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Authored by Ian C. Purdie VK2TIP
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Ohms law, sometimes more correctly called Ohm's Law, named after Mr. Georg Ohm, mathematician and physicist b. 1789 d. 1854  Bavaria, defines the relationship between power, voltage, current and resistance. These are the very basic electrical units we work with. The principles apply to a.c., d.c. or r.f. (radio frequency).
Ohms Law is the a foundation stone of electronics and electricity. These formulae are very easy to learn and are used extensively throughout our tutorials. Without a thorough understanding of "ohms law" you will not get very far either in design or in troubleshooting even the simplest of electronic or electrical circuits.
Would you believe I receive email from fools who assert "all this mathematical rubbish over ohms law is totally unecessary"  actually I've 'cleaned' that up a bit. They are the true nonbelievers, the guaranteed nonachievers of the future.
Mr. Ohm (that is his 'real'name) [Georg Ohm b 1789 d 1854  Bavaria] established in the late 1820's that if a voltage [later found to be either A.C., D.C. or R.F.] was applied to a resistance then "current would flow and then power would be consumed".
Some practical every day examples of this very basic rule are:
Radiators (electric fires), Electric Frypans, Toasters, Irons and electric light bulbs.
Figure 1  ohms law power consumption through a resistance
The radiator consumes power producing heat for warmth, the frypan consumes power producing heat for general cooking, the toaster consumes power producing heat for cooking toast, the iron consumes power producing heat for ironing our clothes and the electric light bulb consumes power producing heat and more important light for lighting up an area. A further example is an electric hot water system. All are examples of ohms law at its most basic.
One VERY important point to observe with ohms law in dealing with some of those examples is that quite often there are two types of resistance values. "Cold Resistance" as would be measured by an ohmmeter or digital multimeter and a "Hot Resistance". The latter is a phenomenem of the material used for forming the the resistance itself, it has a temperature coefficient which often once heated alters the initial resistance value, usually dramatically upward.
A very good working example of this is an electric light bulb. "what may be termed a bright idea " .
I just measured the first light bulb with my digital multimeter. It showed zero resistance, in fact open circuit. That's what you get, when for safety reasons you put a burnt out bulb back into an empty packet and a "neat and tidy" wife puts it back into the cupboard. .
O.K. here's a "goodie" and, it's labelled "240V  60W", it measured an initial "cold resistance" of 73.2 ohms. Then I measured our actual voltage at a power point as being 243.9V A.C. at the moment [note: voltages vary widely during a day due to locations and loads  remember that fact  also for pure resistances, the principles apply equally to A.C. or D.C.].
Using the formula which you will learn below, the resistance for power consumed should be R = E^{2} / P OR R = 243.9^{2} / 60W = 991 ohms
That is 991 ohms calculated compared to an initial reading of 73.2 ohms with a digital multimeter? The reason? The "hot" resistance is always at least ten times the "cold" resistance.
Now through our "Electronics Q&A" I asked people around the world to perform similar measurements for me. The results were substantially the same even allowing for the different AC voltage levels in different countries.
Another example is what is most often the biggest consumer of power in the average home. The "electric jug", "electric kettle" or what ever it is called in your part of the world. Most people are astonished by that news. My "electric kettle" is labelled as "230  240V 2200W". Yes 2,200 watts! That is why it boils water so quickly. [As a former plumber among my many qualifications, I could give you the formula of power required to boil water in a certain space of time, but I won't  alright, it's at the VERY, VERY bottom of this page.]
To make it much easier for you I have put all the relevent formulas together for you here complete with worked examples of ohms law. You will notice the formulas share a common algebraic relationship with one another.
For the worked examples voltage is E and we have assigned a value of 12V, Current is I and is 2 amperes while resistance is R of 6 ohms. Note that "*" means multiply by, while "/" means divide by.
For voltage [E = I * R] E (volts) = I (current) * R (resistance) OR 12 volts = 2 amperes * 6 ohms
For current [I = E / R] I (current) = E (volts) / R (resistance) OR 2 amperes = 12 volts / 6 ohms
For resistance [R = E / I] R (resistance) = E (volts) / I (current) OR 6 ohms = 12 volts / 2 amperes
Notice how simple it is?
Now let's calculate power using the same examples.
For power P = E^{2} / R OR Power = 24 watts = 12^{2} volts / 6 ohms
Also P = I^{2} * R OR Power = 24 watts = 2^{2} amperes * 6 ohms
Also P = E * I OR Power = 24 watts = 12 volts * 2 amperes
That's all you need for ohms law  remember just two formulas:
for voltage E = I * R and;
for power P = E^{2} / R
You can always determine the other formulas with elementary algebra.
Knowing two quantities in ohms law will always reveal the third value. I suggest you print these formulas out and paste them onto scrap cardboard to keep your ohms law as a handy reference until you are quite familiar with it.
If you prefer I've added [2nd May, 2001] a graphical representation here in figure 2.
See further below for related topics and links including FREE downloads.
Figure 2  ohms law graphical chart
If you are involved in electronics then consider joining our "electronics Questions and Answers" news group to ask your question there as well as sharing your thorny questions and answers. Help out your colleagues!.
The absolute fastest way to get your question answered and yes, I DO read most posts.
This is a mutual help group with a very professional air about it. I've learn't things. It is an excellent learning resource for lurkers as well as active contributors.
electron theory
voltage
current
resistance
resistor colour code chart
NASA Ohms Law Page
Georg Ohm's Story
Ohms Law Calculator
"Ohms Law Calculator was designed to make life simpler for electronics students, teachers, technicians and hobbyists alike. Ohms Law Calculator will calculate Power (Watts), Current (Amps), Voltage (Volts) and Resistance (Ohms) when any two of the above variables are known. Just enter two of the values and the program will give you the third".
Ohms law calculator based on scripts originally written by Bill Bowden
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Updated 27th September, 2001