Physics formula for area – Formula for finding area in physics

Cross-sectional area as an electrical quantity

The conductivity of the wire depends on the cross-section.
As an example of the cross-section, you can consider cutting the product at an angle of 90 degrees relative to the transverse axis. The outline of the resulting figure is determined by the configuration of the object. The cable looks like a small pipe, so when cut it will come out in the form of two circles of a certain thickness. When a round metal rod is cut transversely, the shape of a circle is obtained.

In electrical engineering, the PS area will mean the rectangular cross-section of the conductor in relation to its longitudinal part. The cross-section of the cores will always be round. The parameter is measured in mm2.

Novice electricians may confuse the diameter and cross-section of elements. To determine what cross-sectional area the core has, you need to take into account its round shape and use the formula:

S = πxR2, where:

• S – area of ​​the circle;
• π—constant value 3.14;
• R is the radius of the circle.

If the area indicator is known, it is easy to find the resistivity of the manufacturing material and the length of the wire. Next, the current resistance is calculated.

For convenience of calculations, the initial formula is transformed:

1. The radius is ½ the diameter.
2. To calculate area, π is multiplied by D (diameter) divided by 4, or 0.8 multiplied by 2 diameters.

When calculating, use the diameter indicator, since its incorrect selection can cause overheating and ignition of the cable.

Next, you select the product size.

To make the calculator easier to use, we have developed an interactive search bar that will make it easier to select product sizes

If it is round steel, then the list shows the diameters (rebar 10, 12, etc., circle).

If you want to know the weight of the pipe, then pay attention to the wall thickness.

To find out the weight of the sheet, you need to select the thickness, and then the weight will be calculated per square meters.

Calculation goals

Cross-section of wires for lighting
It is necessary to calculate the parameters of the cross-sectional area of ​​the conductor for several purposes:

• obtaining the required amount of electricity to power household appliances;
• eliminating overpayments for unused energy;
• wiring safety and fire prevention;
• the ability to connect high-power equipment to the network;
• prevention of melting of the insulating layer and short circuits;
• proper organization of the lighting system.

The optimal wire cross-section for lighting is 1.5 mm2 for the line, 4-6 mm2 for the input.

Ratio of cable diameter to cross-sectional area

Determining the cross-sectional area of ​​conductors using a formula takes a long time. In some cases, it is appropriate to use data from a table. Since copper cable is used to organize modern wiring, the following parameters are entered into the table:

• diameter;
• cross-section in accordance with the diameter indicator;
• maximum load power of conductors in networks with voltages of 220 and 380 V.

By looking at the data in the appropriate columns, you can find out the necessary parameters for the power line of a residential building or industrial facility.

Steel circle weight table

The theoretical mass of 1 linear meter of a circle will be given in the table below. It will describe data on all cut diameters from 5 to 300 mm. And also the number of meters in a ton.

Having the above table at hand, you will always know the exact weight of a steel circle of all diameters. And also their number of meters in one ton, which will not allow you to spend extra money when purchasing this rolled metal.

Source: domstrousam.ru

Calculation of the cross-section of a stranded conductor

Stranded wire consists of several individual wires. Its cross section is calculated as follows:

1. The indicator of the cross-sectional area of ​​one core is found.
2. Cable cores are recalculated.
3. The quantity is multiplied by the cross-section of one core.

When connecting a stranded conductor, its ends are crimped with a special sleeve using crimping pliers.

Scattering of particle beams

In the frequently encountered case of elastic scattering of a beam of particles moving at the same speed at a certain center, the differential effective cross section

(dσdΩ{\displaystyle {d\sigma /d\Omega }}), characterizing the probability of scattering into a certain solid angle (dΩ{\displaystyle d\Omega }). It is equal to the ratio of the number of particles scattered per unit time per unit solid angle to the flux density of incident particles.

Integration over the full solid angle gives the total cross section

, for scattering at any angle:
σ=∫dσdΩdΩ{\displaystyle \sigma =\int {d\sigma \over d\Omega }d\Omega }
In the presence of inelastic interactions, the total cross section is the sum of the cross section for elastic and inelastic scattering. For each type (channel) of inelastic interactions, a separate effective cross section can be introduced.

Features of self-calculation

Independent calculation of the longitudinal section is performed on a core without an insulating coating. A piece of insulation can be moved or removed on a piece purchased specifically for testing. First you need to determine the diameter and find the cross section using it. Several methods are used for the work.

Using a caliper

The method is justified if the parameters of a truncated or defective cable are measured. For example, VVG may be designated as 3x2.5, but in fact be 3x21. Calculations are made as follows:

1. The insulating coating is removed from the conductor.
2. The diameter is measured with a caliper. You will need to place the wire between the legs of the instrument and look at the scale markings. The integer value is on top, the decimal value is on the bottom.
3. Based on the formula for finding the area of ​​a circle S = π (D/2)2 or its simplified version S = 0.8 D², the cross section is determined.
4. The diameter is 1.78 mm. Substituting the value into the expression and rounding the result to hundredths, we get 2.79 mm2.

For domestic purposes, you will need conductors with a cross section of 0.75; 1.5; 2.5 and 4 mm2.

