Created it, 05/10/15
Update it, 05/11/01
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MATHEMATICAL FORMS 2 “3rd part”
1. - ELECTRONICS
This form is devoted to the electric quantities examined in the first theories. Generally, the statements which precede the fundamental formulas are drawn directly from the theories quoted between brackets after each statement. It can be useful or even necessary to re-examine in the theories the concepts which are at the base of the mathematical formulas and their applications. This form is devoted to the electric quantities examined in the first theories. Generally, the statements which precede the fundamental formulas are drawn directly from the theories quoted between brackets after each statement. It can be useful or even necessary to re-examine in the theories the concepts which are at the base of the mathematical formulas and their applications.
In the forms of electrical engineering, as was already the case in the forms devoted to the geometry and physics, one uses the measuring units of system S.I, or their multiples and submultiples own.
Some of these measuring units were already presented in the theories, when the covered subject required it.
FORMULATE 61 - Calculation of the intensity
of current knowing the quantity of electricity which crosses the section of a
driver in a given time.
Statement : The intensity of current expressed in amps, is given by the quantity of electricity, expressed in coulombs, which crosses during each second a section of the driver.
To translate into formula the statement precede, it is enough to observe that the quantity of electricity passing in one second through the section of a driver, is obtained by dividing the quantity of electricity passing in the interval of time considered by last time.
I = Q / t
Example :
FORMULATE 62 -
Calculation of the quantity
of electricity which crosses the section of a driver in a given time, knowing
the intensity of the current.
(This formula is drawn from formula 61).
FORMULATE 63 - Calculation of time necessary
so that a quantity of electricity given crosses the section of a driver,
intensity of the current being known.
(This formula is drawn from formula 61).
FORMULATE 64 - Calculation of the resistance
of a driver, knowing the resistivity of material, the length and the section of
this driver.
Statement : The resistance of a driver, expressed in ohms, is obtained by multiplying the resistivity expressed out of microhmmeters, by the length expressed in meters, the whole divided by the section expressed into square millimetres.
R = pl / S
Example :
Data relating to a copper driver : p
0,0176 µW.m (resistivity of copper
;
to see table III, figure 1) ; I
= 100 m ; S = 0,7854 mm2.
0,0176 x 100 / 0,7854 = 1,76 / 0,7854 = 2,24 WOBSERVATION : in the central column of table III (figure 1) the values of resistivity of the principal drivers of electricity are indicated; these values are expressed out of microhmmeters (µW.m), submultiple of the measuring unit ohmmeter (W.m).
Sometimes one uses in the technical handbooks the symbol W.mm2 / m (square ohm-millimetre per meter) which with the same significance as µW.m.
One uses sometimes, for a greater simplicity of calculation, the submultiple W.cm (ohm-centimetre).
Moreover, in the same paragraph, one expressed the length of the driver in (cm) and not in (m) and the section in cm2 and not in mm2.
However, that it is in the preceding example or those of the mathematical lessons entitled “the formulas”, the measuring units in such way were chosen that at the end of calculations, the resistance of the driver is expressed in ohms.
The unit of resistivity ohmmeter (W .m) is not used in practice to indicate the resistivity of the drivers.
FORMULATE 65 -
Calculation length of a
driver knowing resistance, the section of the driver and the resistivity of
material.
(This formula is drawn from formula 64).
Data relating to a driver of nickel-chromium: R = 10 W ; S = 0,7854 mm2 ; p = 1,04 µW.m (resistivity of nickel-chromium; table III, figure 1).
FORMULATE 66 - Calculation of the section of
a driver knowing the resistivity of material, the length and the resistance of
this driver.
(This formula is drawn from formula 64).
Data relating to a constantan driver : p = 0,5 µW.m (resistivity of constantan; table III, figure 1); I = 100 m; R = 63,66 W
FORMULATE 67 -
Calculation of the
resistivity of material of a driver knowing the section, the resistance and the
length of this driver.
p = SR / I
(This formula is drawn from formula 64).
Data relating to an electric unknown material driver :
OBSERVATION : so that the result obtained represents indeed the resistivity of material, it is necessary that its composition is homogeneous.
FORMULATE 68 - Calculation of the section of
a thread-like driver knowing the diameter.
0,7854 d2
(This formula is an application of formula 19 of form 1, entitled “geometry”).
0,7854 x 0,12 = 0,7854
x 0,01 = 0,007854 mm2OBSERVATION : In the first two left-hands column of table IV (figure 2), one respectively indicated the values of the diameter and the section of wire of nickel-chromium, constantan and manganin, materials frequently used in the electric installations. If the diameter of a wire is equal to the one of the values indicated in the first column, one can determine the value of the corresponding section by reading it directly in the second column.
The diameters are expressed in millimetres and the sections in square millimetres.
FORMULATE 69 -
Calculation of the diameter
of a wire knowing the value of its section.
OBSERVATION : If the section of the wire corresponds roughly to the one of the values indicated in the second column, one can take as value of the diameter corresponding that deferred in the first column.
For example, for a value of section equal to 0,28 mm2 (or 0,283 mm2 or 0,28274 mm2), one will take the diameter 0,60 mm which gives in table IV (figure 2) a section of 0,2827 mm2
FORMULATE 70 -
Calculation of the
conductance of an electric driver, knowing its resistance.
Statement : The conductance, expressed in mho, is the reverse of the resistance expressed in ohms.
To translate into formula the preceding statement, it is enough to remember that one obtains the reverse of a size by dividing number 1 by the value of the size considered.
FORMULATE 71 - Calculation of the resistance
of a driver knowing its conductance.
(This formula is drawn from formula 70).
FORMULATE 72 - Calculation of the
conductivity of a driver knowing its resistivity.
Statement : The conductivity, expressed in mho per meter, is equal contrary to the resistivity expressed in ohmmeters.
OBSERVATION : If the resistivity is expressed out of microhmmeter (see formula 64), by applying formula 72, one obtains the value of the conductivity expressed in méga mho per meter (MS / m).
The méga mho per meter is indicated by the symbol m / W.mm2 (meter per square ohm-millimetre).
FORMULATE 73 - Calculation of the
resistivity of a driver knowing its conductivity.
(This formula is drawn from formula 72).
(Value deferred in table III, figure 1).
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