power transmission cable is composed of 37 strands of aluminum wire, each 4.0 mm in diameter. The cable is 100 m long and is used to deliver 300 A of current to a commercial power user. Determine … a. the total cross sectional area of the cable, b. the resistance of the cable, and c. the power lost in the cable before it reaches the user. 2. You have decided to build an 800 W 120 V, two slot toaster for your mother. a. How much 25 gauge (0.455 mm diameter) nichrome wire will you need? b. Approximately how many times should the wire be folded so that both sides of each slice of bread will be toasted evenly? (Assume that a typical slice of bread is a 12 cm square.) 3. Which dry pasta offers more resistance to the flow of electricity? o spaghetti lunghi, an extra long variety of string-like pasta, 50 cm long, 1.55 mm in diameter o capelli d'angelo: a very fine hair-like pasta, 25 cm long, 0.965 mm in diameter Assume that both pastas are made from durum semolina wheat prepared under identical conditions. What is the resistance of a roll of 100 pennies? To simplify calculations, assume the pennies are made entirely of copper. o If you use American pennies, assume they were minted before 1982. Pennies minted after 1982 have a zinc core in a copper jacket. o If you use Canadian pennies, assume they were minted before 1996. Pennies minted after 1996 have a zinc or nickel-steel core in a copper jacket. 3. An electric power distribution cable is made of multiple strands of aluminum and steel wire as shown in the diagram below. 2.

The diameters are 2.00 mm and 1.33 mm for the aluminum and steel strands, respectively. Determine the resistance for one kilometer of this cable … 4.

a. b.

assuming that each strand is straight assuming that each aluminum strand is wound with a 16° pitch

4. What dimensions should a 50 nm aluminum film have to yeld a resistance of 40 Ω?

statistical 1. zero-the-meters.txt A group of students were assigned the task of testing various off the shelf

resistors. They were told to gradually increase the voltage across the resistor and measure both the voltage and the current. Unfortunately, they wired the meters in backward and forgot to zero them before taking measurements. The situation is not all that bad, however. Using a spreadsheet program or other similar data analysis software … a. repair the voltage and current data to compensate for the students' errors, b. construct a graph from the repaired voltage and current data, and c. determine the resistance of the resistor to the nearest ohm.

Resources •

•

conducting polymers o 2000 Nobel Prize in Chemistry, "for the discovery and development of conductive polymers" miscellaneous o Toaster Museum Foundation

/http://hypertextbook.com/physics/electricity/resistance -/http://www.pdfcoke.com/doc/17801