Using a ruler and pencil

Calculating PS using a ruler and pencil
If you do not have a special meter, you can use a pencil and ruler. Operations are performed with the test image:

1. An area of ​​5-10 cm is cleared of the insulating layer.
2. The resulting wire is wound around a pencil. Full turns are laid tightly, there should be no space between them, the “tails” are directed up or down.
3. Ultimately, a certain number of turns should be obtained; they need to be counted.
4. The winding is applied to the ruler so that the zero division coincides with the first winding.
5. The length of the segment is measured and divided by the number of turns. The resulting value is the diameter.
6. For example, it turned out 11 turns, which occupy 7.5 mm. When dividing 7.5 by 11, 0.68 mm is the cable diameter. The cross section can be found using the formula.

The accuracy of the calculations is determined by the density and length of the winding.

Table of correspondence between wire diameter and cross-sectional area

If it is not possible to test the diameter or make a calculation when purchasing, you can use a table. The data can be photographed, printed or transcribed, and then used to find the standard or popular core size.

When purchasing an electrical cable, you will need to look at the parameters on the label. For example, VVNG 2x4 is used. The number of cores is the value after “x”. That is, the product consists of two elements with a cross section of 4 mm2. Based on the table, you can check the accuracy of the information.

Most often, the cable diameter is smaller than stated on the package. The user has two options - use a different one or choose a cable with a larger cross-sectional area in diameter. Having chosen the second one, you will need to check the insulation. If it is not solid, thin, or varies in thickness, choose products from another manufacturer.

Units and dimensions [edit | edit code]

Dimension of electrical resistance in the International System of Units: dim R

=
L
2
MT
−3
I
−2 . In the International System of Units (SI), based on the International System of Units, the unit of resistance is the ohm (Russian designation: Ом; international: Ω). In the SGS system as such, the unit of resistance does not have a special name, however, in its extensions (SGSE, SGSM and Gaussian system of units) the following are used [3]:

• stat (in the SGSE and Gaussian system, 1 statΩ = (10 9 s
  −2 ) s/cm = 898 755 178 736.818 Ohm (exactly) ≈ 8.98755 10 11 Ohm, equal to the resistance of the conductor through which a voltage of 1 statvolt flows current 1 statampere);
• abom (in SGSM, 1 abΩ = 1·10 −9 Ohm = 1 nanoohm, equal to the resistance of the conductor through which a current of 1 abamp flows under a voltage of 1 abvolt).

The dimension of resistance in the SGSE and Gaussian system is equal to TL

−1 (that is, it coincides with the dimension of the inverse velocity, s/cm), in the SGSM -
LT
−1 (that is, it coincides with the dimension of velocity, cm/s) [4].

The reciprocal quantity in relation to resistance is electrical conductivity, the unit of measurement of which in the SI system is siemens (1 Sm = 1 Ohm −1), in the SGSE (and Gaussian) system it is staticsiemens, and in the SGSM it is absiemens [5].

Determination of the conductor cross-section at the input

You can check the nominal values ​​in the Energosbyt company or in the documentation for the product. For example, the input rating of the machine is 25 A, the power consumption is 5 kW, the network is single-phase, 220 V.

The cross-section is selected so that the permissible current of the cores over a long period is greater than the rating of the machine. For example, a three-core copper conductor VVGng, laid in an open manner, was installed in a house. The optimal cross-section is 4 mm2, so you will need VVGng 3x4 material.

After this, the indicator of the conditional shutdown current for a machine with a nominal value of 25 A is calculated: 1.45x25 = 36.25 A. For a cable with a cross-sectional area of ​​4 mm2, the parameters of the continuous permissible current are 35 A, conditional - 36.25 A. In this case, it is better to take the input copper conductor with a cross-section of 6 mm2 and a permissible maximum current of 42 A.

Calculation of wire cross-section for a line of sockets

Cable cross-section for home electrical installations
Each electrical appliance has its own power ratings. They are measured in Watts and indicated in the passport or on a sticker on the case. An example of searching for a cross section would be a power line for a 2.4 kW washing machine. The calculations take into account:

• wire material and installation method - three-core VVGng copper cable hidden in the wall;
• cross-section features - the optimal value is 1.5 mm2, i.e. you will need a 3x1.5 cable;
• using a socket. If only an automatic machine is connected, the characteristics will be sufficient;
• The protection system is an automatic machine with a rated current of 10 A.

For double sockets, a copper cable with a cross-section of 2.5 mm2 and a 16 A circuit breaker are used.

Selection of cross-section for a three-phase 380 V line with several devices

Connecting several types of household appliances to a three-phase line involves the flow of consumed current through three wires. Each of them will have a smaller value than a two-core one. Based on this phenomenon, in a three-phase network it is permissible to use a cable with a smaller cross-section.

For example, a generator with a power of 20 kW and a total power of three phases of 52 A is installed in a house. Based on the table values, it turns out that the optimal cable cross-section is 8.4 mm2. Based on the formula, the actual cross-section is calculated: 8.4/1.75 = 4.8 mm2. To connect a 20 kW generator to a three-phase 380 V network, a copper conductor is required, the cross-section of each core is 4.8 mm2.

Then data in meters or tons is entered into one of the fields

If you enter values ​​in the "meters" field ("square meters" to find out the weight of the sheet), then you will know the total weight of the entire length (for example, the weight of the reinforcement).

If you are interested in calculating length by weight, then you need to enter data in the “tons” field.

Wire cross-section in old buildings and maximum load

In Soviet-era high-rise buildings, aluminum wiring is used. Taking into account the correct connection of the nodes in the junction box, the quality of the insulation and the reliability of the connection contacts, it will last from 10 to 30 years.

If it is necessary to connect equipment with high energy consumption in houses with aluminum wiring, the cross-section and diameter of the cores are selected based on the power consumption. All data is shown in the table.