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Form 1. - Electronics :
1. - ELECTRONIC
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.
Calculate the intensity of the current knowing the amount of electricity
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.
Calculate the amount of electricity passing through a driver's section
Q = It
Q = quantity of electricity in C (coulomb)
I = intensity of the current in A (ampere)
t = time in seconds
(This formula is from formula 61).
Example :
Data : I = 2,5 A ; t = 4 s
Quantity of electricity : Q = 2,5 x 4 = 10 C.
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.
Calculate the time needed for a given amount of electricity to pass through a driver's section
t = Q / I
t = time in seconds
Q = quantity of electricity in C (coulomb)
I = intensity of the current in A (ampere)
(This formula is from formula 61).
Example :
Data : Q = 10 C ; I = 2,5 A
Time : t = 10 / 2,5 = 4 s
FORMULA 64 - Calculation of the resistance of a conductor, knowing the resistivity of the material, the length and the section of this conductor.
Calculate the resistance of a conductor, knowing the resistivity of the material
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 mm^{2}.
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.mm^{2} / 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 cm^{2} and not in mm^{2}.
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.
l = (RS) / p
l = length in meter
R = resistance in W (ohm)
S = section in mm^{2}
p = resistivity in µW.m (microhm-meter)
(This formula is from formula 64).
Example :
Data relating to a nickel-chromium conductor : R = 10 W ; S = 0,7854 mm^{2} ; p = 1,04 µW.m (resistivity of nickel-chromium ; Table III, Figure 1).
Conductor length : l = (10 x 0,7854) / 1,04 = 7,854 / 1,04 = 7,552 m
FORMULA 66 - Calculation of the section of a driver knowing the resistivity of the material, the length and the resistance of this conductor.
Calculate the section of a driver who knows the resistivity of the material
S = pl / R
S = section in mm^{2}
p = resistivity in µW.m (microhm-meter)
l = length in m
R = resistance in W
(This formula is from formula 64).
Example :
Data relating to a constantan conductor : p = 0,5 µW.m (constantan resistivity, table III, figure 1) ; l = 100 m ; R = 63,66 W
Conductor section : S = (0,5 x 100) / 63,66 = 50 / 63,66 = 0,7854 mm^{2}
FORMULA 67 - Calculation of the resistivity of the material of a driver knowing the section, the resistance and the length of this conductor.
Calculate the resistivity of a conductor's material
p = SR / l
p = resistivity in µW.m (microhm-meter)
S = section in mm^{2}
R = resistance in W (ohm)
l = length in mètres
(This formula is from formula 64).
Example :
Data relating to an electrical conductor of unknown material :
S = 1,76 mm^{2} ; R = 14 W ; l = 3 m.
Resistivity of the material : p = (1,76 x 14) / 3 = 24,64 / 3 = 8,21 µW.m
OBSERVATION : in order for the result obtained to effectively represent the resistivity of the material, its composition must be homogeneous.
FORMULA 68 - Calculation of the section of a filiform conductor knowing the diameter.
Calculate the section of a thin conductor
S 0,7854 d^{2}
S = section of the wire in mm^{2}
d = diameter of the wire in mm
(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 0,1^{2} = 0,7854 x 0,01 = 0,007854 mm^{2}
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.
Calculate the diameter of a wire
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 mm^{2} (or 0,283 mm^{2} or 0,28274 mm^{2}), the diameter 0,60 mm will be used, which gives in Table IV (Figure 2) a section of 0,2827 mm^{2}
FORMULA 70 - Calculation of the conductance of an electric conductor, knowing its resistance.
Calculate the conductance of an electrical conductor, knowing the 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.
Calculate the resistance of an electrical conductor, knowing its conductance
R = 1 / G
R = resistance in W (ohm)
G = conductance in S (siemens)
(This formula is from formula 70).
Example :
Data : G = 0,25 S
Resistance : R = 1 / 0,25 = 4 W
FORMULA 72 - Calculation of the conductivity of a driver knowing his resistivity.
Calculate the conductivity of a driver knowing his resistivity
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.mm^{2} (meter by ohm-millimeter square).
FORMULA 73 - Calculation of the resistivity of a conductor knowing his conductivity.
Calculate the resistivity of a driver knowing his conductivity
p = 1 / y
p = resistivity in W .m (ohm-meter)
y = conductivity in S / m (siemens per meter)
(This formula is from Formula 72).
Example :
Data : y = 2 000 000 S / m (maximum conductivity of constantan).
Resistivity of the constantan : p = 1 / 2 000 000 = 0,000 0005 W.m = 0,5 µW.m
(Value reported in Table III, Figure 1).
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