This form is devoted to the electrical quantities examined in the first theories. In general, the statements that precede the basic formulas are taken directly from the theories cited in parentheses after each statement. It may be useful or even necessary to revisit in theories the notions underlying mathematical formulas and their applications.
In the electrotechnical forms, as was already the case in the geometry and physics forms, the SI units of the system, or their own multiples and submultiples, are used.
Some of these units of measurement have already been presented in theories, when the subject treated asked for it.
FORMULA 61 -
Calculation of the current intensity knowing the amount of electricity that crosses the section of a conductor in a given time.
Enunciated :
The current intensity expressed in amperes, is given by the amount of electricity, expressed in coulombs, which crosses during each second a section of the conductor.
In order to translate the above statement into a formula, it suffices to observe that the quantity of electricity passing in one second through the section of a conductor is obtained by dividing the quantity of electricity passing in the time interval. considered by the time spent.
I = Q / t
I = intensity of the current in A (ampere)
Q = quantity of electricity in C (coulomb)
t = time in seconds
Example :
Data : Q = 10 C ; t = 4 s
Intensity of the current : I = 10 / 4 = 2,5 A.
FORMULA 62 - Calculation of the amount of electricity that crosses the section of a conductor in a given time, knowing the intensity of the current.
FORMULA 63
- Calculation of the time necessary for a given quantity of electricity to cross the section of a conductor, the intensity of the current being known.
Enunciated :
The resistance of a conductor, expressed in ohms, is obtained by multiplying the resistivity expressed in microhms-meters, by the length expressed in meters, all divided by the section expressed in square millimeters.
R = pl / S
R = resistance in W (ohm)
p = resistivity in µW.m (microhm-meter)
l = length in meters
S = section in square millimeters
Example :
Data relating to a copper conductor :p
0,0176 µW.m (resistivity of copper, see table III, Figure 1) ;
l = 100 m ; S = 0,7854 mm2.
Resistance of the conductor R
0,0176 x 100 / 0,7854 = 1,76 / 0,7854 = 2,24 W
OBSERVATION : in the central column of Table III (Figure 1) are indicated the resistivity values of the main drivers of electricity ; these values are expressed in microhms-meters (µW.m),
submultiple of the unit of measurement ohm-meter (W.m).
1 µW.m = 0,000 001 W.m
1
W.m = 1 000 000 µW.m
The technical symbols sometimes use the symbol W.mm2
/ m (ohm-square millimeter per meter) which has the same meaning as µW.m.
The sub-multiple W.cm
(ohm-centimeter) is sometimes used for greater simplicity of calculation.
1 W.cm = 0,01 W.m
1W.m = 0,01 W.cm
Moreover, in the same paragraph, the length of the conductor was expressed in (cm) and not in (m) and the section in cm2 and not in mm2.
However, whether in the preceding example or in the mathematical lessons entitled "the formulas", the units of measure were chosen so that at the end of the calculations, the resistance of the conductor is expressed in ohms.
The resistivity unit ohm-meter
(W.m)
is not used in practice to indicate the resistivity of the conductors.
FORMULA 65
- Calculation of the length of a driver knowing the resistance, the section of the conductor and the resistivity of the material.
(This formula is an application of Form 19 of Form 1, entitled "Geometry").
Example :
Data : d = 0,1 mm
Wire cross section : S
0,7854 x 0,12 = 0,7854 x 0,01 = 0,007854 mm2
OBSERVATION : In the first two left-hand columns of Table IV (Figure 2), the diameter and section values of the nickel-chromium, constantan and manganin wires, materials frequently used in electrical installations, were respectively reported. If the diameter of a wire is equal to one of the values indicated in the first column, the value of the corresponding section can be determined by reading it directly in the second column.
Diameters are expressed in millimeters and sections in square millimeters.
FORMULA 69
- Calculation of the diameter of a wire knowing the value of its section.
OBSERVATION : If the section of the wire corresponds approximately to one of the values indicated in the second column, one can take as value of the diameter corresponding that postponed in the first column.
For example, for a section value equal to
0,28 mm2 (or
0,283 mm2 or 0,28274 mm2),
the diameter 0,60 mm will be used, which gives in Table IV (Figure 2) a section of 0,2827 mm2
FORMULA 70
- Calculation of the conductance of an electric conductor, knowing its resistance.
Enunciated :
Conductance, expressed in siemens, is the inverse of resistance expressed in ohms.
To translate the preceding statement into a formula, it suffices to remember that the inverse of a quantity is obtained by dividing the number 1 by the value of the quantity considered.
G = 1 / R
G = conductance in S (siemens)
R = resistance in W (ohm)
Example :
Data : R = 20 W
Conductance : G = 1 / 20 = 0,05 S (siemens).
FORMULA 71
- Calculation of the resistance of a conductor knowing his conductance.
Enunciated : The conductivity, expressed in siemens per meter, is equal to the inverse of the resistivity expressed in ohms-meters.
y = 1 / p
y = conductivity in S / m (siemens per meter)
p
= resistivity in W.m (ohm-meter)
Example :
Data : p = 50 W.m (resistivity of the soil in a damp place)
Conductivity : y = 1 / 50 = 0,02 S / m
OBSERVATION :
If the resistivity is expressed in microhm-meter (see Formula 64), by applying the Formula 72, one obtains the value of the conductivity expressed in mega siemens per meter (MS / m).
1 MS / m = 1 000 000 S / m
1 S / m = 0,000 001 MS / m
The mega siemens per meter is indicated by the symbol
m / W.mm2
(meter by ohm-millimeter square).
FORMULA 73 -
Calculation of the resistivity of a conductor knowing his conductivity.
Calculation of the current intensity
0,0176 µW.m (resistivity of copper, see table III, Figure 1) ;
l = 100 m ; S = 0,7854 mm2.
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