Created it, 05/10/15
Update it, 05/10/28
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LAW OF JOULE
We now know the relation which binds the tension and the current to the electric output and the power consumption to produce heat.
However, we know that this production of heat is due to the resistance met by the electric charges of the current during their displacement through a driver. The power consumption thus depends directly on the current and the resistance which it meets.
There is indeed a relation which binds these two sizes to energy. For better including/understanding their action with respect to energy, it is first of all necessary to refer to the power consumption each second in other words with the electric output.
This relation, stated by the English physicist (eh yes!) James Prescott JOULE (1818-1889), is called law of Joule. As we already saw, this physicist also gave his name to the measuring unit of energy like to the heating effect of the current called Joule effect.
The law of Joule can be stated as follows :
The electric output consumed by a resistance to produce heat is obtained by multiplying the value of resistance by the square of the current which crosses it :
If resistance and the current are measured respectively in Ohm and Amp, the power is expressed in Watt.
The law of Joule can result from that already seen: P = V x I. Indeed, of the law of Ohm, the tension V at the boundaries of a resistance is given by V = R x I. If we replace V by this product, we obtain :
We can make two observations starting from this formula.
First is that the consumption increases in the same proportions as resistance, for example if double resistance, the power also doubles.
If it is not the same when the current increases, indeed if for example the double current, the power is multiplied by 4.
We can thus affirm that :
The electric output P increases according to the square of the current.
If in the formula P = V x I we not replace V by his value according to the law of Ohm but I, that is to say I = V / R we find a new formula of the power :
If R double, the power P decreases by half while if V doubles, the power is multiplied by 4.
We can deduce that :
The electric output P increases according to the square of the tension.
We are able now to calculate the power and thus the electric power consumed to produce heat by knowing two of the three electric quantities that the its tension, the current and the resistance whose operation depends on any electric circuit.
But which quantity of heat does one obtain by consuming a given energy ?
The answer was brought per JOULE following the many experiments which it carried out.
First of all, to measure a quantity of heat, it is necessary to give him a clean measuring unit.
To carry out this calculation, the fact is exploited that when a body receives heat, its temperature increases.
Since this increase in heat is measurable using a thermometer, it is possible to deduct the quantity from heat received by the body.
Thus the measuring unit of quantity of heat called was defined Calorie (Cal symbol). It was agreed that :
The calorie is the quantity of heat necessary to raise of a Celcius degree (for example of 20°C at 21°C) the temperature of one gram water.
For the quantities of heat generally met in practice, one uses the kilogram calorie (symbol kCal), this multiple of the calorie is defined while referring either to a gram of water but to one kilogram of water. The kilogram calorie is thousand times larger than the calorie. One also uses megacal (symbol th) which is worth 1 million calories (either a mégacalorie).
Joule quantified its experiments in a precise way by using a driver of known resistance traversed by a known current and this during a given time. It determined that for each joule of power consumption, it obtained 0,238 cal. This quantity of heat is called equivalent thermics of energy. Conversely for a quantity of heat of 1 calorie, one needs 4,185 Joules.
RESISTANCES
AND POWERLet us see now how the new electric quantities that are the power and energy apply to an element such as a resistance.
Let us take again the circuit used during the analysis of the connections series and represented figure 2.
As the provided pile a tension of 9 V while the lamp requires only 6 V, we had to connect in series with the lamp a resistance which cause a voltage drop of 3 V. This given resistance produces heat by consuming electric power. This energy is consumed unnecessarily since the role of the circuit is not to produce heat but to produce light by the means of the lamp and not by the reddish glow of resistance.
Power consumption by resistance to each second, i.e. the electric output must be regarded as dissipated power since it is not used in one way or another. For this reason, resistances are called: elements dissipating of the power.
Now let us try to calculate the power dissipated by resistance R (either PR) and that dissipated by the lamp L (PL). We suppose that the current circulating in the circuit of figure 2 has an intensity of 0,05 A (50mA). This current corresponds to the current absorptive by the lamp.
By applying the formula P = V x I, we obtain the values of PR and PL.
The same values can be obtained by applying the other relations that we know is :
In these cases, it is necessary before to determine the value of resistance R and that of the filament of L by applying the law of Ohm.
What gives for two powers PR and PL :
Resistance R will have to thus be able to dissipate a power at least equal to 150 MW. A resistance is electronic component characterized not only by its ohmic value but also by its maximum power which it can dissipate without risk of destruction.
There are thus resistances which, although having the same resistive value dissipate very different powers, which go from fractions of Watt to several tens of Watts. They are different by their dimensions or the materials with which they are manufactured.
Thus the technique helping, the manufacturers manage to decrease dimensions of resistances while preserving strong powers.
Increase in temperature produced by the dissipation of the power in heat, drift an important fact. Previously, it was known as that the higher the temperature of a body is, the more agitation of its atoms is important, this is true also for resistances and in general for all the drivers.
But if the atoms are agitated with more amplitude, it is easier to them to be on the course of the loads constituting the electrical current which circulates in the driver. We can then deduce from it that:
By increasing the temperature of a driver, its electric resistance increases. This increase in resistance is different from one material to another.
For each one of them, we can know this increase using the temperature coefficient which indicates by how much increases a resistance by 1 Ohm when its temperature increases 1° C and this for a given material.
For resistances, the manufacturers employ materials with low temperature coefficient so that their resistive value does not undergo significant variation, even if the temperature reaches high values.
In the next lesson, we will become acquainted with another fundamental component of the electric circuits: the condenser. But first of all, we will treat few simple concepts of mathematics in order to include/understand well and how to calculate a condenser for example, among others ?
See mathematical, (1st lesson) before among taking the lesson of the condensers.
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