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Resistors

Posted on : Sat , 12 2013 by : virusi

Some Historical Data :


GeorgSimonOhm Georg Simon Ohm was born on March 16, 1789 in the city of Erlangen in Bavaria, which is now Germany. He died on July 6, 1854 in Munich, Bavaria, Germany. Ohm came from a protestant family. Although his parents had not been formally educated, Ohm’s father was a rather remarkable man who had educated himself to a high level and was able to give his sons and excellent education through his own teachings.
In 1805 Ohm entered the University of Erlangen but he became rather carried away with student life. Rather than concentrate on his studies, he spent much time dancing, ice skating and playing billiards. Ohm’s father, angry that his son was wasting the educational opportunity that he himself had never been fortunate enough to experience, demanded that Ohm leave the university after three semesters. Ohm was sent to Switzerland where, in September 1806, took up a post as a mathematics teacher in a school in Gottstadt bei Nydau. Ohm continued working for several other Universities throughout Bavaria and published several papers. In two important papers in 1826, Ohm gave a mathematical description of conduction in circuits modeled of Fourier’s study of heat conduction. These papers continue Ohm’s deduction of results from experimental evidence and, particularly in the second paper, he was able to propose laws which went a long way to explaining results of others working on galvanic electricity. This second paper certainly was a first step in a comprehensive theory which Ohm was able to give in his famous book published in the following year called “Die Galvanische Kette, mathematisch bearbeitet” (1827) which means “The Galvanic Chain, Mathematically worked” and contained what is now know as the ‘Ohm Laws’ and they are for voltage: E=I*R, current: I=E/R, resistance: R=E/I, power: P=E 2/R, also P=I2*R or P=E*I.
At the time Ohm started to write his papers he was on a one year sabbatical doing his research at the Jesuit Gymnasium of Cologne.
In 1849 Ohm took up a post in Munich as curator of the Bavarian Academy’s physical cabinet and began to lecture at the University of Munich. Only in 1852, two years before his death, did ohm achieve his lifelong ambition of being appointed to the chair of physics at the University of Munich.


Resistor Symbol and Markings :


The symbol for a resistor is shown in the following diagram (The ‘box’ symbol for a fixed resistor is popular in the UK and Europe. A ‘zig-zag’ symbol is used in America and Japan) :

the_resistor_symbol
Fig.1 the resistor symbols of different kind of resistors
The unit for measuring resistance is the OHM. (the Greek letter Ω – called Omega). Higher resistance values are represented by “k” (kilo-ohms) and M (meg ohms). For example, 120 000 Ω is represented as 120k, while 1 200 000 Ω is represented as 1M2. The dot is generally omitted as it can easily be lost in the printing process. In some circuit diagrams, a value such as 8 or 120 represents a resistance in ohms. Another common practice is to use the letter E for resistance in ohms. The letter R can also be used. For example, 120E (120R) stands for 120 Ω, 1E2 stands for 1R2 etc.
resistors
Resistance value is marked on the resistor body. Most resistors have 4 bands. The first two bands provide the numbers for the resistance and the third band provides the number of zeros. The fourth band indicates the tolerance. Tolerance values of 5%, 2%, and 1% are most commonly available. Let’s take a look at an example:
ColorCodedExample
Fig. 2 Resistance calculation of the color coded resistor.
As you can see from the example above the first 2 bands will form the number 47(yellow band is 4 and the Violet one is 7). This number is multiplied by 100 and the result will be 4700 which is our resistor value. The last band will indicate the resistor tolerance which is 5 %( 4th band has the color gold color). What is the resistor tolerance? Tolerance indicates how much the measured value of a resistance is different from its theoretical value, and it is calculated using percentages, if you want to know the exact value of the resistor you will have to measure its value with ohmmeter. Let’s take our resistor and calculate which is the maximum and minimum resistor variation.

Maximum resistor value = 4700 + (4700*0.05) = 4700 + 235 = 4935 ohms

Minimum resistor value = 4700 – (4700*0.05) = 4700 – 235 = 4465 ohms

As you can see our resistor value can vary from 4935 ohms to 4435 ohms, so if in your application you need a very precise resistor you will have to chose a resistors with a small tolerance value.


Theory of operation :


Let’s take a look how the current, voltage ant the power are calculated for a resistor. The behavior of an ideal resistor is dictated by the relationship specified by Ohm’s law:

\large V = I * R
(1)
Ohm’s law states that the voltage (V) across a resistor is proportional to the current (I), where the constant of proportionality is the resistance (R). Equivalently, Ohm’s law can be stated:
\large I = \frac{V}{R}
(2)
At any instant of time, the power P consumed by a resistor of resistance R (ohms) is calculated as:
\large P=I^2*R=I*V= \frac{V^2}{R}
(3)
Where V (volts) is the voltage across the resistor and I (amps) is the current flowing through it. The first form is a restatement of Joule’s first law. Using Ohm’s law, the two other forms can be derived. This power is converted into heat which must be dissipated by the resistor’s package so it is important to pick up an resistor that can consume enough power because if you will chose a resistor with a lower power consumption in you scheme your resistor will be damaged. Let’s take our 4700(4.7 k) ohm resistor and calculate the voltage, current and the power dissipated by this resistor.
As you know the current that will flow throw a resistor is equal to:
\large I= \frac{V}{R} = \frac{5V}{4700Ω}=0.00106A  or  1.06 mA
(4)
We have assumed that the voltage which is flowing throw the resistor is 5V and as you can see that the current that will flow throw this resistor will be very small this means that if we want to increase the current that will flow throw this resistor we can increase the input voltage or decrease the resistor value.
Now let’s calculate the power that is consumed by a resistor as you already know the power consumed by a resistor equals to:
\large P = \frac{V^2}{R} = \frac{5^2 V}{4700Ω} = \frac{25V}{4700Ω} = 0.0053W or  5.3 mW
(5)
As you can see from the equation above the power consumed by the 4700 ohm resistor at a 5V will be equal to 0.0053W so will have to take this into account when choosing a resistor for your schematic because if you will chose a resistor that can consume less power than the one flowing it will be damaged.
More formulas that can be derived from the one mentioned before (Ohm’s law and Joule’s first law) are illustrated in the image below:
P V I R formulas


Practical Example :


If you don’t see the example below than you should follow this steps:

– In your browser allow Java SE 7.

– Lower you java security settings (Go to Control Panel >> Java >> Security and set the security level to medium) .

– Edit Site List (Go to Control Panel >> Java >> Security and click on Edit Site List… and add eagerlearning.org in the list).

Sorry, you need a Java-enabled browser to see the simulation.
It is a simple example in which we have connected a 5V source and 100 ohm resistance and you have 3 diagrams. 1 is showing the amount of current that is flowing throw the resistor. 2 diagram is showing the amount of voltage that is flowing throw the resistor. 3 diagram is showing the power that is consumed by the resistor. If you want to change the resistor value or the Voltage from the source you should double click on the object and insert a value.

Last updated on Sat , 07 2015
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